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author | prashantsinalkar | 2017-10-10 12:27:19 +0530 |
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committer | prashantsinalkar | 2017-10-10 12:27:19 +0530 |
commit | 7f60ea012dd2524dae921a2a35adbf7ef21f2bb6 (patch) | |
tree | dbb9e3ddb5fc829e7c5c7e6be99b2c4ba356132c /3432 | |
parent | b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (diff) | |
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initial commit / add all books
Diffstat (limited to '3432')
218 files changed, 4886 insertions, 0 deletions
diff --git a/3432/CH2/EX2.1.b/Ex2_1.sce b/3432/CH2/EX2.1.b/Ex2_1.sce new file mode 100644 index 000000000..7889a6840 --- /dev/null +++ b/3432/CH2/EX2.1.b/Ex2_1.sce @@ -0,0 +1,30 @@ +//Example 2.1
+//(b) step response of Cruise control system
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+
+//------------------------------------------------------------------
+//Cruise control parameters
+m=1000;
+b=50;
+u=500;
+
+// Transfer function
+s=%s; // or
+s=poly(0,'s');
+sys=syslin('c',(1/m)/(s+b/m))
+
+//step response to u=500;
+t=0:0.5:100;
+v=csim('step',t,u*sys);
+plot2d(t,v,2)
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script for setting figure properties
+title('Responses of car velocity to a step in u','fontsize',3)
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('Amplitude','fontsize',2)
+
+//------------------------------------------------------------------
diff --git a/3432/CH2/EX2.1.b/Ex2_1_f0.pdf b/3432/CH2/EX2.1.b/Ex2_1_f0.pdf Binary files differnew file mode 100644 index 000000000..d6872294a --- /dev/null +++ b/3432/CH2/EX2.1.b/Ex2_1_f0.pdf diff --git a/3432/CH2/EX2.5.b/Ex2_5.sce b/3432/CH2/EX2.5.b/Ex2_5.sce new file mode 100644 index 000000000..b4b48e386 --- /dev/null +++ b/3432/CH2/EX2.5.b/Ex2_5.sce @@ -0,0 +1,30 @@ +//Example 2.5
+//(b) step response of pendulum
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+
+//------------------------------------------------------------------
+//Pendulum parameters
+m=0.5;
+l=1;
+g=9.81;
+
+// Transfer function
+s=%s;
+sys=syslin('c',(1/(m*l^2))/(s^2+g/l));
+
+//step response to u=500;
+t=0:0.02:10;
+theta=csim('step',t,sys);
+plot(t,theta*57.3);
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script to set figure properties
+title('Response of pendulum to a step input in the applied torque',...
+'fontsize',3);
+xlabel('Time t (sec.)','fontsize',2);
+ylabel('Pendulum angle (degree)','fontsize',2);
+
+//------------------------------------------------------------------
diff --git a/3432/CH2/EX2.5.b/Ex2_5_f0.pdf b/3432/CH2/EX2.5.b/Ex2_5_f0.pdf Binary files differnew file mode 100644 index 000000000..b396fb554 --- /dev/null +++ b/3432/CH2/EX2.5.b/Ex2_5_f0.pdf diff --git a/3432/CH3/EX3.10/Ex3_10.sce b/3432/CH3/EX3.10/Ex3_10.sce new file mode 100644 index 000000000..e34f28a6f --- /dev/null +++ b/3432/CH3/EX3.10/Ex3_10.sce @@ -0,0 +1,18 @@ +//Example 3.10
+
+//Computing final value for unstable system to show the incorrect
+// use of final value theorem.
+clear;
+clc;
+//------------------------------------------------------------------
+s=poly(0,'s');
+num=3;
+den=s*(s-2);
+Ys=syslin('c',num/den);
+
+//final value theorem, lim s-->0 in s*Y(s)
+Y_final=horner(s*Ys,0);
+disp(Y_final,"The final value of the output y is:");
+disp('The final value computed is incorrect as the system...
+ response is unbounded');
+//------------------------------------------------------------------
diff --git a/3432/CH3/EX3.11/Ex3_11.sce b/3432/CH3/EX3.11/Ex3_11.sce new file mode 100644 index 000000000..a033bf8a2 --- /dev/null +++ b/3432/CH3/EX3.11/Ex3_11.sce @@ -0,0 +1,16 @@ +//Example 3.11
+//Computing DC gain of the system.
+
+clear;
+clc;
+//------------------------------------------------------------------
+//Transfer Function
+s=poly(0,'s');
+num=3*(s+2);
+den=(s^2+2*s+10);
+Ys=syslin('c',num/den);
+
+//The DC gain of the system Y(s) as s-->0 is
+DC_Gain=horner(Ys,0)
+disp(DC_Gain,"The DC gain of the system is:")
+//------------------------------------------------------------------
diff --git a/3432/CH3/EX3.14/Ex3_14.sce b/3432/CH3/EX3.14/Ex3_14.sce new file mode 100644 index 000000000..c1ab83342 --- /dev/null +++ b/3432/CH3/EX3.14/Ex3_14.sce @@ -0,0 +1,23 @@ +//Example 3.14
+//Partial fraction expansion for distinct real roots
+clear;
+clc;
+//------------------------------------------------------------------
+// Transfer function
+s=%s;
+num=2;
+p1=(s+1);
+p2=(s+2);
+p3=(s+4);
+sys=syslin('c',num/(p1*p2*p3))
+
+//Partial fraction expansion is: sys= r1/p1 + r2/p2 + r3/p3
+//residue calculation
+r1=residu(num,p1,(p2*p3))
+r2=residu(num,p2,(p1*p3))
+r3=residu(num,p3,(p1*p2))
+
+disp([r1 r2 r3]',"Residues of the poles p1, p2 and p3 are")
+disp([roots(p1), roots(p2), roots(p3)]',"Poles p1, p2 and p3 are at")
+disp('k=[]')
+//------------------------------------------------------------------
diff --git a/3432/CH3/EX3.15/Ex3_15.sce b/3432/CH3/EX3.15/Ex3_15.sce new file mode 100644 index 000000000..ad9513972 --- /dev/null +++ b/3432/CH3/EX3.15/Ex3_15.sce @@ -0,0 +1,23 @@ +//Example 3.15 Cruise Control Transfer Function.
+//Coefficients of numerator and denominator of the transfer function
+
+clear;
+clc;
+//------------------------------------------------------------------
+// Transfer function coefficients
+num=[0.001 0];
+den=[0 0.05 1];
+
+// Transfer function
+Ns=poly(num,'s','coeff');
+Ds=poly(den,'s','coeff');
+sys=syslin('c',Ns/Ds);
+
+//gain (K) pole (P) and zeros (Z) of the system
+temp=polfact(Ns);
+Z=roots(Ns); //locations of zeros
+P=roots(Ds); //locations of poles
+K=temp(1); //first entry is always gain
+disp( K,"Gain", P, "Poles",Z,"Zeros",)
+
+//------------------------------------------------------------------
diff --git a/3432/CH3/EX3.16/Ex3_16.sce b/3432/CH3/EX3.16/Ex3_16.sce new file mode 100644 index 000000000..84c0062ec --- /dev/null +++ b/3432/CH3/EX3.16/Ex3_16.sce @@ -0,0 +1,32 @@ +//Example 3.16 DC Motor Transfer Function.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//Coefficients of numerator and denominator of the transfer function
+numb=[100];
+denb=[0 101 10.1 1];
+
+// Transfer function
+Ns=poly(numb,'s','coeff');
+Ds=poly(denb,'s','coeff');
+sysb=syslin('c',Ns/Ds);
+
+//gain (K) pole (P) and zeros (Z) of the system
+temp=polfact(Ns);
+Z=roots(Ns); //locations of zeros
+P=roots(Ds); //locations of poles
+K=temp(1); //first entry is always gain
+disp( K,"Gain", P, "Poles",Z,"Zeros",)
+
+//Transient response of DC Motor (consider velocity as output)
+s=%s;
+t=linspace(0,5,501);
+y=csim('step',t,sysb*s)
+plot(t,y)
+exec .\fig_settings.sci; //custom script for setting figure properties
+title('Transient response of DC Motor','fontsize',3)
+xlabel('$Time\,\, t(sec.)$','fontsize',3)
+ylabel('$\omega\,\,(rad/sec)$','fontsize',3)
+//------------------------------------------------------------------
diff --git a/3432/CH3/EX3.16/Ex3_16_f0.pdf b/3432/CH3/EX3.16/Ex3_16_f0.pdf Binary files differnew file mode 100644 index 000000000..13ab47132 --- /dev/null +++ b/3432/CH3/EX3.16/Ex3_16_f0.pdf diff --git a/3432/CH3/EX3.17/Ex3_17.sce b/3432/CH3/EX3.17/Ex3_17.sce new file mode 100644 index 000000000..fe149dd44 --- /dev/null +++ b/3432/CH3/EX3.17/Ex3_17.sce @@ -0,0 +1,21 @@ +//Example 3.17 Transformations
+
+clear;
+clc;
+//-------------------------------------------------------------------
+//Coefficients of numerator and denominator of the transfer function
+numG=[9 3];
+denG=[25 6 1];
+
+// Transfer function
+Ns=poly(numG,'s','coeff');
+Ds=poly(denG,'s','coeff');
+sysG=syslin('c',Ns/Ds);
+
+//gain (K) pole (P) and zeros (Z) of the system
+temp=polfact(Ns);
+Z=roots(Ns); //locations of zeros
+P=roots(Ds); //locations of poles
+K=temp(1); //first entry is always gain
+disp( K,"Gain", P, "Poles",Z,"Zeros",)
+//------------------------------------------------------------------
diff --git a/3432/CH3/EX3.18/Ex3_18.sce b/3432/CH3/EX3.18/Ex3_18.sce new file mode 100644 index 000000000..311eb6f9e --- /dev/null +++ b/3432/CH3/EX3.18/Ex3_18.sce @@ -0,0 +1,71 @@ +//Example 3.18 Satellite Transfer Function
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//(a)
+//Given
+d=1 //meters
+I=5000 //Kg-meter^2
+
+//Coefficients of numerator and denominator of the transfer function
+// of satellite
+numG=[d/I 0];
+denG=[0 0 1];
+
+// Transfer function
+Ns=poly(numG,'s','coeff');
+Ds=poly(denG,'s','coeff');
+sysG=syslin('c',Ns/Ds);
+t=0:0.01:10;
+[i j]=size(t);
+
+//------------------------------------------------------------------
+//(b)
+// Thrust input after 5 sec.
+u=zeros(1,j);
+w=find(t>=5 & t<=5+0.1);
+u(w)=25;
+plot(t,u);
+exec .\fig_settings.sci; //custom script for setting figure properties
+title("Transient response of the satellite...
+ (a) Thrust input",'fontsize',3);
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('Fc','fontsize',2)
+
+//Transient response of the satellite to the thrust input as a pulse
+sysd=dscr(sysG,0.01); //sample data system model
+y=flts(u,sysd); //impulse response
+figure, plot(t,y*180/%pi);
+exec .\fig_settings.sci; //custom script for setting figure properties
+title("Transient response of the satellite(double-pulse)...
+ (b) satellite attitude",'fontsize',3);
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('$\theta(deg)$','fontsize',2)
+//------------------------------------------------------------------
+// Thrust input double-pulse.
+u=zeros(1,j);
+w1=find(t>=5 & t<=5+0.1);
+u(w1)=25;
+w2=find(t>=6.1 & t<=6.1+0.1);
+u(w2)=-25;
+figure,
+plot(t,u);
+exec .\fig_settings.sci; //custom script for setting figure properties
+title("Transient response of the satellite (double-pulse)...
+ (a) Thrust input",'fontsize',3);
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('Fc','fontsize',2)
+
+//Transient response of the satellite to the thrust input as a pulse
+sysd=dscr(sysG,0.01); //sample data system model
+y=flts(u,sysd); //impulse response
+figure, plot(t,y*180/%pi);
+exec .\fig_settings.sci; //custom script for setting figure properties
+title("Transient response of the satellite(double-pulse)...
+ (b) satellite attitude",'fontsize',3);
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('$\theta(deg)$','fontsize',2)
+
+//------------------------------------------------------------------
diff --git a/3432/CH3/EX3.18/Ex3_18_f1.pdf b/3432/CH3/EX3.18/Ex3_18_f1.pdf Binary files differnew file mode 100644 index 000000000..b79b5d1e6 --- /dev/null +++ b/3432/CH3/EX3.18/Ex3_18_f1.pdf diff --git a/3432/CH3/EX3.18/Ex3_18_f3.pdf b/3432/CH3/EX3.18/Ex3_18_f3.pdf Binary files differnew file mode 100644 index 000000000..ef8fa00d4 --- /dev/null +++ b/3432/CH3/EX3.18/Ex3_18_f3.pdf diff --git a/3432/CH3/EX3.21/Ex3_21.sce b/3432/CH3/EX3.21/Ex3_21.sce new file mode 100644 index 000000000..57a2481db --- /dev/null +++ b/3432/CH3/EX3.21/Ex3_21.sce @@ -0,0 +1,42 @@ +//Example 3.21
+//Series, Parallel and Feedback connections of TF blocks
+//to get effective TF.
+
+clear;
+clc;
+//------------------------------------------------------------------
+//Transfer function block G1
+num1=[2];
+den1=[1];
+Ns=poly(num1,'s','coeff');
+Ds=poly(den1,'s','coeff');
+sysG1=syslin('c',Ns/Ds);
+
+//Transfer function block G2
+num2=[4];
+den2=[0 1];
+Ns=poly(num2,'s','coeff');
+Ds=poly(den2,'s','coeff');
+sysG2=syslin('c',Ns/Ds);
+
+//Transfer function block G4
+num4=[1];
+den4=[0 1];
+Ns=poly(num4,'s','coeff');
+Ds=poly(den4,'s','coeff');
+sysG4=syslin('c',Ns/Ds);
+
+//Transfer function block G6
+num6=[1];
+den6=[1];
+Ns=poly(num6,'s','coeff');
+Ds=poly(den6,'s','coeff');
+sysG6=syslin('c',Ns/Ds);
+
+//Effective transfer function
+// (+) operator for paralle connection,
+// (*) operator for series connection
+// (/.)operator for feedback connection
+sysG=(sysG1 + sysG2) * sysG4 /. sysG6
+disp(sysG, "The effective transfer function is")
+//------------------------------------------------------------------
diff --git a/3432/CH3/EX3.22/Ex3_22.sce b/3432/CH3/EX3.22/Ex3_22.sce new file mode 100644 index 000000000..b49701f23 --- /dev/null +++ b/3432/CH3/EX3.22/Ex3_22.sce @@ -0,0 +1,47 @@ +//Example 3.22 Response Versus Pole Locations, Real Roots
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//Transfer function
+numH=[1 2];
+denH=[2 3 1];
+Ns=poly(numH,'s','coeff');
+Ds=poly(denH,'s','coeff');
+sysH=syslin('c',Ns/Ds);
+
+//Pole-zero locations
+//Partial fraction method to see the effect of sperated poles
+temp=polfact(Ds);
+p1s=temp(2);
+p2s=temp(3);
+
+//residues at poles
+r1=residu(Ns,p1s,p2s);
+r2=residu(Ns,p2s,p1s);
+
+//Note that - H1(s)+H2(s)=H(s)
+H1s=syslin('c',r1/p1s);
+H2s=syslin('c',r2/p2s);
+
+//impulse response of the H1(s), H2(s) and H(s)
+t=0:0.02:10;
+h1=csim('impuls',t,H1s);
+h2=csim('impuls',t,H2s);
+h=csim('impuls',t,sysH);
+figure,
+plot(t,h1,'r--',t,h2,'m-.', t, h, 'b')
+plot(t,h2,'m-.')
+plot(t,h)
+
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(['impulse response of the system and subsystems with...
+ independent poles.';'(h1(t) is faster than h2(t))'],'fontsize',3)
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('h(t), h1(t), h2(t)','fontsize',2)
+h=legend('h1(t) with pole at -2','h2(t) with pole at -1'...
+,'h(t)=h1(t)+h2(t)')
+h.legend_location = "in_upper_right"
+h.fill_mode='off'
+//------------------------------------------------------------------
diff --git a/3432/CH3/EX3.22/Ex3_22_f0.pdf b/3432/CH3/EX3.22/Ex3_22_f0.pdf Binary files differnew file mode 100644 index 000000000..52d43ff12 --- /dev/null +++ b/3432/CH3/EX3.22/Ex3_22_f0.pdf diff --git a/3432/CH3/EX3.23/Ex3_23.sce b/3432/CH3/EX3.23/Ex3_23.sce new file mode 100644 index 000000000..613d47c19 --- /dev/null +++ b/3432/CH3/EX3.23/Ex3_23.sce @@ -0,0 +1,49 @@ +//Example 3.23 Oscillatory Time Response
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//Transfer function of second order underdamped system
+numH=[1 2];
+denH=[5 2 1];
+Ns=poly(numH,'s','coeff');
+Ds=poly(denH,'s','coeff');
+sysH=syslin('c',Ns/Ds);
+
+//damping factor (xi) and natural frequency (wn)
+[wn xi]=damp(sysH);
+wn=wn(1);
+xi=xi(1);
+sigma=xi*wn;
+wd=wn*sqrt(1-xi^2);
+
+//denominator in sigma-wn form H(s)=H1(s)+H2(s)
+s=%s;
+p=(s+sigma)^2+wd^2
+temp=polfact(Ns);
+k=temp(1),zr=temp(2);
+h1=(s+sigma)/p;
+h2=-((s+sigma)-temp(2))*wd/p;
+H1s=syslin('c',k*h1);
+H2s=syslin('c',k*h2/wd);
+
+// responses with exponential envelope
+Env=syslin('c',k/(s+sigma));
+t=0:0.02:10;
+//impulse response
+ht=csim('impuls',t,sysH);
+envt=csim('impuls',t,Env);
+envt_neg=csim('impuls',t,-Env);
+
+plot(t,ht)
+plot(t,envt,'r--')
+plot(t,envt_neg,'r--')
+exec .\fig_settings.sci; //custom script for setting figure properties
+title('Impulse response of the underdamped system','fontsize',3)
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('h(t)','fontsize',2)
+xset("font",1,2)
+xstring(1,0.75,"$e^{-\sigma t}$",0,0)
+xstring(1,-0.85,"$-e^{-\sigma t}$",0,0)
+//------------------------------------------------------------------
diff --git a/3432/CH3/EX3.23/Ex3_23_f0.pdf b/3432/CH3/EX3.23/Ex3_23_f0.pdf Binary files differnew file mode 100644 index 000000000..a3886b855 --- /dev/null +++ b/3432/CH3/EX3.23/Ex3_23_f0.pdf diff --git a/3432/CH3/EX3.25/Ex3_25.sce b/3432/CH3/EX3.25/Ex3_25.sce new file mode 100644 index 000000000..337747160 --- /dev/null +++ b/3432/CH3/EX3.25/Ex3_25.sce @@ -0,0 +1,52 @@ +//Example 3.25 Aircraft Response
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//(a)impulse response of aircraft
+
+//Transfer function of aircraft
+numG=[-6 1];
+denG=[0 13 4 1];
+Ns=30*poly(numG,'s','coeff');
+Ds=poly(denG,'s','coeff');
+u=-1 //impulsive elevator input of 1 degree
+sysG=syslin('c',u*Ns/Ds);
+
+//impulse response
+t=0:0.02:10;
+gt=csim('impuls',t,sysG);
+plot(t,gt)
+exec .\fig_settings.sci; //custom script for setting figure properties
+title('Response of an airplanes altitude to an impulsive elevator input','fontsize',3)
+xlabel('Time (sec.)','fontsize',2)
+ylabel('Altitude (ft)','fontsize',2)
+
+//final value theorem, lim s-->0 in s*G(s)
+s=%s;
+gt_final=horner(s*sysG,0)
+disp(gt_final,"The final value of the output altitude is:")
+//------------------------------------------------------------------
+//(b)response specifications
+
+//damping factor (xi) and natural frequency (wn)
+[wn xi]=damp(sysG);
+wn=wn(2);//natural frequency (wn)
+xi=xi(2);//damping factor
+disp(wn,xi,"Damping factor and natural frequency (rad)...
+ of the response are:")
+
+tr=1.8/wn; //rise time
+disp(tr,"Rise time (sec) of the response is:")
+
+sigma=xi*wn
+ts=4.6/sigma; //settling time
+disp(ts,"Settling time (sec) of the response is:")
+
+Mp=exp(-xi*%pi/sqrt(1-xi^2))
+wd=wn*sqrt(1-xi^2);
+tp=%pi/wd;
+disp(tp, Mp,"Overshoot and time of overshoot (sec)...
+ in the response are:")
+
+//------------------------------------------------------------------
diff --git a/3432/CH3/EX3.25/Ex3_25_f0.pdf b/3432/CH3/EX3.25/Ex3_25_f0.pdf Binary files differnew file mode 100644 index 000000000..0ea8ea81d --- /dev/null +++ b/3432/CH3/EX3.25/Ex3_25_f0.pdf diff --git a/3432/CH3/EX3.29/Ex3_29.sce b/3432/CH3/EX3.29/Ex3_29.sce new file mode 100644 index 000000000..2f1871052 --- /dev/null +++ b/3432/CH3/EX3.29/Ex3_29.sce @@ -0,0 +1,40 @@ +//Example 3.29
+//Stability versus parameter range
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//Stability versus parameter range
+
+numT=[-1];//zeros
+denT=[1 0 -6];//poles
+Ns=poly(numT,'s','roots');
+Ds=poly(denT,'s','roots');
+Gfs=syslin('c',Ns/Ds); //forward transfer function block
+
+num=[1];
+den=[1 0];
+Ns=poly(num,'s','coeff');
+Ds=poly(den,'s','coeff');
+Hs=syslin('c',Ns/Ds); //feedback transfer function block
+
+//check the step responses with the forward path gain K=7.5, 13, 25
+t=0:0.02:12;
+i=1;
+
+for K=[7.5, 13, 25]
+ sysT= (K * Gfs) /. Hs;
+ yt(i,:)=csim('step',t,sysT);
+ i=i+1;
+end
+//Step response
+plot(t',yt')
+exec .\fig_settings.sci; //custom script for setting figure properties
+title("Transient response for different values of K",'fontsize',3);
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('y(t)','fontsize',2)
+h=legend('K=7.5','K=13', 'K=25')
+h.legend_location = "in_upper_right"
+h.fill_mode='off'
+//------------------------------------------------------------------
diff --git a/3432/CH3/EX3.29/Ex3_29_f0.pdf b/3432/CH3/EX3.29/Ex3_29_f0.pdf Binary files differnew file mode 100644 index 000000000..1dcf45953 --- /dev/null +++ b/3432/CH3/EX3.29/Ex3_29_f0.pdf diff --git a/3432/CH3/EX3.30/Ex3_30.sce b/3432/CH3/EX3.30/Ex3_30.sce new file mode 100644 index 000000000..5a06bc33a --- /dev/null +++ b/3432/CH3/EX3.30/Ex3_30.sce @@ -0,0 +1,46 @@ +//Example 3.30
+//Stability versus two parameter ranges
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//Stability versus parameter ranges
+
+num=[1 0];//zeros
+den=[-1 -2];//poles
+Ns=poly(num,'s','coeff');
+Ds=poly(den,'s','roots');
+Gfs=syslin('c',Ns/Ds); //forward transfer function block
+
+num=[1];
+den=[1 0];
+Ns=poly(num,'s','coeff');
+Ds=poly(den,'s','coeff');
+Hs=syslin('c',Ns/Ds); //feedback transfer function block
+
+//check the step responses with the forward, path gain K=7.5, 13, 25
+t=0:0.02:12;
+i=1;
+num=[5 10;1 1;0 1];
+
+for i=1:3
+ den=[0 1];
+ Ns=poly(num(i,:),'s','coeff');
+ Ds=poly(den,'s','coeff');
+ Gcs=syslin('c',Ns/Ds); //Controller transfer function block
+ sysT= Gcs * Gfs /. Hs;
+ yt(i,:)=csim('step',t,sysT);
+ i=i+1;
+end
+
+//Transient response for different values of K and Ki
+plot(t',yt')
+exec .\fig_settings.sci; //custom script for setting figure properties
+title("Transient response for the system",'fontsize',3);
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('y(t)','fontsize',2)
+xset("font",1,1)
+xstring(1.4,1.05,'$K=10,K_I=5$');
+xstring(3.3,0.8,'$K=1,K_I=1$');
+xstring(5.5,0.35,'$K=1,K_I=0$')
+//------------------------------------------------------------------
diff --git a/3432/CH3/EX3.30/Ex3_30_f0.pdf b/3432/CH3/EX3.30/Ex3_30_f0.pdf Binary files differnew file mode 100644 index 000000000..f056d31d9 --- /dev/null +++ b/3432/CH3/EX3.30/Ex3_30_f0.pdf diff --git a/3432/CH3/EX3.4/Ex3_4.sce b/3432/CH3/EX3.4/Ex3_4.sce new file mode 100644 index 000000000..dacf05a5f --- /dev/null +++ b/3432/CH3/EX3.4/Ex3_4.sce @@ -0,0 +1,65 @@ +//Example 3.4
+//Frequency response
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//(a) Frequency response of 1/(s+k)
+k=1;
+fmin=1e-2;
+fmax=1e2;
+// Transfer function
+s=poly(0,'s');
+sysH=syslin('c',1/(s+k))
+
+//Frequency response for k=1
+//Note that - magnitude plot semilog plot unlike log-log plot in the book.
+bode(sysH,fmin,fmax)
+title('Frequency response for k=1','fontsize',3)
+
+//------------------------------------------------------------------
+//(b) Response to u=sin(10*t);
+t=0:0.02:10;
+u=sin(10*t);
+y=csim(u,t,sysH);
+figure, plot(t,y)
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Complete transient response','fontsize',3)
+xlabel('Time (sec.)','fontsize',2)
+ylabel('Output','fontsize',2)
+
+//phase lag
+figure, plot(t,y)
+plot(t,u,'r')
+zoom_rect([9 -1 10 1])
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Phase lag between output and input','fontsize',3)
+xlabel('Time (sec.)','fontsize',2)
+ylabel('Output, Input','fontsize',2)
+h=legend('y(t)','u(t)')
+h.legend_location = "in_upper_right"
+h.fill_mode='off'
+
+// time lag
+w=find(t>=9.4 & t<=10);
+T=t(w);
+Y=y(w);
+U=u(w);
+wu=find(U==max(U))
+wy=find(Y==max(Y))
+
+//Responses
+plot2d3(T(wy),Y(wy))
+plot2d3(T(wu),U(wu))
+delta_t=T(wu)-T(wy); //time lag sec.
+xstring(9.64,-0.1,"$\delta t$",0,0)
+xarrows([9.58;9.72], [0;0], 0.7, 1)
+xarrows([9.72;9.58], [0;0], 0.7, 1)
+t=get("hdl")
+disp(abs(delta_t), "Time lag of output in sec. is")
+disp(abs(delta_t)*10, "Phase lag of output in radians is")
+
+//------------------------------------------------------------------
diff --git a/3432/CH3/EX3.4/Ex3_4_f0.pdf b/3432/CH3/EX3.4/Ex3_4_f0.pdf Binary files differnew file mode 100644 index 000000000..8910b81c6 --- /dev/null +++ b/3432/CH3/EX3.4/Ex3_4_f0.pdf diff --git a/3432/CH3/EX3.4/Ex3_4_f1.pdf b/3432/CH3/EX3.4/Ex3_4_f1.pdf Binary files differnew file mode 100644 index 000000000..1a5b20a54 --- /dev/null +++ b/3432/CH3/EX3.4/Ex3_4_f1.pdf diff --git a/3432/CH3/EX3.8/Ex3_8.sce b/3432/CH3/EX3.8/Ex3_8.sce new file mode 100644 index 000000000..d0fe5567f --- /dev/null +++ b/3432/CH3/EX3.8/Ex3_8.sce @@ -0,0 +1,26 @@ +//Example 3.8
+//Partial fraction expansion for distinct real roots.
+
+clear;
+clc;
+//------------------------------------------------------------------
+//Partial fraction expansion for distinct real roots
+// Transfer function
+s=%s;
+num=(s+2)*(s+4)
+p1=s;
+p2=(s+1);
+p3=(s+3);
+sys=syslin('c',num/(p1*p2*p3))
+//------------------------------------------------------------------
+//Partial fraction expansion is: sys= r1/p1 + r2/p2 + r3/p3
+//residue calculation
+r1=residu(num,p1,(p2*p3))
+r2=residu(num,p2,(p1*p3))
+r3=residu(num,p3,(p1*p2))
+
+disp([r1 r2 r3]',"Residues of the poles p1, p2 and p3 are")
+disp([roots(p1), roots(p2), roots(p3)]',"Poles p1, p2 and p3 are at")
+disp('k=[]')
+
+//------------------------------------------------------------------
diff --git a/3432/CH3/EX3.9/Ex3_9.sce b/3432/CH3/EX3.9/Ex3_9.sce new file mode 100644 index 000000000..b061c050c --- /dev/null +++ b/3432/CH3/EX3.9/Ex3_9.sce @@ -0,0 +1,22 @@ +//Example 3.9
+//Computing final value (use of final value theorem).
+
+clear;
+clc;
+
+//------------------------------------------------------------------
+
+//Computing final value (use of final value theorem)
+// Output of the system
+s=poly(0,'s');
+num=3*(s+2);
+den=s*(s^2+2*s+10);
+Ys=syslin('c',num/den);
+
+
+//final value theorem, lim s-->0 in s*Y(s)
+
+Y_final=horner(s*Ys,0)
+disp(Y_final,"The final value of the output y is:")
+
+//------------------------------------------------------------------
diff --git a/3432/CH4/EX4.6/Ex4_6.sce b/3432/CH4/EX4.6/Ex4_6.sce new file mode 100644 index 000000000..e621d8a2d --- /dev/null +++ b/3432/CH4/EX4.6/Ex4_6.sce @@ -0,0 +1,97 @@ +//Example 4.6
+//PID Control of DC Motor Speed.
+
+//------------------------------------------------------------------
+//NOTE THAT--
+
+//The model as given in matlab program for this example in the book is
+
+//num=Ra*s + La*s^2 ;
+//den=Ke*ki + (Ra*Ke*Ke+Ke*kp)*s + (Ra*b+Ke*Ke+Ke*kd)*s^2 + Jm*La*s^3;
+
+//this does not match to the model of DC motor given on page 43.
+//Also, if we assume this model, disturbance response given
+//in figure 4.13 (a)
+//is different from expected.
+//For instance, with P control, output should asymptotically go to 0
+//for disturbance step input, because numerator is s(Ra + La*s)
+//and system is type 0 (no pole at origin).
+//i.e. y(inf)=lim s->0 s*Y(s)= s*[s(Ra + La*s)/den]*1/s=0;
+
+//In following code, we have considered correct model of DC motor as
+//given on page 43. Note that, this model must have been used
+//by authors of the book for
+//step reference tracking as it is correctly shown in figure 4.13 (b)
+
+//------------------------------------------------------------------
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+
+//------------------------------------------------------------------
+// System parameters
+Jm=0.0113; // N-m-s^2/rad
+b=0.028; // N-m-s/rad
+La=0.1; // henry
+Ra=0.45; // ohms
+Kt=0.067 // n-m/amp
+Ke=0.067; // V-sec/amp
+
+// Controller parameters
+kp=3;
+ki=15; // sec^-1
+kd=0.3; // sec
+
+// DC Motor Transfer function as given on page 43 of book (edition 5)
+//G=Kt/[Jm*La s^2 + (Jm*Ra + La*b)s +(Ra*b +Kt*Ke)]
+s=%s;
+num=[Kt];
+den=[(Ra*b +Kt*Ke) (Jm*Ra + La*b) Jm*La];
+Ns=poly(num,'s','coeff');
+Ds=poly(den,'s','coeff');
+G=syslin('c',Ns/Ds)
+
+//PID controller, Gc=(kd s^2 + kp s + ki)/s
+num=[ki kp kd;ki kp 0;0 kp 0]; //numerator parameters of controller)
+ //(row wise for PID, PI and P)
+den=[0 1]; //denominator parameters of controller
+Ds=poly(den,'s','coeff'); //denominator polynomial of controller
+t=0:0.005:10; // Simulation time
+//------------------------------------------------------------------
+//Step disturbance response with P, PI and PID controller.
+
+for i=1:3
+Ns=poly(num(i,:),'s','coeff');//numerator polynomial of controller
+sysG=syslin('c',Ns/Ds);
+sysD=G/. sysG;
+v(i,:)=csim('step',t,sysD);
+end
+plot(t',v');
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script to set the figure properties
+title('Responses of P,PI and PID control to step disturbance...
+ input','fontsize',3)
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('Amplitude','fontsize',2)
+hl=legend(['PID','PI','P']);
+
+//------------------------------------------------------------------
+//Reference step response
+
+figure
+for i=1:3
+Ns=poly(num(i,:),'s','coeff');
+Gc=syslin('c',Ns/Ds);
+// Step reference response with P, PI and PID controller.
+sysR=G*Gc/(1+G*Gc);
+v(i,:)=csim('step',t,sysR);
+end
+plot(t',v')
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script to set the figure properties
+title('Responses of PID control to step reference input','fontsize',3)
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('Amplitude','fontsize',2)
+hl=legend(['PID','PI','P']);
+
+//------------------------------------------------------------------
diff --git a/3432/CH4/EX4.6/Ex4_6_f0.pdf b/3432/CH4/EX4.6/Ex4_6_f0.pdf Binary files differnew file mode 100644 index 000000000..9a65a241f --- /dev/null +++ b/3432/CH4/EX4.6/Ex4_6_f0.pdf diff --git a/3432/CH4/EX4.6/Ex4_6_f1.pdf b/3432/CH4/EX4.6/Ex4_6_f1.pdf Binary files differnew file mode 100644 index 000000000..4aff13b10 --- /dev/null +++ b/3432/CH4/EX4.6/Ex4_6_f1.pdf diff --git a/3432/CH4/EX4.7/Ex4_7.sce b/3432/CH4/EX4.7/Ex4_7.sce new file mode 100644 index 000000000..923a951e6 --- /dev/null +++ b/3432/CH4/EX4.7/Ex4_7.sce @@ -0,0 +1,26 @@ +//Example 4.7
+//Discrete Equivalent.
+//------------------------------------------------------------------
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+
+// Transfer function
+s=%s;
+num=[1 11];
+den=[1 3]
+Us=poly(num,'s','coeff');
+Es=poly(den,'s','coeff');
+Ds=syslin('c',Us/Es);
+sysc=tf2ss(Ds)
+
+//Discretize the system using sampling time Ts=1 and Bilinear Transform
+Ts=1;
+sysd=cls2dls(sysc,Ts);
+
+//Pulse transfer function
+Dd=ss2tf(sysd)
+disp(Dd,"Dd=")
+disp("Note that, multiply numerator and denomintor each by 7...
+ will give the result as in book.")
+//------------------------------------------------------------------
diff --git a/3432/CH4/EX4.8/Ex4_8.sce b/3432/CH4/EX4.8/Ex4_8.sce new file mode 100644 index 000000000..5f5e37109 --- /dev/null +++ b/3432/CH4/EX4.8/Ex4_8.sce @@ -0,0 +1,150 @@ +//Example 4.8 +//Equivalent discrete controller for DC motor speed control. +//------------------------------------------------------------------ +//NOTE THAT-- The system response (continuous) to sampled control +//input depends on +//the sampling time set for continuous signal in SIMULATION. +//In this example we consider sampling period of 0.009 sec +//to represent continuous time signal. +//------------------------------------------------------------------ + +xdel(winsid())//close all graphics Windows +clear; +clc; +//------------------------------------------------------------------ +// Continuous time system and controller +// System transfer function +s=%s; +num=[45 0]; +den=[45 14 1] +Nms=poly(num,'s','coeff'); +Dns=poly(den,'s','coeff'); +Gp=syslin('c',Nms/Dns); //system transfer function + +// Controller + +numDa=[6 1]; +denDa=[0 1] +Nms=poly(numDa,'s','coeff'); +Dns=poly(denDa,'s','coeff'); +sysD=syslin('c',1.4*Nms/Dns); //controller transfer function + +//Closed loop responses + +num=[1 0]; +den=[1 0]; +Nms=poly(num,'s','coeff'); +Dns=poly(den,'s','coeff'); +H=syslin('c',Nms/Dns) + +sysDa=Gp*sysD/.H; + +//step response and control input +t=0:0.009:5; +yt=csim('step',t,sysDa); //step response +figure(0) +plot2d(t,yt,1) +Gu=sysD/(1+Gp*sysD); +ut=csim('step',t,Gu); //control input +figure(1) +plot2d(t,ut,1) +//------------------------------------------------------------------ + +sys=tf2ss(Gp); //state space model of the system +con=tf2ss(sysD); //controller state space model + +// discrete-time time system and controller + +//Discretize the system and control with sampling time Ts=0.07 +// using Bilinear Transform +Ts=0.07; +sysDd=cls2dls(sys,Ts); // discrete-time system state space model +conDd=cls2dls(con,Ts); // discrete-time controller state space model + +//Pulse transfer function of system +Gpz=ss2tf(sysDd); +//Pulse transfer function of controller +Gcz=ss2tf(conDd); +//Closed loop response +Gz=Gpz*Gcz/(1+Gpz*Gcz) +//Control input pulse transfer function +Guz=Gcz/(1+Gpz*Gcz) +T=0:Ts:5; +r=ones(1,length(T)); +yd=flts(r,Gz);............//Discrete respnse to discrete input +ud=flts(r,Guz); //Discrete Control input +//continuous response for digital input +t=0:0.009:5; +k=0; + +for i=1:length(yd) + for j=1:8 + if (k+j)>length(t) then + break + else + YD(1,k+j)=yd(i); + end + end + k=k+j; +end + +yt=csim(1-YD,t,Gp*sysD); +scf(0) +plot2d(t,yt,5); +scf(1) +plot2d2(T,ud,5); +//------------------------------------------------------------------ +//Discretize the system and control with sampling time Ts=0.035 +// using Bilinear Transform +Ts=0.035; +sysDd=cls2dls(sys,Ts); // discrete-time system state space model +conDd=cls2dls(con,Ts); // discrete-time controller state space model + +Gpz=ss2tf(sysDd); //Pulse transfer function of system +Gcz=ss2tf(conDd); //Pulse transfer function of controller + +//Closed loop response +Gz=Gpz*Gcz/(1+Gpz*Gcz) +//Control input pulse transfer function +Guz=Gcz/(1+Gpz*Gcz) +T=0:Ts:5; +r=ones(1,length(T)); +yd=flts(r,Gz);............//Discrete respnse to discrete input +ud=flts(r,Guz); //Discrete Control input +t=0:0.009:5; +k=0; + +for i=1:length(yd) + for j=1:4 + if (k+j)>length(t) then + break + else + YD(1,k+j)=yd(i); + end + end + k=k+j; +end + +yt=csim(1-YD,t,Gp*sysD); +scf(0) +plot2d(t,yt,2); +scf(1) +plot2d2(T,ud,2); + +scf(0) +//Title, labels and grid to the figure +exec .\fig_settings.sci; //custom script to set the figure properties +title('Comparision plots of Speed-control system with continuous... + and discrete controllers','fontsize',3) +xlabel('Time t (sec.)','fontsize',2) +hl=legend(['Continuous time','Discrete-time, Ts=0.07 s'... +,'Discrete-time, Ts=0.035 s'],4); +scf(1) +//Title, labels and grid to the figure +exec .\fig_settings.sci; //custom script to set the figure properties +title('Comparision plots of Speed-control system with continuous... + and discrete controllers','fontsize',3) +xlabel('Time t (sec.)','fontsize',2) +hl=legend(['Continuous time','Discrete-time, Ts=0.07 s',... +'Discrete-time, Ts=0.035 s']); +//------------------------------------------------------------------ diff --git a/3432/CH4/EX4.8/Ex4_8_f0.pdf b/3432/CH4/EX4.8/Ex4_8_f0.pdf Binary files differnew file mode 100644 index 000000000..dbe4cf6bd --- /dev/null +++ b/3432/CH4/EX4.8/Ex4_8_f0.pdf diff --git a/3432/CH4/EX4.8/Ex4_8_f1.pdf b/3432/CH4/EX4.8/Ex4_8_f1.pdf Binary files differnew file mode 100644 index 000000000..63a7f87d4 --- /dev/null +++ b/3432/CH4/EX4.8/Ex4_8_f1.pdf diff --git a/3432/CH5/EX5.1/Ex5_1.sce b/3432/CH5/EX5.1/Ex5_1.sce new file mode 100644 index 000000000..ae71ca2e4 --- /dev/null +++ b/3432/CH5/EX5.1/Ex5_1.sce @@ -0,0 +1,26 @@ +//Example 5.1
+//Root locus of a Motor Position Control.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+
+//------------------------------------------------------------------
+
+//System transfer function and its root locus
+
+s=poly(0,'s');
+Ls=1/(s*(s+1));
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script for setting figure properties
+evans(Ls)
+title(['Root locus for', '$L(s)=1/[s(s+1)]$'],'fontsize',3)
+zoom_rect([-2 -1.5 2 1.5])
+sgrid([0.5],1,5)
+xset("font",1,1.5)
+xstring(-1.2,1.1,'$\theta=sin^{-1} \xi$",0,0)
+h=legend('');
+h.visible = "off"
+
+//------------------------------------------------------------------
diff --git a/3432/CH5/EX5.1/Ex5_1_f0.pdf b/3432/CH5/EX5.1/Ex5_1_f0.pdf Binary files differnew file mode 100644 index 000000000..0ff03c9ed --- /dev/null +++ b/3432/CH5/EX5.1/Ex5_1_f0.pdf diff --git a/3432/CH5/EX5.10/Ex5_10.sce b/3432/CH5/EX5.10/Ex5_10.sce new file mode 100644 index 000000000..ed860c1d3 --- /dev/null +++ b/3432/CH5/EX5.10/Ex5_10.sce @@ -0,0 +1,56 @@ +//Example 5.10
+//Design using Lead compensator.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function and its root locus
+
+s=poly(0,'s');
+
+NumG=1;
+DenG=s*(s+1);
+NumD=(s+2);
+DenD=(s+10);
+
+G=NumG/DenG;
+D=NumD/DenD;
+
+L=G*D; //open loop transfer function
+
+figure(0)
+evans(L)
+sgrid(0.5,7,6);
+
+xstring(-2,4,"Damping=0.5",0,0)
+xstring(-7,4,"w=7",0,0)
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Root locus for lead design','fontsize',3)
+zoom_rect([-14 -8 4 8])
+h=legend('');
+h.visible = "off"
+//------------------------------------------------------------------
+// Unit step response
+//closed loop system
+K=70;
+sysc=K*L/(1+K*L);
+sysc=syslin('c',sysc);
+t=linspace(0,10,1000);
+y=csim('step',t,sysc);
+figure(1)
+plot(t,y);
+title('Step response for the system with lead compensator','fontsize',3)
+xlabel('Time (sec)','fontsize',2)
+ylabel('Amplitude','fontsize',2)
+set(gca(),"grid",[0.3 0.3])
+zoom_rect([0 0 1.8 1.4])
+exec .\fig_settings.sci;
+
+scf(0)
+pl=roots(DenG*DenD+K*NumG*NumD) //closed loop poles at K=70;
+plot(real(pl),imag(pl),'ro') //closed loop pole-locations at K=70;
+xstring(-5.8,6,"K=70",0,0)
+//------------------------------------------------------------------
+
diff --git a/3432/CH5/EX5.10/Ex5_10_f0.pdf b/3432/CH5/EX5.10/Ex5_10_f0.pdf Binary files differnew file mode 100644 index 000000000..35fbc649b --- /dev/null +++ b/3432/CH5/EX5.10/Ex5_10_f0.pdf diff --git a/3432/CH5/EX5.10/Ex5_10_f1.pdf b/3432/CH5/EX5.10/Ex5_10_f1.pdf Binary files differnew file mode 100644 index 000000000..8ce55517b --- /dev/null +++ b/3432/CH5/EX5.10/Ex5_10_f1.pdf diff --git a/3432/CH5/EX5.11/Ex5_11.sce b/3432/CH5/EX5.11/Ex5_11.sce new file mode 100644 index 000000000..ca9925b0d --- /dev/null +++ b/3432/CH5/EX5.11/Ex5_11.sce @@ -0,0 +1,78 @@ +//Example 5.11
+//A second Lead compensation Design.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function and its root locus
+
+s=poly(0,'s');
+
+NumG=1;
+DenG=s*(s+1);
+NumD=(s+5.4);
+DenD=(s+20);
+
+Gs=NumG/DenG;
+Ds=NumD/DenD;
+
+Ls=Gs*Ds; //open loop transfer function
+
+zr=roots(NumD*NumG); //open loop system zeros
+pl=roots(DenD*DenG); //open loop system poles
+pd=-3.5+3.5*sqrt(3)*%i; //desired pole
+
+//Construction for placing a specific point on the root locus.
+figure(0)
+plzr(Ls)
+plot(real(pd),imag(pd),'ro')
+xarrows([real(pl(1));real(pd)],[imag(pl(1));imag(pd)],0,2)
+xarrows([real(pl(2));real(pd)],[imag(pl(2));imag(pd)],0,2)
+xarrows([real(pl(3));real(pd)],[imag(pl(3));imag(pd)],0,2)
+xarrows([real(zr);real(pd)],[imag(zr);imag(pd)],0,6)
+xarrows([real(zr);-3],[0;0],0,6)
+xarc(-6.4,1,2,2,0,72.6*64)
+xset('font size',1.5);
+xstring(-4.7,0.5,"$\psi$")
+exec .\fig_settings.sci; //custom script for setting figure properties
+title('Construction for placing a specific point on the root locus',...
+'fontsize',3)
+h=legend('');
+h.visible = "off"
+//------------------------------------------------------------------
+//Root locus of system transfer function with controller
+figure(1)
+evans(Ls)
+sgrid(0.5,7,6)
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(['Root locus for','$ L(s)=\frac {s+5.4}{s(s+1)(s+20)}$'],...
+'fontsize',3)
+zoom_rect([-20 -8 5 8])
+h=legend('');
+h.visible = "off"
+//------------------------------------------------------------------
+// Unit step response
+//closed loop system
+
+K=127; // from root locus gain is computed
+sysc=K*Ls/(1+K*Ls)
+sysc=syslin('c',sysc);
+t=linspace(0,10,1000);
+y=csim('step',t,sysc);
+figure(2)
+plot(t,y);
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(['Step response for K=127', 'and',...
+'$ L(s)=\frac {s+5.4}{s(s+1)(s+20)}$']...
+,'fontsize',3)
+xlabel('Time (sec)','fontsize',2)
+ylabel('Amplitude','fontsize',2)
+zoom_rect([0 0 1.8 1.4])
+
+pl=roots(DenG*DenD+K*NumG*NumD) //closed loop poles at K=127;
+scf(1)
+plot(real(pl),imag(pl),'ro') //closed loop pole-locations at K=127;
+//------------------------------------------------------------------
+
diff --git a/3432/CH5/EX5.11/Ex5_11_f1.pdf b/3432/CH5/EX5.11/Ex5_11_f1.pdf Binary files differnew file mode 100644 index 000000000..bc4787a5a --- /dev/null +++ b/3432/CH5/EX5.11/Ex5_11_f1.pdf diff --git a/3432/CH5/EX5.11/Ex5_11_f2.pdf b/3432/CH5/EX5.11/Ex5_11_f2.pdf Binary files differnew file mode 100644 index 000000000..0c849448b --- /dev/null +++ b/3432/CH5/EX5.11/Ex5_11_f2.pdf diff --git a/3432/CH5/EX5.12/Ex5_12.sce b/3432/CH5/EX5.12/Ex5_12.sce new file mode 100644 index 000000000..fdff14884 --- /dev/null +++ b/3432/CH5/EX5.12/Ex5_12.sce @@ -0,0 +1,24 @@ +//Example 5.12
+//Negative root Locus for an Airplane.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+
+
+//------------------------------------------------------------------
+//System transfer function and its root locus
+
+s=poly(0,'s');
+Ls=-(s-6)/(s*(s^2+4*s+13));
+evans(Ls)
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(['Negative root locus for','$L(s)=\frac{s-6}{s(s^2+4s+13)}$'],...
+'fontsize',3)
+zoom_rect([-5 -6 10 6])
+h=legend('');
+h.visible = "off"
+
+//------------------------------------------------------------------
diff --git a/3432/CH5/EX5.12/Ex5_12_f0.pdf b/3432/CH5/EX5.12/Ex5_12_f0.pdf Binary files differnew file mode 100644 index 000000000..2dee94767 --- /dev/null +++ b/3432/CH5/EX5.12/Ex5_12_f0.pdf diff --git a/3432/CH5/EX5.2/Ex5_2.sce b/3432/CH5/EX5.2/Ex5_2.sce new file mode 100644 index 000000000..74f73049d --- /dev/null +++ b/3432/CH5/EX5.2/Ex5_2.sce @@ -0,0 +1,22 @@ +//Example 5.2
+//Root locus with respect to a plant open loop pole.
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+
+//------------------------------------------------------------------
+//System transfer function and its root locus
+s=poly(0,'s');
+Gs=s/(s*s+1);
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script for setting figure properties
+evans(Gs,100)
+title(['Root locus vs. damping factor','$c$',...
+'for','$1+G(s)=1+1/[s(s+c)]=0$'],'fontsize',3)
+zoom_rect([-2 -1.5 2 1.5])
+h=legend('');
+h.visible = "off"
+
+//------------------------------------------------------------------
+
diff --git a/3432/CH5/EX5.2/Ex5_2_f0.pdf b/3432/CH5/EX5.2/Ex5_2_f0.pdf Binary files differnew file mode 100644 index 000000000..e1e4da3cb --- /dev/null +++ b/3432/CH5/EX5.2/Ex5_2_f0.pdf diff --git a/3432/CH5/EX5.3/Ex5_3.sce b/3432/CH5/EX5.3/Ex5_3.sce new file mode 100644 index 000000000..95d400cc2 --- /dev/null +++ b/3432/CH5/EX5.3/Ex5_3.sce @@ -0,0 +1,22 @@ +//Example 5.3
+//Root locus for satellite attitude control with PD control.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+
+//------------------------------------------------------------------
+//System transfer function and its root locus
+
+s=poly(0,'s');
+sysS=(s+1)/(s^2);
+evans(sysS,100)
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title(['Root locus for','$L(s)=G(s)=(s+1)/s^2$'],'fontsize',3)
+zoom_rect([-6 -3 2 3])
+h=legend('');
+h.visible = "off"
+
+//------------------------------------------------------------------
diff --git a/3432/CH5/EX5.3/Ex5_3_f0.pdf b/3432/CH5/EX5.3/Ex5_3_f0.pdf Binary files differnew file mode 100644 index 000000000..3f4f9cdb7 --- /dev/null +++ b/3432/CH5/EX5.3/Ex5_3_f0.pdf diff --git a/3432/CH5/EX5.4/Ex5_4.sce b/3432/CH5/EX5.4/Ex5_4.sce new file mode 100644 index 000000000..2a17aed83 --- /dev/null +++ b/3432/CH5/EX5.4/Ex5_4.sce @@ -0,0 +1,23 @@ +//Example 5.4
+//Root locus for satellite attitude control with modified
+//PD control or Lead compensator.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+
+//------------------------------------------------------------------
+//System transfer function and its root locus
+
+s=poly(0,'s');
+sysL=(s+1)/(s^2*(s+12));
+evans(sysL,100)
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title(['Root locus for', '$L(s)=(s+1)/s^2(s+12)$'],'fontsize',3)
+zoom_rect([-6 -3 2 3])
+h=legend('');
+h.visible = "off"
+
+//------------------------------------------------------------------
diff --git a/3432/CH5/EX5.4/Ex5_4_f0.pdf b/3432/CH5/EX5.4/Ex5_4_f0.pdf Binary files differnew file mode 100644 index 000000000..d81a20eb1 --- /dev/null +++ b/3432/CH5/EX5.4/Ex5_4_f0.pdf diff --git a/3432/CH5/EX5.5/Ex5_5.sce b/3432/CH5/EX5.5/Ex5_5.sce new file mode 100644 index 000000000..2773f40d9 --- /dev/null +++ b/3432/CH5/EX5.5/Ex5_5.sce @@ -0,0 +1,22 @@ +//Example 5.5
+//Root locus for satellite control with Lead compensator.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+
+//------------------------------------------------------------------
+//System transfer function and its root locus
+
+s=poly(0,'s');
+sysL=(s+1)/(s^2*(s+4));
+evans(sysL)
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title(['Root locus for', '$L(s)=(s+1)/s^2(s+4)$'],'fontsize',3)
+zoom_rect([-6 -3 2 3])
+h=legend('');
+h.visible = "off"
+
+//------------------------------------------------------------------
diff --git a/3432/CH5/EX5.5/Ex5_5_f0.pdf b/3432/CH5/EX5.5/Ex5_5_f0.pdf Binary files differnew file mode 100644 index 000000000..abef9d50a --- /dev/null +++ b/3432/CH5/EX5.5/Ex5_5_f0.pdf diff --git a/3432/CH5/EX5.6/Ex5_6.sce b/3432/CH5/EX5.6/Ex5_6.sce new file mode 100644 index 000000000..a2573d6e7 --- /dev/null +++ b/3432/CH5/EX5.6/Ex5_6.sce @@ -0,0 +1,23 @@ +//Example 5.6
+//Root locus for satellite attitude control with a
+//Transition value for the pole.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+
+//------------------------------------------------------------------
+//System transfer function and its root locus
+
+s=poly(0,'s');
+sysL=(s+1)/(s^2*(s+9));
+evans(sysL)
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title(['Root locus for', '$L(s)=(s+1)/(s^2(s+9))$'],'fontsize',3)
+zoom_rect([-6 -3 2 3])
+h=legend('');
+h.visible = "off"
+
+//------------------------------------------------------------------
diff --git a/3432/CH5/EX5.6/Ex5_6_f0.pdf b/3432/CH5/EX5.6/Ex5_6_f0.pdf Binary files differnew file mode 100644 index 000000000..9fc7e6451 --- /dev/null +++ b/3432/CH5/EX5.6/Ex5_6_f0.pdf diff --git a/3432/CH5/EX5.7/Ex5_7.sce b/3432/CH5/EX5.7/Ex5_7.sce new file mode 100644 index 000000000..756952ff6 --- /dev/null +++ b/3432/CH5/EX5.7/Ex5_7.sce @@ -0,0 +1,116 @@ +//Example 5.7
+//Root locus for satellite control with a Collocated Flexibility.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+
+//------------------------------------------------------------------
+//System transfer function with controller.
+
+s=poly(0,'s');
+NumD=(s+1);
+DenD=(s+12);
+D=NumD/DenD;
+
+NumG=(s+0.1)^2+36
+DenG=s^2*((s+0.1)^2+(6.6)^2)
+
+G=NumG/DenG;
+
+NumL=NumD*NumG;
+DenL=DenD*DenG;
+
+L=NumL/DenL;
+
+zr=roots(NumL);
+pl=roots(DenL);
+
+//------------------------------------------------------------------
+//Angle of departure.
+//Find angle of departure from pole at phi1= - 0.1 + 6.6i
+//(real poles don't have angle of departure,
+//they move along real axis only)
+//psi1=angle[(Departing pole)- (zero at - 0.1 + 6.6i)]
+[Mpsi1, psi1] = polar(pl(2)-zr(1))
+psi1=real(psi1)*180/%pi; //angle in degree
+
+//psi2=angle[(Departing pole)- (zero at - 0.1 - 6.6i)]
+[Mpsi2, psi2] = polar(pl(2)-zr(2))
+psi2=real(psi2)*180/%pi; //angle in degree
+
+//psi3=angle[(Departing pole)- (zero at - 1)]
+[Mpsi3, psi3] = polar(pl(2)-zr(3))
+psi3=real(psi3)*180/%pi; //angle in degree
+
+//phi2=angle[(Departing pole)- (pole at 0)]
+[Mphi2, phi2] = polar(pl(2)-pl(4))
+phi2=real(phi2)*180/%pi; //angle in degree
+
+//phi3 is same as phi2, as pole is repeated at 0.
+phi3=phi2;
+
+//phi4=angle[(Departing pole)-(pole at - 0.1 - 6.6i )]
+[Mphi4, phi4] = polar(pl(2)-pl(3))
+phi4=real(phi4)*180/%pi; //angle in degree
+
+//phi5=angle[(Departing pole)- (pole at - 12 )]
+[Mphi5, phi5] = polar(pl(2)-pl(1))
+phi5=real(phi5)*180/%pi; //angle in degree
+
+//Therefore angle of departure phi1 at - 0.1 + 6.6i is
+//phi1 = 180 + sum(angle to zeros) - sum(angle to poles)
+
+phi1 = 180 + sum(psi1+psi2+psi3) - sum(phi2+phi3+phi4+phi5)
+
+//angle contributions in figure
+figure(0)
+plzr(L)
+xset('font size',1.5)
+xarrows([real(pl(1));real(pl(2))],[imag(pl(1));imag(pl(2))],0,2)
+xarc(-13,1,2,2,0,phi5*64)
+xstring(-11,0.05,"$\phi_5$")
+
+
+xarrows([real(zr(3));real(pl(2))],[imag(zr(3));imag(pl(2))],0,4)
+xarc(-2,1,2,2,0,psi3*64)
+xstring(-0.7,1,"$\psi_3$")
+
+xarrows([real(pl(4));real(pl(2))],[imag(pl(4));imag(pl(2))],0,5)
+xarc(-1,1,2,2,0,phi2*64)
+xstring(0.8,0.5,"$\phi_2,\,\phi_3$")
+
+
+xarrows([real(pl(3));real(pl(2))],[imag(pl(3));imag(pl(2))],0,3)
+xarc(-1,-6.6,2,2,0,phi4*64)
+xstring(0.8,-7,"$\phi_4$")
+
+xarrows([real(zr(2));real(pl(2))],[imag(zr(2));imag(pl(2))],0,6)
+xarc(-1,-5,2,2,0,psi2*64)
+xstring(0.8,-5.5,"$\psi_2$")
+
+xarrows([real(zr(1));real(pl(2))],[imag(zr(1));imag(pl(2))],0,24)
+xstring(0.3,5.5,"$\psi_1$")
+xstring(0.3,6.5,"$\phi_1$")
+
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(['Figure for computing a departure angle for',...
+'$L(s)=\frac{s+1}{s+12}\frac{(s+0.1)^2+6^2}{s^2[(s+0.1)^2+6.6^2]}$'],...
+'fontsize',3)
+zoom_rect([-15 -8 5 8])
+h=legend('');
+h.visible = "off"
+
+//------------------------------------------------------------------
+//Root locus system transfer function with controller.
+figure(1)
+evans(L)
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(['Root locus for','$L(s)=\frac{s+1}{s+12}\frac{(s+0.1)^2+6^2}...
+{s^2[(s+0.1)^2+6.6^2]}$'],'fontsize',3)
+zoom_rect([-15 -8 5 8])
+h=legend('');
+h.visible = "off"
+
+//------------------------------------------------------------------
diff --git a/3432/CH5/EX5.7/Ex5_7_f0.pdf b/3432/CH5/EX5.7/Ex5_7_f0.pdf Binary files differnew file mode 100644 index 000000000..a336a6931 --- /dev/null +++ b/3432/CH5/EX5.7/Ex5_7_f0.pdf diff --git a/3432/CH5/EX5.7/Ex5_7_f1.pdf b/3432/CH5/EX5.7/Ex5_7_f1.pdf Binary files differnew file mode 100644 index 000000000..9bbc5ea37 --- /dev/null +++ b/3432/CH5/EX5.7/Ex5_7_f1.pdf diff --git a/3432/CH5/EX5.8/Ex5_8.sce b/3432/CH5/EX5.8/Ex5_8.sce new file mode 100644 index 000000000..9df35f11c --- /dev/null +++ b/3432/CH5/EX5.8/Ex5_8.sce @@ -0,0 +1,105 @@ +//Example 5.8
+//Root locus for noncollocated case.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+
+//------------------------------------------------------------------
+//System transfer function with controller
+
+s=poly(0,'s');
+NumD=(s+1);
+DenD=(s+12);
+sysD=NumD/DenD;
+
+NumG=1
+DenG=s^2*((s+0.1)^2+(6.6)^2)
+
+sysG=NumG/DenG;
+
+NumL=NumD*NumG;
+DenL=DenD*DenG;
+
+sysL=NumL/DenL;
+
+zr=roots(NumL);
+pl=roots(DenL);
+
+//------------------------------------------------------------------
+//Angle of departure.
+//Find angle of departure from pole at phi1= - 0.1 + 6.6i
+//(real poles don't have angle of departure,
+//they move along real axis only)
+
+//psi1=angle[(Departing pole)- (zero at - 1]
+[Mpsi1, psi1] = polar(pl(2)-zr(1))
+psi1=real(psi1)*180/%pi; //angle in degree
+
+//phi2=angle[(Departing pole)- (pole at 0)]
+[Mphi2, phi2] = polar(pl(2)-pl(4))
+phi2=real(phi2)*180/%pi; //angle in degree
+
+//phi3 is same as phi2, as pole is repeated at 0.
+phi3=phi2;
+
+//phi4=angle[(Departing pole)-(pole at - 0.1 - 6.6i )]
+[Mphi4, phi4] = polar(pl(2)-pl(3))
+phi4=real(phi4)*180/%pi; //angle in degree
+
+//phi5=angle[(Departing pole)- (pole at - 12 )]
+[Mphi5, phi5] = polar(pl(2)-pl(1))
+phi5=real(phi5)*180/%pi; //angle in degree
+
+//Therefore angle of departure phi1 at - 0.1 + 6.6i is
+//phi1 = 180 + sum(angle to zeros) - sum(angle to poles)
+
+phi1 = 180 + sum(psi1) - sum(phi2+phi3+phi4+phi5)
+
+//angle contributions in figure
+figure(0)
+plzr(sysL)
+xset('font size',1.5)
+xarrows([real(pl(1));real(pl(2))],[imag(pl(1));imag(pl(2))],0,2)
+xarrows([real(pl(1)); -10],[0;0],0,2)
+xarc(-13,1,2,2,0,phi5*64)
+xstring(-11,0.05,"$\phi_5$")
+
+xarrows([real(zr(1));real(pl(2))],[imag(zr(1));imag(pl(2))],0,6)
+xarrows([real(zr(1)); -0.3],[0;0],0,6)
+xarc(-2,1,2,2,0,psi1*64)
+xstring(-0.7,1,"$\psi_1$")
+
+xarrows([real(pl(4));real(pl(2))],[imag(pl(4));imag(pl(2))],0,5)
+xarrows([real(pl(4)); 1],[0;0],0,5)
+xarc(-1,1,2,2,0,phi2*64)
+xstring(0.8,0.5,"$\phi_2,\,\phi_3$")
+
+xarrows([real(pl(3));real(pl(2))],[imag(pl(3));imag(pl(2))],0,17)
+xarrows([real(pl(3)); 2],[imag(pl(3));imag(pl(3))],0,17)
+xarc(-1.1,-5.6,2,2,0,phi4*64)
+xstring(0.8,-5.5,"$\phi_4$")
+
+xstring(0.3,6.5,"$\phi_1$")
+
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(['Figure to compute a departure angle for',...
+'$L(s)=\frac{s+1}{s+12}\frac{1}{s^2[(s+0.1)^2+6.6^2]}$'],...
+'fontsize',3)
+zoom_rect([-15 -8 5 8])
+h=legend('');
+h.visible = "off"
+
+//------------------------------------------------------------------
+//Root locus of system transfer function with controller
+figure(1)
+evans(sysL)
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(['Root locus for','$L(s)=\frac{s+1}{s+12}\frac{1}...
+{s^2[(s+0.1)^2+6.6^2]}$'],'fontsize',3)
+zoom_rect([-15 -8 5 8])
+h=legend('');
+h.visible = "off"
+
+//------------------------------------------------------------------
diff --git a/3432/CH5/EX5.8/Ex5_8_f0.pdf b/3432/CH5/EX5.8/Ex5_8_f0.pdf Binary files differnew file mode 100644 index 000000000..c6c995945 --- /dev/null +++ b/3432/CH5/EX5.8/Ex5_8_f0.pdf diff --git a/3432/CH5/EX5.8/Ex5_8_f1.pdf b/3432/CH5/EX5.8/Ex5_8_f1.pdf Binary files differnew file mode 100644 index 000000000..c177764d6 --- /dev/null +++ b/3432/CH5/EX5.8/Ex5_8_f1.pdf diff --git a/3432/CH5/EX5.9/Ex5_9.sce b/3432/CH5/EX5.9/Ex5_9.sce new file mode 100644 index 000000000..8b88c950b --- /dev/null +++ b/3432/CH5/EX5.9/Ex5_9.sce @@ -0,0 +1,81 @@ +//Example 5.9
+//Root locus for the system having complex multiple roots.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function
+
+s=poly(0,'s');
+
+NumL=1;
+DenL=s*(s+2)*[(s+1)^2+4];
+
+L=NumL/DenL;
+
+zr=roots(NumL);
+pl=roots(DenL);
+
+//------------------------------------------------------------------
+//Angle of departure.
+//Find angle of departure from pole at phi1= - 1 + 2i
+//(real poles don't have angle of departure,
+// they move along real axis only)
+
+//phi2=angle[(Departing pole)- (pole at 0)]
+[Mphi1, phi1] = polar(pl(1)-pl(4))
+phi1=real(phi1)*180/%pi; //angle in degree
+
+//phi2=angle[(Departing pole)- (pole at -2)]
+[Mphi2, phi2] = polar(pl(1)-pl(3))
+phi2=real(phi2)*180/%pi; //angle in degree
+
+//phi2=angle[(Departing pole)- (pole at - 1 - 2i)]
+[Mphi4, phi4] = polar(pl(1)-pl(2))
+phi4=real(phi4)*180/%pi; //angle in degree
+
+//Therefore angle of departure phi1 at - 1 + 2i is
+//phi3 = 180 + sum(angle to zeros) - sum(angle to poles)
+
+phi3 = 180 - sum(phi1+phi2+phi4)
+
+//angle contributions in figure
+figure(0)
+plzr(L)
+xset('font size',1.5)
+xarrows([real(pl(4));real(pl(1))],[imag(pl(4));imag(pl(1))],0,2)
+xarrows([real(pl(4)); 1],[0;0],0,2)
+xarc(-0.5,0.5,1,1,0,phi1*64)
+xstring(0.5,0.25,"$\phi_1$")
+
+xarrows([real(pl(3));real(pl(1))],[imag(pl(3));imag(pl(1))],0,5)
+xarrows([real(pl(3)); -1.3],[0;0],0,5)
+xarc(-2.5,0.5,1,1,0,phi2*64)
+xstring(-1.5,0.25,"$\phi_2$")
+
+xarrows([real(pl(2));real(pl(1))],[imag(pl(2));imag(pl(1))],0,17)
+xarrows([real(pl(2)); -0.3],[-2;-2],0,17)
+xarc(-1.5,-1.5,1,1,0,phi4*64)
+xstring(-0.5,-1.7,"$\phi_4$")
+
+xstring(-0.8,2,"$\phi_1$")
+
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(['Figure to computing a departure angle for',...
+'$L(s)=\frac{1}{s(s+2)[(s+1)^2+4]}$'],'fontsize',3)
+zoom_rect([-4 -3 4 3])
+h=legend('');
+h.visible = "off"
+//------------------------------------------------------------------
+//Root locus of system transfer function with controller
+figure(1)
+evans(L)
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title(['Root locus for','$L(s)=\frac{1}{s(s+2)[(s+1)^2+4]}$']...
+,'fontsize',3)
+zoom_rect([-4 -3 4 3])
+h=legend('');
+h.visible = "off"
+//------------------------------------------------------------------
diff --git a/3432/CH5/EX5.9/Ex5_9_f0.pdf b/3432/CH5/EX5.9/Ex5_9_f0.pdf Binary files differnew file mode 100644 index 000000000..32d94e99e --- /dev/null +++ b/3432/CH5/EX5.9/Ex5_9_f0.pdf diff --git a/3432/CH5/EX5.9/Ex5_9_f1.pdf b/3432/CH5/EX5.9/Ex5_9_f1.pdf Binary files differnew file mode 100644 index 000000000..f2f030a15 --- /dev/null +++ b/3432/CH5/EX5.9/Ex5_9_f1.pdf diff --git a/3432/CH6/EX6.10/Ex6_10.sce b/3432/CH6/EX6.10/Ex6_10.sce new file mode 100644 index 000000000..f1f5c205f --- /dev/null +++ b/3432/CH6/EX6.10/Ex6_10.sce @@ -0,0 +1,46 @@ +//Example 6.10
+// Nyquist plot for an Open-loop unstable system.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function
+s=poly(0,'s');
+sysG=(s+1)/(s*(s/10-1));
+evans(sysG,50)
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(["Root Locus for","$G(s)=(s+1)/[s(s/10-1)]$"],'fontsize',3)
+zoom_rect([-5 -4 5 4])
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+h=legend('');
+h.visible = "off"
+
+g1=syslin('c',(s+1)/(s*(s/10-1)));
+//------------------------------------------------------------------
+//The bode plot of the system
+figure;
+bode(g1,0.1/2/%pi,100/2/%pi,"rad")
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(["Bode plot for","$G(s)=(s+1)/[s(s/10-1)]$"],'fontsize',3)
+//bode(g,2*%pi*0.1,2*%pi*100)
+//------------------------------------------------------------------
+figure;
+//The nyquist plot of the system
+nyquist(g1,0.5/2/%pi,100/2/%pi,0.05)
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(["Nyquist plot for","$G(s)=(s+1)/[s(s/10-1)]$"],'fontsize',3)
+f=gca();
+f.x_location = "origin";
+f.y_location = "origin";
+zoom_rect([-2 -2 1 2]);
+xset("color",2);
+xset("font size", 3);
+xstring(-1,1.5,"${\fgcolor{blue}{\omega>0}}$",0,0);
+xstring(-1,-1.5,"${\fgcolor{blue}{\omega<0}}$",0,0);
+xstring(-1.5,0,"${\fgcolor{blue}{\omega=\pm \sqrt{10}}}$",0,0);
+xstring(-0.5,0.1,"${\fgcolor{blue}{\omega=\infty}}$",0,0);
+xarrows([-0.2;0],[0.2;0],-1,2)
+//------------------------------------------------------------------
diff --git a/3432/CH6/EX6.10/Ex6_10_f0.pdf b/3432/CH6/EX6.10/Ex6_10_f0.pdf Binary files differnew file mode 100644 index 000000000..36c7a5102 --- /dev/null +++ b/3432/CH6/EX6.10/Ex6_10_f0.pdf diff --git a/3432/CH6/EX6.10/Ex6_10_f1.pdf b/3432/CH6/EX6.10/Ex6_10_f1.pdf Binary files differnew file mode 100644 index 000000000..b0d811d78 --- /dev/null +++ b/3432/CH6/EX6.10/Ex6_10_f1.pdf diff --git a/3432/CH6/EX6.11/Ex6_11.sce b/3432/CH6/EX6.11/Ex6_11.sce new file mode 100644 index 000000000..4a782342d --- /dev/null +++ b/3432/CH6/EX6.11/Ex6_11.sce @@ -0,0 +1,28 @@ +//Example 6.11
+// Stability properties for a conditionally stable system.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function
+s=poly(0,'s');
+Gs=(s+10)^2/(s^3);
+evans(Gs,100)
+exec .\fig_settings.sci; //custom script for setting figure properties
+zoom_rect([-40 -20 5 20])
+title(["Root locus for","$G(s)=(s+10)^2/s^3$"],'fontsize',3)
+h=legend('');
+h.visible = "off"
+Gs1=syslin('c',(s+10)^2/(s^3));
+//------------------------------------------------------------------
+//The nyquist plot of the system
+figure;
+nyquist(7*Gs1,8/2/%pi,100/2/%pi,0.005)
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(["Nyquist plot for","$G(s)=(s+10)^2/s^3$"],'fontsize',3)
+f=gca();
+f.x_location = "origin";
+f.y_location = "origin";
+xset("color",2);
+//------------------------------------------------------------------
diff --git a/3432/CH6/EX6.11/Ex6_11_f0.pdf b/3432/CH6/EX6.11/Ex6_11_f0.pdf Binary files differnew file mode 100644 index 000000000..68c587741 --- /dev/null +++ b/3432/CH6/EX6.11/Ex6_11_f0.pdf diff --git a/3432/CH6/EX6.11/Ex6_11_f1.pdf b/3432/CH6/EX6.11/Ex6_11_f1.pdf Binary files differnew file mode 100644 index 000000000..3b2765043 --- /dev/null +++ b/3432/CH6/EX6.11/Ex6_11_f1.pdf diff --git a/3432/CH6/EX6.12/Ex6_12.sce b/3432/CH6/EX6.12/Ex6_12.sce new file mode 100644 index 000000000..ae6ce2fd2 --- /dev/null +++ b/3432/CH6/EX6.12/Ex6_12.sce @@ -0,0 +1,40 @@ +//Example 6.12
+// Nyquist plot for a system with Multiple Crossover frequencies
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function
+s=poly(0,'s');
+K=85;
+g1=K*(s+1)/(s^2*(s^2+2*s+82));
+g2=(s^2+2*s+43.25)/(s^2+2*s+101);
+
+Gs=syslin('c',g2*g1);
+//------------------------------------------------------------------
+figure;
+//The nyquist plot of the system
+nyquist(Gs,0.5/2/%pi,100/2/%pi,0.005)
+title(["Nyquist plot for the complex system";...
+"$G(s)=85(s+1)(s^2+2s+43.25)/[((s^2+2s+82)(s^2+2s+101)]$"],...
+'fontsize',3)
+exec .\fig_settings.sci; //custom script for setting figure properties
+zoom_rect([-2 -1 0.6 1])
+f=gca();
+f.x_location = "origin";
+f.y_location = "origin";
+xset("color",2);
+//------------------------------------------------------------------
+//The bode plot of the system
+gm=g_margin(Gs);
+pm=p_margin(Gs)
+disp(pm,"Phase margin",gm,"Gain margin")
+figure(1)
+bode(Gs,0.01/2/%pi,100/2/%pi,0.01)
+title(["Bode plot for";...
+"$G(s)=85(s+1)(s^2+2s+43.25)/[((s^2+2s+82)(s^2+2s+101)]$"],...
+'fontsize',3)
+exec .\fig_settings.sci; //custom script for setting figure properties
+//------------------------------------------------------------------
+
diff --git a/3432/CH6/EX6.12/Ex6_12_f0.pdf b/3432/CH6/EX6.12/Ex6_12_f0.pdf Binary files differnew file mode 100644 index 000000000..2c7078720 --- /dev/null +++ b/3432/CH6/EX6.12/Ex6_12_f0.pdf diff --git a/3432/CH6/EX6.12/Ex6_12_f1.pdf b/3432/CH6/EX6.12/Ex6_12_f1.pdf Binary files differnew file mode 100644 index 000000000..6a3728170 --- /dev/null +++ b/3432/CH6/EX6.12/Ex6_12_f1.pdf diff --git a/3432/CH6/EX6.13/Ex6_13.sce b/3432/CH6/EX6.13/Ex6_13.sce new file mode 100644 index 000000000..3d2221428 --- /dev/null +++ b/3432/CH6/EX6.13/Ex6_13.sce @@ -0,0 +1,77 @@ +//Example 6.13
+// Use of simple design criterion for spacecraft attitude control.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function
+s=poly(0,'s');
+G=1/s^2;
+g1=syslin('c',G);
+
+//The bode plot of the system
+zoom_rect([0.01 -20 100 60])
+bode(g1,0.05/2/%pi,2/2/%pi,"rad")
+exec .\fig_settings.sci; //custom script for setting figure properties
+title('Magnitude of the spacecrafts frequency','fontsize',3)
+//------------------------------------------------------------------
+
+K=1;
+Td=20;
+Ds=(Td*s+1);
+gd1=syslin('c',K*Ds*G);
+
+////The bode plot of compnenstaed open loop system
+figure
+bode(gd1,0.01/2/%pi,1/2/%pi,"rad")
+exec .\fig_settings.sci; //custom script for setting figure properties
+title('Bode plot for compensated open-loop transfer function'...
+,'fontsize',3)
+xstring(0.02,70,"-40db/decade",0,0);
+xstring(0.2,40,"-20db/decade",0,0);
+
+//The bode plot of compnenstaed closed loop system
+K=0.01;
+gc1=K*gd1/(1+K*gd1);
+gcl1=syslin('c',gc1);
+figure
+bode(gcl1,0.01/2/%pi,10/2/%pi,"rad")
+title('Closesd loop frequency response','fontsize',3)
+exec .\fig_settings.sci; //custom script for setting figure properties
+
+//Bandwidth
+[frq, repf,splitf]=repfreq(gc1,[0.01/2/%pi:0.001:10/2/%pi]);
+[db, phi]=dbphi(repf);
+w=find(db<=db(1)-3);
+wc=w(1);
+frqc=frq(wc)*2*%pi;
+
+plot2d3(frqc,db(wc),5)
+
+[r c]=size(frq(1:w(1)));
+magn=db(wc)*ones(r,c)
+plot(frq(1:w(1))*2*%pi,magn,"b--")
+temp_db=db(w);
+[r c]=size(db(w));
+temp_w=frqc*ones(r,c);
+plot(temp_w,temp_db,"b--")
+xset("font size", 3);
+xstring(0.04,-16,"$\omega_{BW}$");
+xstring(frqc,-4,"-3db");
+xset("line style",4)
+xarrows([0.01;frqc],[-10;-10],-0.2,5)
+xarrows([frqc;0.01],[-10;-10],-0.2,5)
+//------------------------------------------------------------------
+//Step response of PD compnensation
+figure
+t=0:0.5:100;
+v=csim('step',t,gcl1);
+plot2d(t,v)
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script for setting figure properties
+title('Step response for PD compensation','fontsize',3)
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('$\theta$','fontsize',2)
+//-------------------------------------------------------------------
diff --git a/3432/CH6/EX6.13/Ex6_13_f0.pdf b/3432/CH6/EX6.13/Ex6_13_f0.pdf Binary files differnew file mode 100644 index 000000000..d57831e64 --- /dev/null +++ b/3432/CH6/EX6.13/Ex6_13_f0.pdf diff --git a/3432/CH6/EX6.13/Ex6_13_f3.pdf b/3432/CH6/EX6.13/Ex6_13_f3.pdf Binary files differnew file mode 100644 index 000000000..42cd3fa60 --- /dev/null +++ b/3432/CH6/EX6.13/Ex6_13_f3.pdf diff --git a/3432/CH6/EX6.14/Ex6_14.sce b/3432/CH6/EX6.14/Ex6_14.sce new file mode 100644 index 000000000..4ccf15583 --- /dev/null +++ b/3432/CH6/EX6.14/Ex6_14.sce @@ -0,0 +1,93 @@ +//Example 6.14 +//Lead compensation for DC motor. + +xdel(winsid())//close all graphics Windows +clear; +clc; +//------------------------------------------------------------------ +//System transfer function +s=poly(0,'s'); +g=1/s/(s+1); +K=10; //DC gain +KGs=syslin('c',K*g); + +//Lead compensator +numD=s/2+1; +denD=s/10+1; +D=numD/denD; +Ds=syslin('c',D); + +KGDs=Ds*KGs; //compensated system +//------------------------------------------------------------------ +//(a) The bode plot of the system +bode([KGs;KGDs],0.1/2/%pi,100/2/%pi,['KG(s)';'D(s)G(s)'],"rad"); +exec .\fig_settings.sci; //custom script for setting figure properties +title('Frequency response of lead compensation design','fontsize',3) + +//root locus +figure(1) +evans(KGDs/K) +xset("font size", 3); +xstring(-10,4,"$KD(s)=\frac{s/2+1}{s/10+1}$",0,0) +xstring(-10,2,"$G(s)=\frac{1}{s(s+1)}$",0,0) + +//Title, labels and grid to the figure +exec .\fig_settings.sci; // custom script for setting figure properties +title('Root locus for lead compensation design','fontsize',3) +zoom_rect([-14 -8 4 8]) +f=gca(); +f.x_location = "origin"; +f.y_location = "origin"; +h=legend(''); +h.visible = "off" +//------------------------------------------------------------------ +//(b) digital version of lead compensator +//Discretize the system using sampling time Ts=0.05 and Bilinear Transform +Ts=0.05; //in book its 0.005, which may not give expected responses +D=tf2ss(KGDs/K/g); +sysD=cls2dls(D,Ts); + +//Pulse transfer function +Ddz=ss2tf(sysD) +disp(Ddz,"Ddz=") + +//------------------------------------------------------------------ +//(c) Compare step and ramp responses. +//step response switch sw=1 and for ramp response sw=0 +//------------------------------------------------------------------ + +//step response +sw=1; +importXcosDiagram(".\Ex6_14_model.xcos") + +xcos_simulate(scs_m,4); +scs_m.props.context +figure, +a1=newaxes(); +a1.axes_bounds=[0,0,1.0,0.5]; +plot(time_resp.time,time_resp.values) + +xlabel('time'); +ylabel('y'); +title(["Lead-compensation design (a) step Response... + (b) ramp response"],'fontsize',3) +exec .\fig_settings.sci; //custom script for setting figure properties +legend("continuous controller","digital controller",4) +//------------------------------------------------------------------ +//ramp response +sw=0; +importXcosDiagram(".\Ex6_14_model.xcos") + +xcos_simulate(scs_m,4); +scs_m.props.context + +a2=newaxes(); +a2.axes_bounds=[0,0.5,1.0,0.5]; +plot(time_resp.time,time_resp.values) + +xlabel('time'); +ylabel('y'); +title("(b)",'fontsize',3) +exec .\fig_settings.sci; //custom script for setting figure properties +legend("continuous controller","digital controller",4) +//------------------------------------------------------------------ diff --git a/3432/CH6/EX6.14/Ex6_14_f1.pdf b/3432/CH6/EX6.14/Ex6_14_f1.pdf Binary files differnew file mode 100644 index 000000000..107b25e38 --- /dev/null +++ b/3432/CH6/EX6.14/Ex6_14_f1.pdf diff --git a/3432/CH6/EX6.14/Ex6_14_f2.pdf b/3432/CH6/EX6.14/Ex6_14_f2.pdf Binary files differnew file mode 100644 index 000000000..69288dbce --- /dev/null +++ b/3432/CH6/EX6.14/Ex6_14_f2.pdf diff --git a/3432/CH6/EX6.14/Ex6_14_model.xcos b/3432/CH6/EX6.14/Ex6_14_model.xcos new file mode 100644 index 000000000..98c1caa97 --- /dev/null +++ b/3432/CH6/EX6.14/Ex6_14_model.xcos @@ -0,0 +1 @@ +<?xml version="1.0" 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\ No newline at end of file diff --git a/3432/CH6/EX6.15/Ex6_15.sce b/3432/CH6/EX6.15/Ex6_15.sce new file mode 100644 index 000000000..2a3b9a491 --- /dev/null +++ b/3432/CH6/EX6.15/Ex6_15.sce @@ -0,0 +1,78 @@ +//Example 6.15 +//Lead compensation for Temperature Control System. + +xdel(winsid())//close all graphics Windows +clear; +clc; +//------------------------------------------------------------------ +//System transfer function +s=poly(0,'s'); +numG=1; +denG=(s/0.5+1)*(s+1)*(s/2+1); +sysG=numG/denG; +//Dc gain +K=9; + +KGs=syslin('c',K*sysG); + +//Lead compensator 1 +numD=s+1; +denD=s/3+1; +D1=numD/denD; +D1s=syslin('c',D1); + +KGD1s=D1s*KGs; //compensated system + +//Lead compensator 2 +numD=s/1.5+1; +denD=s/15+1; +D2=numD/denD; +D2s=syslin('c',D2); + +KGD2s=D2s*KGs; //compensated system + +//The bode plot of the system with K +bode([KGs;KGD1s;KGD2s],0.1/2/%pi,10/2/%pi,['KG';'KGD1';'KGD2'],"rad"); +exec .\fig_settings.sci; // custom script for setting figure properties +title('Bode plot for lead compensation design','fontsize',3) +//------------------------------------------------------------------ +//Margins of uncompensated and compensated systems +[gm1,wcg1]=g_margin(KGs); +[pm1,wcp1]=p_margin(KGs); +disp(wcp1*2*%pi,"Wcp",wcg1*2*%pi,"Wcg",pm1,... +"Phase margin",gm1,"Gain margin",... +"Uncompensated system :") + +[gm2,wcg2]=g_margin(KGD1s); +[pm2,wcp2]=p_margin(KGD1s); +disp(wcp2*2*%pi,"Wcp",wcg2*2*%pi,"Wcg",pm2,... +"Phase margin",gm2,"Gain margin",... +"System with D1 compensator :") + +[gm3,wcg3]=g_margin(KGD2s); +[pm3,wcp3]=p_margin(KGD2s); +disp(wcp3*2*%pi,"Wcp",wcg3*2*%pi,"Wcg",pm3,... +"Phase margin",gm3,"Gain margin",... +"System with D2 compensator :") +//------------------------------------------------------------------ +//step response comparison +//closed loop system +Gc1=KGD1s/(KGD1s+1); +Gc2=KGD2s/(KGD2s+1); +figure; +t=0:0.05:20; +v1=csim('step',t,Gc1); +v2=csim('step',t,Gc2); +plot2d([t',t'],[v1',v2']) + +//Title, labels and grid to the figure +exec .\fig_settings.sci; //custom script for setting figure properties +title('Step response for lead compensation design','fontsize',3) +xlabel('Time t (sec.)','fontsize',2) +ylabel('y','fontsize',2) + +xset("font size", 3); +xarrows([2.5;1.5],[1.3;1.2],-1,1) +xstring(2.5,1.3,"D2",0,0) +xstring(4,1.2,"D1",0,0) +//------------------------------------------------------------------ diff --git a/3432/CH6/EX6.15/Ex6_15_f0.pdf b/3432/CH6/EX6.15/Ex6_15_f0.pdf Binary files differnew file mode 100644 index 000000000..1e7a2c442 --- /dev/null +++ b/3432/CH6/EX6.15/Ex6_15_f0.pdf diff --git a/3432/CH6/EX6.15/Ex6_15_f1.pdf b/3432/CH6/EX6.15/Ex6_15_f1.pdf Binary files differnew file mode 100644 index 000000000..7726e01ca --- /dev/null +++ b/3432/CH6/EX6.15/Ex6_15_f1.pdf diff --git a/3432/CH6/EX6.16/Ex6_16.sce b/3432/CH6/EX6.16/Ex6_16.sce new file mode 100644 index 000000000..a21196a34 --- /dev/null +++ b/3432/CH6/EX6.16/Ex6_16.sce @@ -0,0 +1,55 @@ +//Example 6.16 +//Lead compensation for Servomechanism System. + +xdel(winsid())//close all graphics Windows +clear; +clc; +//------------------------------------------------------------------ +//System transfer function +s=poly(0,'s'); +numG=10; +denG=s*(s/2.5+1)*(s/6+1); +G=numG/denG; +//Dc gain +K=1; + +KGs=syslin('c',K*G); + +//Lead compensator 1 +numD=s/2+1; +denD=s/20+1; +D1=numD/denD; +D1s=syslin('c',D1); + +KGD1s=D1s*KGs; //compensated system + +//Lead compensator 2 +numD=s/4+1; +denD=s/40+1; +D2=D1*numD/denD; //double compensator +D2s=syslin('c',D2); + + +KGD2s=D2s*KGs; //compensated system + +//The bode plot of the system with K +bode([KGs;KGD1s;KGD2s],0.1/2/%pi,100/2/%pi,['KG';'KGD1';'KGD2'],"rad"); +exec .\fig_settings.sci; //custom script for setting figure properties +title('Bode plot for lead compensation design','fontsize',3) +//------------------------------------------------------------------ +//Margins of uncompensated and compensated systems +[gm1,wcg1]=g_margin(KGs); +[pm1,wcp1]=p_margin(KGs); +disp(wcp1*2*%pi,"Wcp",wcg1*2*%pi,"Wcg",pm1,... +"Phase margin",gm1,"Gain margin","Uncompensated system :") + +[gm2,wcg2]=g_margin(KGD1s); +[pm2,wcp2]=p_margin(KGD1s); +disp(wcp2*2*%pi,"Wcp",wcg2*2*%pi,"Wcg",pm2,... +"Phase margin",gm2,"Gain margin","System with D1 compensator :") + +[gm3,wcg3]=g_margin(KGD2s); +[pm3,wcp3]=p_margin(KGD2s); +disp(wcp3*2*%pi,"Wcp",wcg3*2*%pi,"Wcg",pm3,... +"Phase margin",gm3,"Gain margin","System with D2 compensator :") +//------------------------------------------------------------------ diff --git a/3432/CH6/EX6.16/Ex6_16_f0.pdf b/3432/CH6/EX6.16/Ex6_16_f0.pdf Binary files differnew file mode 100644 index 000000000..b236af65f --- /dev/null +++ b/3432/CH6/EX6.16/Ex6_16_f0.pdf diff --git a/3432/CH6/EX6.17/Ex6_17.sce b/3432/CH6/EX6.17/Ex6_17.sce new file mode 100644 index 000000000..22af946e4 --- /dev/null +++ b/3432/CH6/EX6.17/Ex6_17.sce @@ -0,0 +1,57 @@ +//Example 6.17 +//Lag compensation for Temperature Control System. + +xdel(winsid())//close all graphics Windows +clear; +clc; +//------------------------------------------------------------------ +//System transfer function +s=poly(0,'s'); +numG=1; +denG=(s/0.5+1)*(s+1)*(s/2+1); +G=numG/denG; +//Dc gain +K=3; //to set phase requirement + +KGs=syslin('c',K*G); + +//Lag compensator +numD=5*s+1; +denD=15*s+1; +D=3*numD/denD; +Ds=syslin('c',D); + +KGDs=Ds*KGs; //compensated system + +//The bode plot of the system with K +bode([KGs;KGDs],0.01/2/%pi,10/2/%pi,['KG';'KGD'],"rad"); +exec .\fig_settings.sci; //custom script for setting figure properties +title('Frequency response of lag-compensation design','fontsize',3) + +//------------------------------------------------------------------ +//Margins of uncompensated and compensated systems +[gm1,wcg1]=g_margin(KGs); +[pm1,wcp1]=p_margin(KGs); +disp(wcp1*2*%pi,"Wcp",wcg1*2*%pi,"Wcg",pm1,"Phase margin",... +gm1,"Gain margin","Uncompensated system :") + +[gm2,wcg2]=g_margin(KGDs); +[pm2,wcp2]=p_margin(KGDs); +disp(wcp2*2*%pi,"Wcp",wcg2*2*%pi,"Wcg",pm2,"Phase margin",... +gm2,"Gain margin","Compensated system :") + +//------------------------------------------------------------------ +//step response +//closed loop system +Gc=KGDs/(KGDs+1); +figure; +t=0:0.05:20; +v=csim('step',t,Gc); +plot2d(t,v) + +//Title, labels and grid to the figure +exec .\fig_settings.sci; //custom script for setting figure properties +title('Step response for lag compensation design','fontsize',3) +xlabel('Time t (sec.)','fontsize',2) +ylabel('y','fontsize',2) +//------------------------------------------------------------------ diff --git a/3432/CH6/EX6.17/Ex6_17_f0.pdf b/3432/CH6/EX6.17/Ex6_17_f0.pdf Binary files differnew file mode 100644 index 000000000..441cf5bdb --- /dev/null +++ b/3432/CH6/EX6.17/Ex6_17_f0.pdf diff --git a/3432/CH6/EX6.17/Ex6_17_f1.pdf b/3432/CH6/EX6.17/Ex6_17_f1.pdf Binary files differnew file mode 100644 index 000000000..607607c60 --- /dev/null +++ b/3432/CH6/EX6.17/Ex6_17_f1.pdf diff --git a/3432/CH6/EX6.18/Ex6_18.sce b/3432/CH6/EX6.18/Ex6_18.sce new file mode 100644 index 000000000..0ec43ba46 --- /dev/null +++ b/3432/CH6/EX6.18/Ex6_18.sce @@ -0,0 +1,42 @@ +//Example 6.18 +//Lag compensation for DC motor. + +xdel(winsid())//close all graphics Windows +clear; +clc; +//------------------------------------------------------------------ +//System transfer function +s=poly(0,'s'); +g=1/s/(s+1); +K=10; //DC gain +KGs=syslin('c',K*g); + +//Lag compensator +numD=10*s+1; //0.1 +denD=100*s+1; //0.01 +D=numD/denD; +Ds=syslin('c',D); + +KGDs=Ds*KGs; //compensated system + +//The bode plot of the system +bode([KGs;KGDs],0.001/2/%pi,10/2/%pi,['KG(s)';'D(s)G(s)'],"rad"); +exec .\fig_settings.sci; // custom script for setting figure properties +title('Frequency response of lag-compensation design... + of DC motor','fontsize',3) +//------------------------------------------------------------------ +//step response +//closed loop system +Gc=KGDs/(KGDs+1); +figure; +t=0:0.05:50; +v=csim('step',t,Gc); +plot(t,v,2) + +//Title, labels and grid to the figure +exec .\fig_settings.sci; // custom script for setting figure properties +title('Step response for Lag-compensation design... + of DC motor','fontsize',3) +xlabel('Time t (sec.)','fontsize',2) +ylabel('y','fontsize',2) +//------------------------------------------------------------------ diff --git a/3432/CH6/EX6.18/Ex6_18_f0.pdf b/3432/CH6/EX6.18/Ex6_18_f0.pdf Binary files differnew file mode 100644 index 000000000..5f85523a2 --- /dev/null +++ b/3432/CH6/EX6.18/Ex6_18_f0.pdf diff --git a/3432/CH6/EX6.18/Ex6_18_f1.pdf b/3432/CH6/EX6.18/Ex6_18_f1.pdf Binary files differnew file mode 100644 index 000000000..e43c621c4 --- /dev/null +++ b/3432/CH6/EX6.18/Ex6_18_f1.pdf diff --git a/3432/CH6/EX6.19/Ex6_19.sce b/3432/CH6/EX6.19/Ex6_19.sce new file mode 100644 index 000000000..126f637d0 --- /dev/null +++ b/3432/CH6/EX6.19/Ex6_19.sce @@ -0,0 +1,74 @@ +//Example 6.19 +//PID compensation design for spacecraft attitude control. + +xdel(winsid())//close all graphics Windows +clear; +clc; +//------------------------------------------------------------------ +//System transfer function +s=poly(0,'s'); +G1=(0.9/s^2); +G2=(2/(s+2)); +G=G1*G2; +Gs=syslin('c',G); + +// PID controller parameters +Td_inv=0.1; // Td_inv=1/Td=0.1 +Kd=1/Td_inv; //Kd=Td=Td_inv (derivative gain) + +Ti_inv=0.005; // Ti_inv=1/Ti=0.005 +Ki=Ti_inv; //Ki=Ti_inv (integral gain) + +Kp=0.05 //Kp (Proportional gain) + +D=Kp*(Kd*s+1)*(Ki/s+1); //PID Compensator + +Dsc=syslin('c',D); + +Ds=syslin('c',D/Kp); //PID Compensator with Kp=1 +// Compensated system with Kp=1 +GDs=Gs*Ds; +//PID compensated system Kp=0.05; +GDsc=Gs*Dsc; +//------------------------------------------------------------------ +//The bode plots +bode([Gs;GDs;GDsc],0.01/2/%pi,100/2/%pi,... +['G(s)';'D(s)G(s) with (Kp=1)';'D(s)G(s) with (Kp=0.05)'],"rad"); +exec .\fig_settings.sci; //custom script for setting figure properties +title('Compensation for PID design','fontsize',3) + +//Phase margin of pid compensated system with Kp=0.05; +[pm wcp]=p_margin(GDsc); + +//------------------------------------------------------------------ +//closed loop system +//step response +Gc=GDsc/(GDsc+1); +figure; +t=0:0.05:40; +y=csim('step',t,Gc); +plot(t,y,2) + +//Title, labels and grid to the figure +exec .\fig_settings.sci; //custom script for setting figure properties +title('Step response for PID compensation of spacecraft'... +,'fontsize',3) +xlabel('Time t (sec.)','fontsize',2) +ylabel('$theta$','fontsize',2) +//------------------------------------------------------------------ +//step disturbance response +Gc=G1/((G1*G2*D)+1); +Gcs=syslin('c',Gc); +figure; +t=0:0.5:1000; +u=0.1*ones(1,length(t)); +y=csim(u,t,Gcs) +plot(t,y,2) + +//Title, labels and grid to the figure +exec .\fig_settings.sci; // custom script for setting figure properties +title('Step disturbance response for PID compensation... + of spacecraft','fontsize',3) +xlabel('Time t (sec.)','fontsize',2) +ylabel('$theta$','fontsize',2) +//------------------------------------------------------------------ diff --git a/3432/CH6/EX6.19/Ex6_19_f0.pdf b/3432/CH6/EX6.19/Ex6_19_f0.pdf Binary files differnew file mode 100644 index 000000000..f2687e07e --- /dev/null +++ b/3432/CH6/EX6.19/Ex6_19_f0.pdf diff --git a/3432/CH6/EX6.19/Ex6_19_f1.pdf b/3432/CH6/EX6.19/Ex6_19_f1.pdf Binary files differnew file mode 100644 index 000000000..c4b8b9759 --- /dev/null +++ b/3432/CH6/EX6.19/Ex6_19_f1.pdf diff --git a/3432/CH6/EX6.2.b/Ex6_2.sce b/3432/CH6/EX6.2.b/Ex6_2.sce new file mode 100644 index 000000000..03eae0b42 --- /dev/null +++ b/3432/CH6/EX6.2.b/Ex6_2.sce @@ -0,0 +1,28 @@ +//Example 6.2
+//Frequency response characteristics of Lead compensator.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function and its bode plot
+K=1, T=1, alpha=0.1
+s=poly(0,'s');
+sysD=syslin('c',K*(T*s+1)/(alpha*T*s+1));
+
+//The bode plot of the system
+
+fmin=0.1/2/%pi; //mininmum frq. in Hz for response (0.1 rad/sec)
+fmax=100/2/%pi; //maximum frq. in Hz for response (100 read/sec)
+//------------------------------------------------------------------
+//Bode plot for frequency in Hz (scilab ver. 5.4.1)
+//bode(g,fmin,fmax);
+//OR
+//Bode plot for frequency in rad/sec (scilab ver. 5.5.1)
+bode(sysD,fmin,fmax,"rad")
+
+//------------------------------------------------------------------
+title('(a) Magnitude and (b) phase for the lead compensator',...
+'fontsize',3)
+exec .\fig_settings.sci; //custom script for setting figure properties
+//------------------------------------------------------------------
diff --git a/3432/CH6/EX6.2.b/Ex6_2_f0.pdf b/3432/CH6/EX6.2.b/Ex6_2_f0.pdf Binary files differnew file mode 100644 index 000000000..827a43a3d --- /dev/null +++ b/3432/CH6/EX6.2.b/Ex6_2_f0.pdf diff --git a/3432/CH6/EX6.3/Ex6_3.sce b/3432/CH6/EX6.3/Ex6_3.sce new file mode 100644 index 000000000..bb49eb066 --- /dev/null +++ b/3432/CH6/EX6.3/Ex6_3.sce @@ -0,0 +1,65 @@ +//Example 6.3
+//Bode Plot for Real Poles and Zeros.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function and its bode plot
+K=2000;
+s=poly(0,'s');
+Gs=syslin('c',(K*(s+0.5))/(s*(s+10)*(s+50)));
+
+//The bode plot of the system
+wmin=0.1; // mininmum frq. in rad/sec for response
+wmax=100; // maximum frq. in red/sec for response
+fmin=wmin/2/%pi // mininmum frq. in Hz for response
+fmax=wmax/2/%pi // maximum frq. in Hz for response
+//------------------------------------------------------------------
+//Bode plot for frequency in Hz (scilab ver. 5.4.1)
+//bode(g,fmin,fmax)
+//OR
+//(Only for scilab ver. 5.5.1)
+//Bode (frequency scale in rad/sec)
+// or gainplot or phaseplot plot with asymptotes
+figure(0)
+gainplot(Gs,fmin,fmax);
+bode_asymp(Gs,wmin,wmax);
+xstring(0.03,22,"slope=-1(-20db/dec)",0,0);
+xstring(0.2,9,"slope=0",0,0);
+xstring(3,7,"slope=-1(-20db/dec)",0,0)
+xstring(0.9,-8,"slope=-2(-40db/dec)",0,0)
+title('Composit plots (a) magnitude plot','fontsize',3);
+h=legend('');
+exec .\fig_settings.sci; //custom script for setting figure properties
+h.visible = "off"
+//------------------------------------------------------------------
+
+//phase plot for poles and zeros
+zr=((s/0.5)+1)/s //infact this is zero and pole at origin.
+zr=syslin('c', zr);
+pl1=1/((s/10)+1)
+pl1=syslin('c', pl1);
+pl2=1/((s/50)+1)
+pl2=syslin('c', pl2);
+figure(1)
+phaseplot([Gs;zr;pl1;pl2],fmin,fmax);
+xstring(5.5,-14,"$\frac {1}{s/0.5+1}$",0,0);
+xstring(2.8,-22,"$\frac{1}{s/50+1}$",0,0);
+xstring(2.5,-60,"$\frac{1}{s/10+1}$",0,0);
+xstring(1.2,-100,["Composite";"(Actual)"],0,0);
+title('Composit plots (b) Phase','fontsize',3);
+exec .\fig_settings.sci; //custom script for setting figure properties
+
+//------------------------------------------------------------------
+figure(2)
+bode(Gs,fmin,fmax,"rad"); //frequency scale n radians
+bode_asymp(Gs,wmin,wmax);
+exec .\fig_settings.sci; //custom script for setting figure properties
+title('(c) magnitude plot and phase plot approximate and actual...
+','fontsize',3)
+xstring(2.8,-22,"$\frac{1}{s/50+1}$",0,0);
+h=legend('');
+h.visible = "off"
+
+//------------------------------------------------------------------
diff --git a/3432/CH6/EX6.3/Ex6_3_f0.pdf b/3432/CH6/EX6.3/Ex6_3_f0.pdf Binary files differnew file mode 100644 index 000000000..f3440487a --- /dev/null +++ b/3432/CH6/EX6.3/Ex6_3_f0.pdf diff --git a/3432/CH6/EX6.3/Ex6_3_f1.pdf b/3432/CH6/EX6.3/Ex6_3_f1.pdf Binary files differnew file mode 100644 index 000000000..fa0837daa --- /dev/null +++ b/3432/CH6/EX6.3/Ex6_3_f1.pdf diff --git a/3432/CH6/EX6.4/Ex6_4.sce b/3432/CH6/EX6.4/Ex6_4.sce new file mode 100644 index 000000000..6e1124ae6 --- /dev/null +++ b/3432/CH6/EX6.4/Ex6_4.sce @@ -0,0 +1,28 @@ +//Example 6.4
+//Bode Plot with Complex Poles.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function and its bode plot
+K=10;
+s=poly(0,'s');
+Gs=syslin('c',(K)/(s*(s^2+0.4*s+4)));
+//The bode plot of the system
+
+fmin=0.1/2/%pi; //mininmum frq. in Hz for response (0.1 rad/sec)
+fmax=10/2/%pi; //maximum frq. in Hz for response (100 read/sec)
+//------------------------------------------------------------------
+//Bode plot for frequency in Hz (scilab ver. 5.4.1)
+//bode(g,fmin,fmax);
+//OR
+//Bode plot for frequency in rad/sec (scilab ver. 5.5.1)
+bode(Gs,fmin,fmax,0.01,"rad")
+
+//------------------------------------------------------------------
+title(['Bode plot for a transfer function with complex poles';...
+ '(a) magnitude...
+ (b) phase'],'fontsize',3)
+
+//------------------------------------------------------------------
diff --git a/3432/CH6/EX6.4/Ex6_4_f0.pdf b/3432/CH6/EX6.4/Ex6_4_f0.pdf Binary files differnew file mode 100644 index 000000000..58d9414da --- /dev/null +++ b/3432/CH6/EX6.4/Ex6_4_f0.pdf diff --git a/3432/CH6/EX6.6/Ex6_6.sce b/3432/CH6/EX6.6/Ex6_6.sce new file mode 100644 index 000000000..a70ab9c7a --- /dev/null +++ b/3432/CH6/EX6.6/Ex6_6.sce @@ -0,0 +1,30 @@ +//Example 6.6
+//Bode Plot for Complex Poles and Zeros:
+//Satellite with Flexible appendages.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function and its bode plot
+K=0.01;
+s=poly(0,'s');
+NumG=K*(s^2+0.01*s+1);
+DenG=s^2*((s^2/4)+0.02*(s/2)+1)
+sysG=syslin('c',NumG/DenG);
+
+fmin=0.09/2/%pi; //mininmum frq. in Hz for response (0.1 rad/sec)
+fmax=11/2/%pi; //maximum frq. in Hz for response (100 read/sec)
+//------------------------------------------------------------------
+//Bode plot for frequency in Hz (scilab ver. 5.4.1)
+//bode(g,fmin,fmax);
+//OR
+//Bode plot for frequency in rad/sec (scilab ver. 5.5.1)
+bode(sysG,fmin,fmax,0.01,"rad")
+
+//------------------------------------------------------------------
+title(["Bode plot for a transfer function with complex...
+poles and zeros"; "(a) magnitude (b) phase"],'fontsize',3)
+//------------------------------------------------------------------
+
+disp('NOTE : Result of the above example can be verified by checking the figures shown in example 6.5')
diff --git a/3432/CH6/EX6.6/Ex6_6_f0.pdf b/3432/CH6/EX6.6/Ex6_6_f0.pdf Binary files differnew file mode 100644 index 000000000..9e2dc1595 --- /dev/null +++ b/3432/CH6/EX6.6/Ex6_6_f0.pdf diff --git a/3432/CH6/EX6.7/EX6_7_f0.pdf b/3432/CH6/EX6.7/EX6_7_f0.pdf Binary files differnew file mode 100644 index 000000000..9e46a121d --- /dev/null +++ b/3432/CH6/EX6.7/EX6_7_f0.pdf diff --git a/3432/CH6/EX6.7/Ex6_7.sce b/3432/CH6/EX6.7/Ex6_7.sce new file mode 100644 index 000000000..0ea6d5b7f --- /dev/null +++ b/3432/CH6/EX6.7/Ex6_7.sce @@ -0,0 +1,44 @@ +//Example 6.7
+//Computation of velocity error constant Kv from Bode plot
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function and its bode plot
+K=10;
+s=poly(0,'s');
+Gs=syslin('c',(K)/(s*(s+1)));
+//The bode plot of the system
+
+fmin=0.01/2/%pi; //mininmum frq. in Hz for response (0.1 rad/sec)
+fmax=10/2/%pi; //maximum frq. in Hz for response (100 read/sec)
+//------------------------------------------------------------------
+//Bode plot for frequency in Hz (scilab ver. 5.4.1)
+//bode(g,fmin,fmax);
+//OR
+//Bode plot for frequency in rad/sec (scilab ver. 5.5.1)
+bode(Gs,fmin,fmax,0.01,"rad")
+title(['Determination of Kv from the Bode plot for the system',...
+'$10/[s(s+1)]$'],'fontsize',3)
+//choose frequency (rad) and magnitude from bode plot and calculate Kv
+//Here at w=0.01, magngitude in db is M=60
+//i.e actual magnitude of the reponse is |A|=10^(M/20)
+w=0.01; // in rad
+M=60 // in db
+A=10^(M/20) //actual gain
+
+//Velocity error constant Kv=w*|A(w)|
+Kv=w*A;
+disp(Kv,"The Velocity error Constant from bode plot is: ")
+//------------------------------------------------------------------
+// Computation of the Kv
+[frq repf]=repfreq(Gs,fmin,fmax);
+//frq in Hz, repf is freq. response in rectangular form.
+//From bode plot, Kv=w*|A(w)|
+//i.e Kv=2*pi*f*|A(2*pi*f)|
+
+idx=1;//selecting the frequency and response at that frequency from arrays
+Kv=2*%pi*frq(idx)*abs(repf(idx))
+disp(Kv,"The Velocity error Constant is computed at 0.0015915 Hz (0.01 rad/sec) : ")
+//------------------------------------------------------------------
diff --git a/3432/CH6/EX6.8/Ex6_8.sce b/3432/CH6/EX6.8/Ex6_8.sce new file mode 100644 index 000000000..6625052d3 --- /dev/null +++ b/3432/CH6/EX6.8/Ex6_8.sce @@ -0,0 +1,48 @@ +//Example 6.8
+// Nyquist plot for a second order system.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function and its root locus
+s=poly(0,'s');
+g=1/(s+1)^2;
+sysG=syslin('c',g);
+
+evans(sysG);
+exec .\fig_settings.sci; //custom script for setting figure properties
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+title(['Root locus of','$G(s)=1/(s+1)^2$','with respect to K'],...
+'fontsize',3)
+zoom_rect([-3,-2,2,3])
+h=legend('');
+h.visible = "off"
+//------------------------------------------------------------------
+figure(1)
+//The bode plot of the system
+fmin=0.01/2/%pi; //mininmum frq. in Hz for response (0.1 rad/sec)
+fmax=100/2/%pi; //maximum frq. in Hz for response (100 read/sec)
+
+//Bode plot for frequency in Hz (scilab ver. 5.4.1)
+//bode(g,fmin,fmax);
+//OR
+//Bode plot for frequency in rad/sec (scilab ver. 5.5.1)
+bode(sysG,fmin,fmax,0.01,"rad")
+title(['Open loop bode plot for', '$G(s)=1/(s+1)^2$'],'fontsize',3);
+exec .\fig_settings.sci; //custom script for setting figure properties
+//------------------------------------------------------------------
+
+figure(2)
+//The nyquist plot of the system
+nyquist(sysG);
+title('Nyquist plot of the evaluation of K G(s) for s=C1 and K=1'...
+,'fontsize',3);
+exec .\fig_settings.sci; //custom script for setting figure properties
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+xset('color',2)
+//------------------------------------------------------------------
diff --git a/3432/CH6/EX6.8/Ex6_8_f0.pdf b/3432/CH6/EX6.8/Ex6_8_f0.pdf Binary files differnew file mode 100644 index 000000000..2bb5cdb61 --- /dev/null +++ b/3432/CH6/EX6.8/Ex6_8_f0.pdf diff --git a/3432/CH6/EX6.8/Ex6_8_f1.pdf b/3432/CH6/EX6.8/Ex6_8_f1.pdf Binary files differnew file mode 100644 index 000000000..690c6b5e1 --- /dev/null +++ b/3432/CH6/EX6.8/Ex6_8_f1.pdf diff --git a/3432/CH6/EX6.9/Ex6_9.sce b/3432/CH6/EX6.9/Ex6_9.sce new file mode 100644 index 000000000..a66b127dc --- /dev/null +++ b/3432/CH6/EX6.9/Ex6_9.sce @@ -0,0 +1,53 @@ +//Example 6.9
+// Nyquist plot for a third order system.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function
+s=poly(0,'s');
+g=syslin('c',1/(s*(s+1)^2));
+
+//The bode plot of the system
+fmin=0.01/2/%pi;
+fmax=100/2/%pi;
+//[frq,repf]=repfreq(g1,fmin,fmax,0.01);
+bode(g,fmin,fmax,"rad");
+frq=[1,10]/2/%pi;
+[frq, repf]=repfreq(g,frq);
+[db, phi]=dbphi(repf);
+plot(frq*2*%pi,db,'ro');
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(["Bode plot for","$G(s)=1/[s(s+1)^2]$"],'fontsize',3)
+//zoom_rect([[0.1 0] -70 [12 -180] 20])
+xset("font size", 3);
+
+xstring(1,0,"$C\,\, (\omega=1)$",0,0);
+xstring(2,-75,"$E\,\, (\omega=10)$",0,0);
+f=gca();
+
+//------------------------------------------------------------------
+//The nyquist plot of the system
+figure;
+nyquist(g,0.8/2/%pi,10/2/%pi,0.02)
+
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(["Nyquist plot for","$G(s)=1/[s(s+1)]^2$"],'fontsize',3)
+f=gca();
+f.x_location = "origin";
+f.y_location = "origin";
+zoom_rect([-1 -0.2 0.5 0.2]);
+xset("clipping", -1.2, 0.2, 1.4,0.4);
+xset("font size", 3);
+xset("color",2);
+xstring(-0.6,0.1,"${\fgcolor{blue}{\omega<0}}$",0,0);
+xstring(-0.6,-0.1,"${\fgcolor{blue}{\omega>0}}$",0,0);
+xstring(-0.7,0.005,"${\fgcolor{blue}{\omega=\pm 1}}$",0,0);
+xstring(-1,-0.2,...
+"${\fgcolor{blue}{\text{From \infty at \omega=0^+}}$",0,0);
+ xstring(-0.7,0.15,"${\fgcolor{blue}...
+ {\text{Towards \infty at \omega=0^-}}$",0,0);
+xstring(-0.525,-0.04,"C",0,0);
+xstring(-0.075,0,"E",0,0);
+//------------------------------------------------------------------
diff --git a/3432/CH6/EX6.9/Ex6_9_f0.pdf b/3432/CH6/EX6.9/Ex6_9_f0.pdf Binary files differnew file mode 100644 index 000000000..0717e6cf9 --- /dev/null +++ b/3432/CH6/EX6.9/Ex6_9_f0.pdf diff --git a/3432/CH6/EX6.9/Ex6_9_f1.pdf b/3432/CH6/EX6.9/Ex6_9_f1.pdf Binary files differnew file mode 100644 index 000000000..482ef9388 --- /dev/null +++ b/3432/CH6/EX6.9/Ex6_9_f1.pdf diff --git a/3432/CH6/EX7.29/Ex7_29.sce b/3432/CH6/EX7.29/Ex7_29.sce new file mode 100644 index 000000000..a0c479432 --- /dev/null +++ b/3432/CH6/EX7.29/Ex7_29.sce @@ -0,0 +1,74 @@ +//Example 7.29
+// A reduced order compensator design for a satellite attitude control
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+// State space representation
+F=[0 1;0 0];
+G=[0 1]';
+H=[1 0];
+J=0;
+n=sqrt(length(F));//order of the system
+
+//partioned system
+Faa=F(1,1); Fab=F(1,2);
+Fba=F(2,1); Fbb=F(2,2);
+Ga=G(1);Gb=G(2);
+
+// Desired estimator poles
+Pe=[-5];
+// Observer gain matrix for system
+L=ppol(Fbb',Fab',Pe);
+L=L';
+disp(L,"L=" );
+//------------------------------------------------------------------
+//State feedback control law u=-Kx=-(K+[L*k2 0])[y xc]';
+k1=1; k2=sqrt(2);
+K=[k1 k2];
+Kc=K+[L*k2 0];
+//------------------------------------------------------------------
+//compensator differential equation
+//xc_dot=(Fbb-L*Fab)*xb_hat + (Fba - L*Faa)*y + (Gb - L*Ga)*u
+//xc_dot=((Fbb-L*Fab)-k2)*xc + [(Fba - L*Faa)-(Gb - L*Ga)*(k1+L*k2)+L*(Fbb-L*Fab)]*y
+Fc=(Fbb-L*Fab)-Gb*k2
+Fy=(Fba - L*Faa)-(Gb - L*Ga)*(k1+k2*L)+(Fbb-L*Fab)*L
+//compensator transfer function
+s=poly(0,'s');
+Gest=syslin('c',Fy/(s-Fc))//estimator transfer function
+Dcr=-[k1+L*k2+k2*Gest]
+disp(Dcr,'Dcr','compensator transfer function')
+//------------------------------------------------------------------
+//Root locus with reduced order compensator
+G=1/s^2;
+G=syslin('c',G);
+exec('./zpk_dk.sci', -1);
+[pl,zr Kp]=zpk_dk(Dcr);
+
+Dcr=poly(zr,'s','roots')/poly(pl,'s','roots')
+Dcr=syslin('c',Dcr);
+evans(G*Dcr)
+zoom_rect([-8 -4 2 4])
+
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+xset("color",2);
+h=legend('');
+h.visible = "off"
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(['Root locus of a reduced order controller and',"$1/s^2$",...
+ "process"],'fontsize',3);
+//------------------------------------------------------------------
+//Frequnecy response for 1/s^2 and compensated
+
+figure,
+bode([-Kp*G*Dcr;G],0.01/2/%pi,100/2/%pi,"rad");
+title(["Frequency response","$G(s)=1/s^2$", "with a reduced...
+ order estimator"],'fontsize',3)
+exec .\fig_settings.sci; //custom script for setting figure properties
+legend('Compensated','Uncompensated')
+//------------------------------------------------------------------
diff --git a/3432/CH6/EX7.29/Ex7_29_f0.pdf b/3432/CH6/EX7.29/Ex7_29_f0.pdf Binary files differnew file mode 100644 index 000000000..c2a23bbb2 --- /dev/null +++ b/3432/CH6/EX7.29/Ex7_29_f0.pdf diff --git a/3432/CH6/EX7.29/Ex7_29_f1.pdf b/3432/CH6/EX7.29/Ex7_29_f1.pdf Binary files differnew file mode 100644 index 000000000..5b330b97d --- /dev/null +++ b/3432/CH6/EX7.29/Ex7_29_f1.pdf diff --git a/3432/CH7/EX7.10/Ex7_10.sce b/3432/CH7/EX7.10/Ex7_10.sce new file mode 100644 index 000000000..e4accd101 --- /dev/null +++ b/3432/CH7/EX7.10/Ex7_10.sce @@ -0,0 +1,21 @@ +//Example 7.10
+//Transformation of Thermal System from Control to Modal Form
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+// State space matrices of the given system
+Ac=[-7 1; -12 0];
+Bc=[1;2];
+Cc=[1 0];
+Dc=0;
+//------------------------------------------------------------------
+// State space representation in modal canonical form
+T=[4 -3;-1 1]
+Am=T\Ac*T;
+Bm=T\Bc;
+Cm=Cc*T;
+Dm=Dc;
+disp(Dm,"Dm",Cm,"Cm", Bm,"Bm",Am,"Am","Thermal System in modal canonical form")
+//------------------------------------------------------------------
diff --git a/3432/CH7/EX7.11/Ex7_11.sce b/3432/CH7/EX7.11/Ex7_11.sce new file mode 100644 index 000000000..e1ad0bce1 --- /dev/null +++ b/3432/CH7/EX7.11/Ex7_11.sce @@ -0,0 +1,48 @@ +//Example 7.11 +//Poles and Zeros of Tape Drive System. +//Also, Transform the system into modal form + +xdel(winsid())//close all graphics Windows +clear; +clc; +//------------------------------------------------------------------ +// State space matrices of Tape Drive System + +F=[0 2 0 0 0; +-0.1 -0.35 0.1 0.1 0.75; +0 0 0 2 0; +0.4 0.4 -0.4 -1.4 0; +0 -0.03 0 0 -1]; +G=[0 0 0 0 1]'; +H2=[0 0 1 0 0]; +H3=[0.5 0 0.5 0 0]; +Ht=[-0.2 -0.2 0.2 0.2 0]; +//------------------------------------------------------------------ +// Poles (eigen values) of the system +p=clean(spec(F)); +disp(p,"Poles of Tape Drive System are") + +//It requires complete state-space model. +sys=syslin('c',F,G,[Ht;H2;H3],[0;0;0]) + +// zeros of the system +[tr]=trzeros(sys) +disp(tr,"Transmission zeros of Tape Drive System are") +//------------------------------------------------------------------ +// State space representation in modal canonical form with H3 output only. + +[m Am1]=spec(F) +T1=[1/2 -%i/2;1/2 %i/2]; +//transformation for a complex pair of eigen values. +temp=eye(5,5); +T=[T1 zeros(2,3);zeros(3,2) eye(3,3)]; +temp(1,1)=-1; temp(2,2)=-1; //for change in input output signs as desired +M=m*T*temp //real Modal transformation + +Am=clean(M\F*M); +Bm=clean(M\G); +Cm=clean(H3*M); +Dm=0; + +disp(Dm,"Dm",Cm,"Cm", Bm,"Bm",Am,"Am","Tape Drive System in modal canonical form") +//------------------------------------------------------------------------------ diff --git a/3432/CH7/EX7.12/Ex7_12.sce b/3432/CH7/EX7.12/Ex7_12.sce new file mode 100644 index 000000000..2eaead769 --- /dev/null +++ b/3432/CH7/EX7.12/Ex7_12.sce @@ -0,0 +1,23 @@ +//Example 7.12
+//Transformation of Thermal System from state description
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+// State space model of Thermal System
+s=%s;
+F=[-7 -12; 1 0];
+G=[1;0];
+H=[1 2];
+J=0;
+sys=syslin('c',F,G,H,J)
+//------------------------------------------------------------------
+//Transfer function model of Thermal System
+[ch num den]=ss2tf(sys);
+disp(num/den, "G=","Transfer function model of Thermal System")
+//------------------------------------------------------------------
+
+
+
+
diff --git a/3432/CH7/EX7.13/Ex7_13.sce b/3432/CH7/EX7.13/Ex7_13.sce new file mode 100644 index 000000000..82c5e3b49 --- /dev/null +++ b/3432/CH7/EX7.13/Ex7_13.sce @@ -0,0 +1,24 @@ +//Example 7.13
+//Zeros for the Thermal System from a State Description
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+// State space model of the given system
+F=[-7 -12; 1 0];
+G=[1;0];
+H=[1 2];
+J=0;
+sysG=syslin('c',F,G,H,J)
+//------------------------------------------------------------------
+//Transfer function model
+[d num den]=ss2tf(sysG);
+zr=roots(num);
+disp(zr,'zr=');
+//Alternately, it can be obtained as
+zr=trzeros(sysG);
+disp(zr,'zr=');
+//------------------------------------------------------------------
+
+
diff --git a/3432/CH7/EX7.14/Ex7_14.sce b/3432/CH7/EX7.14/Ex7_14.sce new file mode 100644 index 000000000..1812532d1 --- /dev/null +++ b/3432/CH7/EX7.14/Ex7_14.sce @@ -0,0 +1,74 @@ +//Example 7.14 +//Analysis of state equations of Tape Drive. +//compute the poles, zeros and transfer function of Tape Drive System. + +xdel(winsid())//close all graphics Windows +clear; +clc; +//------------------------------------------------------------------ +// State space matrices of Tape Drive System + +F=[0 2 0 0 0; +-0.1 -0.35 0.1 0.1 0.75; +0 0 0 2 0; +0.4 0.4 -0.4 -1.4 0; +0 -0.03 0 0 -1]; +G=[0 0 0 0 1]'; +H2=[0 0 1 0 0]; +H3=[0.5 0 0.5 0 0]; +Ht=[-0.2 -0.2 0.2 0.2 0]; +//------------------------------------------------------------------ +//Poles (eigen values) of the system +p=clean(spec(F)); + +disp(p,"P","Poles of Tape Drive System are (for any output)") +disp("************************************************************") + + +disp("pole and zero polynomials and transfer function... + for a system with output H2") +sys2=syslin('c',F,G,H2,0); +[d2 num2 den2]=ss2tf(sys2); +N2=coeff(num2); +D2=coeff(den2); +disp(D2,"D2",N2,"N2") +// zeros of the system with output H2 +[zer2]=trzeros(sys2) +disp(zer2,"ZER2","zeros are") +// transfer function of the system with output H2 +G2=clean(num2/den2); +disp(G2,"G2(s)=N2(s)/D2(s)=") +disp("************************************************************") + +disp("pole and zero polynomials and transfer function for a... + system with output H3") +sys3=syslin('c',F,G,H3,0); +[d3 num3 den3]=ss2tf(sys3); +N3=coeff(num3); +D3=coeff(den3); +disp(D3,"D3",N3,"N3") +// zeros of the system with output H3 +[zer3]=trzeros(sys3) +disp(zer3,"ZER3","zeros are") +// transfer function of the system with output H3 +G3=clean(num2/den2); +disp(G3,"G3(s)=N3(s)/D3(s)=") +disp("************************************************************") + + +disp("pole and zero polynomials and transfer function for a... + system with output Ht") +syst=syslin('c',F,G,Ht,0); +[dt numt dent]=ss2tf(syst); +Nt=coeff(numt); +Dt=coeff(dent); +disp(Dt,"Dt",Nt,"Nt","zeros are") +// zeros of the system with output Ht +[zert]=trzeros(syst) +disp(zert,"ZERT") +// transfer function of the system with output Ht +Gt=clean(numt/dent); +disp(Gt,"G(s)=Nt(s)/Dt(s)=") +disp("************************************************************") +//------------------------------------------------------------------ + diff --git a/3432/CH7/EX7.15/Ex7_15.sce b/3432/CH7/EX7.15/Ex7_15.sce new file mode 100644 index 000000000..b0b2aa556 --- /dev/null +++ b/3432/CH7/EX7.15/Ex7_15.sce @@ -0,0 +1,46 @@ +//Example 7.15 +//Control law for a pendulum. + +xdel(winsid())//close all graphics Windows +clear; +clc; +//------------------------------------------------------------------ +//Pendulum state model; +w0=1; + +F=[0 1;-w0^2 0]; +G=[0 1]'; +H=eye(2,2); //representing x1 and x2 states as outputs +J=[0 0]'; + +sys=syslin('c',F,G,H,J); //open loop system + +x0=[1 0]' //initial condition +t=0:0.2:7; +y=csim('impulse',t,sys); //open loop response +//------------------------------------------------------------------ + +//simulation for closed loop system +x0=[1 0]' //initial condition + +//control law u=-Kx; +K=[3*w0^2 4*w0]; +syscl=syslin('c',(F-G*K),G,H,J); //closed loop system + + +t=0:0.1:7; +u=zeros(1,length(t)); +[x z]=csim(u,t,syscl,x0); //closed loop response +plot(t',x'); + +u=-K*x; +plot(t',u'/4,'r--'); //control law u plot (scaled to 1/4 in figure); +legend("x1","x2","u/4") + +//Title, labels and grid to the figure +exec .\fig_settings.sci; //custom script for setting figure properties +title('Impulse response of undamped oscillator with full-state... + feedback(w0=1)','fontsize',3) +xlabel('Time t (sec.)','fontsize',2) +ylabel('Amplitude','fontsize',2) +//------------------------------------------------------------------ diff --git a/3432/CH7/EX7.15/Ex7_15_f0.pdf b/3432/CH7/EX7.15/Ex7_15_f0.pdf Binary files differnew file mode 100644 index 000000000..fda837dd8 --- /dev/null +++ b/3432/CH7/EX7.15/Ex7_15_f0.pdf diff --git a/3432/CH7/EX7.16/Ex7_16.sce b/3432/CH7/EX7.16/Ex7_16.sce new file mode 100644 index 000000000..36e32f805 --- /dev/null +++ b/3432/CH7/EX7.16/Ex7_16.sce @@ -0,0 +1,25 @@ +//Example 7.16 +//Ackermann's formula for undamped oscillator. + +xdel(winsid())//close all graphics Windows +clear; +clc; +//------------------------------------------------------------------ +//undamped oscillator (Pendulum) state model; +w0=1; + +F=[0 1;-w0^2 0]; +G=[0 1]'; +H=eye(2,2); //representing x1 and x2 states as outputs +J=[0 0]'; +//------------------------------------------------------------------ +//Ackermann's formula for feedback gain computation + +pc=[-2 -2]; //desired poles +exec('./acker_dk.sci', -1); +[K,eig]=acker_dk(F,G,pc) +disp(K,"Feedback gain K=") +disp(eig,"Closed loop eigen values are ") +//------------------------------------------------------------------ + + diff --git a/3432/CH7/EX7.17/Ex7_17.sce b/3432/CH7/EX7.17/Ex7_17.sce new file mode 100644 index 000000000..3d564e36a --- /dev/null +++ b/3432/CH7/EX7.17/Ex7_17.sce @@ -0,0 +1,35 @@ +//Example 7.17 How zero location affect control law
+// Obtain state feedback gain matrix for the given system
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//(a) state feedback gain matrix for zero at 2.
+//Location of system Zero
+z0=2;
+
+// State space representation
+Ao=[-7 1;-12 0];
+Bo=[1 -z0]';
+Co=[1 0];
+Do=0;
+
+// Desired poles
+Pd=[1 2 4];
+Pc=roots(Pd);
+
+
+// State feedback gain matrix for system zero at -2.0
+K=ppol(Ao,Bo,Pc)
+disp(K,"K=","State feeback gain for a system with zero at 2" )
+//------------------------------------------------------------------
+//Location of system Zero
+z0=-2.99
+B=[1 -z0]';
+// State feedback gain matrix for system zero...
+// at -2.99 (by ackermann's formula)
+exec('./acker_dk.sci', -1);
+K1=acker_dk(Ao,B,Pc)
+disp(K1,"K1","State feeback gain for a system with zero at -2.99")
+//------------------------------------------------------------------
diff --git a/3432/CH7/EX7.18/Ex7_18.sce b/3432/CH7/EX7.18/Ex7_18.sce new file mode 100644 index 000000000..5be65a2a6 --- /dev/null +++ b/3432/CH7/EX7.18/Ex7_18.sce @@ -0,0 +1,56 @@ +//Example 7.18 +//Introducing the reference input. + +xdel(winsid())//close all graphics Windows +clear; +clc; +//------------------------------------------------------------------ +//Pendulum state model; +w0=1; + +F=[0 1;-w0^2 0]; +G=[0 1]'; +H=[1 0]; //representing x1 and x2 states as outputs +J=0; +n=sqrt(length(F)); + +//computing state feedback matrix to place poles at [-2 -2] +exec('./acker_dk.sci', -1); +K=acker_dk(F,G,[-2, -2]); +//------------------------------------------------------------------ +//augmented matrix for tracking the reference +A=[F G;H J]; +N=A\[zeros(1,n) 1]'; +Nx=N(1:n); +Nu=N(n+1); + +//feedforward gain (input weight) +Ntilde=Nu+K*Nx; + +//------------------------------------ +//Alternately, it can be computed as / +Ntilde1=-inv(H*inv(F-G*K)*G); // / +//------------------------------------ + +//Closed loop system and step response +syscl=syslin('c',(F-G*K),G*Ntilde,H,J); //closed loop system + +t=0:0.1:7; +[y x]=csim('step',t,syscl); //closed loop response +plot(t',x'); + +u=-K*x+Ntilde; +plot(t',u'/4,'r--'); //control law u plot (scaled to 1/4 in figure); +legend("x1","x2","u/4"); +xset('font size',3); +xstring(5,0.93,"$x_{ss}$") +xstring(5,0.25,"$u_{ss}$") + +//Title, labels and grid to the figure +exec .\fig_settings.sci; //custom script for setting figure properties +title('Step response of undamped oscillator to reference input',... +'fontsize',3); +xlabel('Time t (sec.)','fontsize',2); +ylabel('Amplitude','fontsize',2); + +//------------------------------------------------------------------ diff --git a/3432/CH7/EX7.18/Ex7_18_f0.pdf b/3432/CH7/EX7.18/Ex7_18_f0.pdf Binary files differnew file mode 100644 index 000000000..18e8af6f6 --- /dev/null +++ b/3432/CH7/EX7.18/Ex7_18_f0.pdf diff --git a/3432/CH7/EX7.19/Ex7_19.sce b/3432/CH7/EX7.19/Ex7_19.sce new file mode 100644 index 000000000..013575d69 --- /dev/null +++ b/3432/CH7/EX7.19/Ex7_19.sce @@ -0,0 +1,56 @@ +//Example 7.19
+//Reference input to Type-1 control system: DC Motor
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+
+//Location of system Zero
+z0=2;
+
+// State space representation
+F=[0 1;0 -1];
+G=[0 1]';
+H=[1 0];
+J=0;
+n=sqrt(length(F)); //order of the system
+
+//computing state feedback matrix to place poles at assumed location [-1 -2]
+exec('./acker_dk.sci', -1);
+K=acker_dk(F,G,[-1, -2]); //assume pd=[-1 -2]
+//------------------------------------------------------------------
+//augmented matrix for tracking the reference
+A=[F G;H J];
+N=A\[zeros(1,n) 1]';
+Nx=N(1:n);
+Nu=N(n+1);
+disp(Nx,"Nx",Nu,"Nu")
+
+//feedforward gain (input weight)
+Ntilde=Nu+K*Nx;
+disp(Ntilde,"N_tilde","Input gain: N_tilde =Nu+K Nx")
+//------------------------------------------------------------------
+// Verify if ||y-r|| -> 0;
+
+syscl=syslin('c',(F-G*K),G*Ntilde,H,J); //closed loop system
+
+t=0:0.1:10;
+r=ones(1,length(t));//reference input
+[y x]=csim('step',t,syscl); //closed loop response
+
+e=sqrt((r-y).^2) //norm of error
+plot(t,y);
+plot(t,r,'m:'); //reference input
+plot(t,e,'r-.'); //norm of error
+xset('font size',3);
+xstring(3,0.83,"y")
+xstring(2,1,"r")
+xstring(3,0.1,"$\|e\|$")
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Step response of undamped oscillator to reference input','fontsize',3);
+xlabel('Time t (sec.)','fontsize',2);
+ylabel('Amplitude','fontsize',2);
+zoom_rect([0 -0.1 10 1.1])
+//------------------------------------------------------------------
diff --git a/3432/CH7/EX7.19/Ex7_19_f0.pdf b/3432/CH7/EX7.19/Ex7_19_f0.pdf Binary files differnew file mode 100644 index 000000000..67707bcb4 --- /dev/null +++ b/3432/CH7/EX7.19/Ex7_19_f0.pdf diff --git a/3432/CH7/EX7.2.b/Ex7_2.sce b/3432/CH7/EX7.2.b/Ex7_2.sce new file mode 100644 index 000000000..3cffa9bfa --- /dev/null +++ b/3432/CH7/EX7.2.b/Ex7_2.sce @@ -0,0 +1,36 @@ +//Example 7.2
+//Cruise control system step response.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+clc;
+//------------------------------------------------------------------
+//Cruise control system parameters
+m=1000;
+b=50;
+u=500;
+
+// Transfer function
+s=%s; // or
+s=poly(0,'s');
+sys1=syslin('c',(1/m)/(s+b/m));
+disp(sys1)
+//------------------------------------------------------------------
+F=[0 1; 0 -b/m];
+G=[0;1/m];
+H=[0 1];
+J=0;
+sys=syslin('c',F,G,H,J);
+//------------------------------------------------------------------
+//step response to u=500;
+t=0:0.5:100;
+v=csim('step',t,u*sys);
+plot(t,v,2)
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Responses of car velocity to a step in u','fontsize',3)
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('Amplitude','fontsize',2)
+//------------------------------------------------------------------
diff --git a/3432/CH7/EX7.2.b/Ex7_2_f0.pdf b/3432/CH7/EX7.2.b/Ex7_2_f0.pdf Binary files differnew file mode 100644 index 000000000..4b40aab00 --- /dev/null +++ b/3432/CH7/EX7.2.b/Ex7_2_f0.pdf diff --git a/3432/CH7/EX7.20/Ex7_20.sce b/3432/CH7/EX7.20/Ex7_20.sce new file mode 100644 index 000000000..14140dde4 --- /dev/null +++ b/3432/CH7/EX7.20/Ex7_20.sce @@ -0,0 +1,79 @@ +//Example 7.20
+// Pole Placement as a Dominant Second-Order System
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+
+clc;
+clear all;
+
+// State space representation
+F=[0 2 0 0 0;-0.10 -0.35 0.1 0.1 0.75; 0 0 0 2 0;...
+ 0.4 0.4 -0.4 -1.4 0; 0 -0.03 0 0 -1];
+G=[0 0 0 0 1]';
+H=[0.5 0 0.5 0 0]; //Tape position at the head
+Ht=[-0.2 -0.2 0.2 0.2 0]; //Tension output
+J=0;
+n=sqrt(length(F))
+// Desired poles
+Pc=[-0.707+0.707*%i -0.707-0.707*%i -4 -4 -4]/1.5;
+//------------------------------------------------------------------
+// State feedback gain matrix via LQR (riccati equation)
+Q = eye(5,5);
+R =1
+// Riccati equation
+P=riccati(F, G*inv(R)*G', Q, 'c')
+K1=inv(R)*G'*P
+//------------------------------------------------------------------
+// State feedback gain matrix via pole-placement
+exec('./acker_dk.sci', -1);
+K2=acker_dk(F,G,Pc);
+disp(K2,'K2=',"Gain by ackermans formula" );
+//------------------------------------------------------------------
+Ntilde1=-inv(H*inv(F-G*K1)*G); //input gain for LQR feedback gain.
+Ntilde2=-inv(H*inv(F-G*K2)*G); //input gain for Ackerman's feedback gain.
+
+syscl1=syslin('c',(F-G*K1),G*Ntilde1,H,J); //closed loop system with K1
+syscl2=syslin('c',(F-G*K2),G*Ntilde2,H,J); //closed loop system with K2
+
+t=0:0.1:12;
+[y1 x1]=csim('step',t,syscl1); //response of position head with K1
+[y2 x2]=csim('step',t,syscl2); //response of position head with K2
+
+//plot of a position of read write head
+plot(t,y1,"m-."); //Design via LQR
+plot(t,y2,2); //Design via Ackerman's Formula
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Step response of tape servomotor designs','fontsize',3);
+xlabel('Time t (sec.)','fontsize',2);
+ylabel('Tape Posotion','fontsize',2);
+
+xstring(2.5,1.1,"LQR")
+xarrows([3;4],[1.1;0.95],-1,1)
+xstring(5,0.7,["Dominant";"second order"])
+xarrows([5;4.2],[0.8;0.9],-1.5,1)
+//------------------------------------------------------------------
+
+//response as a tape tension
+yt1=Ht*x1;
+yt2=Ht*x2;
+
+figure(1)
+plot(t,yt1,"m-."); //Design via LQR
+plot(t,yt2,2); //Design via Ackerman's Formula
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Tension plots for tape servomotor step responses','fontsize',3);
+xlabel('Time t (sec.)','fontsize',2);
+ylabel('Tape Tension','fontsize',2);
+
+xstring(3.5,0,"LQR")
+xarrows([3.7;4.7],[0;0],-1)
+xstring(6.1,-0.015,["Dominant";"second order"])
+xarrows([6;6],[-0.013;-0.002],-1)
+//------------------------------------------------------------------
diff --git a/3432/CH7/EX7.20/Ex7_20_f0.pdf b/3432/CH7/EX7.20/Ex7_20_f0.pdf Binary files differnew file mode 100644 index 000000000..3fe7ab6e3 --- /dev/null +++ b/3432/CH7/EX7.20/Ex7_20_f0.pdf diff --git a/3432/CH7/EX7.20/Ex7_20_f1.pdf b/3432/CH7/EX7.20/Ex7_20_f1.pdf Binary files differnew file mode 100644 index 000000000..2569de48e --- /dev/null +++ b/3432/CH7/EX7.20/Ex7_20_f1.pdf diff --git a/3432/CH7/EX7.21/Ex7_21.sce b/3432/CH7/EX7.21/Ex7_21.sce new file mode 100644 index 000000000..59ceda7f6 --- /dev/null +++ b/3432/CH7/EX7.21/Ex7_21.sce @@ -0,0 +1,42 @@ +//Example 7.21
+// Symmetric root locus (SRL) for servo speed control
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//Transfer function model of the given system
+a=1.5;//assume
+s=poly(0,'s');
+nums=1;
+dens=s+a;
+num_s=1;
+den_s=-s+a;
+G0s=syslin('c',nums/dens); //G0(s)
+G0_s=syslin('c',num_s/den_s); //G0(-s)
+
+evans(G0s)
+evans(G0_s)
+zoom_rect([-3 -0.1 3 0.1])
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+xset("color",2);
+h=legend('');
+h.visible = "off"
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Symmetric root locus for a first order system','fontsize',3);
+//------------------------------------------------------------------
+//Root locus design
+//rho>0; choose rho=2
+rho=2;
+//optimal pole p=-sqrt(a^2+rho)
+p=-sqrt(a^2+rho)
+sig=real(p);
+omega=imag(p);
+plot(sig,omega,'ro')
+xstring(-2.5,0.02,["pole location at";"$\rho=2$"])
+xarrows([-2.2;-2.07],[0.02;0.002],-1.5,1)
+//------------------------------------------------------------------
diff --git a/3432/CH7/EX7.21/Ex7_21_f0.pdf b/3432/CH7/EX7.21/Ex7_21_f0.pdf Binary files differnew file mode 100644 index 000000000..7ae1c591e --- /dev/null +++ b/3432/CH7/EX7.21/Ex7_21_f0.pdf diff --git a/3432/CH7/EX7.22/Ex7_22.sce b/3432/CH7/EX7.22/Ex7_22.sce new file mode 100644 index 000000000..4e277f626 --- /dev/null +++ b/3432/CH7/EX7.22/Ex7_22.sce @@ -0,0 +1,46 @@ +//Example 7.22
+// SRL design for satellite attitude control
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//Transfer function for satellite attitude control system
+s=poly(0,'s');
+nums=1;
+dens=s^2;
+num_s=1;
+den_s=(-s)^2;
+G0s=syslin('c',nums/dens); //G0(s)
+G0_s=syslin('c',num_s/den_s); //G0(-s)
+//evans(G0s*G0_s)
+evans(1/s^4)
+zoom_rect([-3 -3 3 3])
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+xset("color",2);
+h=legend('');
+h.visible = "off"
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script for setting figure properties
+title('Symmetric root locus for the satellite','fontsize',3);
+//------------------------------------------------------------------
+//Root locus design
+//choose rho=4.07 that places pole at -1+-j
+rho=4.07;
+chr_eqn=(1+rho*G0s*G0_s)
+p=[-1+%i, -1-%i];
+sig=real(p);
+omega=imag(p);
+plot(sig,omega,'ro')
+xstring(-2.2,0.5,["pole locations at";"$\rho=4.07$"])
+//------------------------------------------------------------------
+//pole-placement design;
+sys=tf2ss(G0s);
+exec('./acker_dk.sci', -1);
+K=acker_dk(sys.A,sys.B,p);
+syscl=syslin('c',(sys.A-sys.B*K),sys.B, sys.C, sys.D)
+disp(spec(syscl.A),"Closed loop eigen values");
+//------------------------------------------------------------------
diff --git a/3432/CH7/EX7.22/Ex7_22_f0.pdf b/3432/CH7/EX7.22/Ex7_22_f0.pdf Binary files differnew file mode 100644 index 000000000..ebc7654c5 --- /dev/null +++ b/3432/CH7/EX7.22/Ex7_22_f0.pdf diff --git a/3432/CH7/EX7.23/Ex7_23.sce b/3432/CH7/EX7.23/Ex7_23.sce new file mode 100644 index 000000000..c2e1d2e46 --- /dev/null +++ b/3432/CH7/EX7.23/Ex7_23.sce @@ -0,0 +1,70 @@ +//Example 7.23
+// SRL Design for an Inverted Pendulum
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+
+//Transfer function model of Inverted Pendulum.
+s=poly(0,'s');
+
+nums=-(s+2);
+dens=(s^2-1)
+num_s=-(-s+2);
+den_s=((-s)^2-1)
+G0s=syslin('c',nums/dens); //G0(s)
+G0_s=syslin('c',num_s/den_s); //G0(-s)
+sysGG=G0s*G0_s;
+evans(sysGG)
+title('Symmetric root locus for Inverted Pendulum')
+zoom_rect([-3 -2 3 2])
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+xset("color",2);
+h=legend('');
+h.visible = "off"
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Symmetric root locus for the inverted pendulum','fontsize',3);
+//------------------------------------------------------------------
+//Root locus design
+//choose rho=1 that places pole at -1.36+-j0.606
+rho=1;
+p=[-1.36+0.606*%i, -1.36-0.606*%i];
+sig=real(p);
+omega=imag(p);
+plot(sig,omega,'ro')
+xstring(-1.25,0.5,["pole locations at";"$\rho=1$"])
+//------------------------------------------------------------------
+//pole-placement design;
+Ac=[0 1;1 0];Bc=[0 -1]'; Cc=[2 1];Dc=0;
+exec('./acker_dk.sci', -1);
+K=acker_dk(Ac,Bc,p);
+disp(K,"K=",spec(Ac-Bc*K),"Closed loop eigen values");
+
+//input gain calculation
+n=sqrt(length(Ac));
+A=[Ac Bc;Cc Dc];
+N=A\[zeros(1,n) 1]';
+Nx=N(1:n);
+Nu=N(n+1);
+
+//feedforward gain (input gain)
+Ntilde=Nu+K*Nx;
+
+//Step respose
+t=0:0.1:4.5;
+syscl=syslin('c',(Ac-Bc*K),Bc*Ntilde, Cc, Dc)
+[y x]=csim('step',t,syscl); //closed loop response
+figure,
+plot(t,y);
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Step response for inverted pendulum','fontsize',3);
+xlabel('Time t (sec.)','fontsize',2);
+ylabel(["Position","$x_1$"],'fontsize',2);
+//------------------------------------------------------------------
diff --git a/3432/CH7/EX7.23/Ex7_23_f0.pdf b/3432/CH7/EX7.23/Ex7_23_f0.pdf Binary files differnew file mode 100644 index 000000000..ec5d19937 --- /dev/null +++ b/3432/CH7/EX7.23/Ex7_23_f0.pdf diff --git a/3432/CH7/EX7.23/Ex7_23_f1.pdf b/3432/CH7/EX7.23/Ex7_23_f1.pdf Binary files differnew file mode 100644 index 000000000..0caae0420 --- /dev/null +++ b/3432/CH7/EX7.23/Ex7_23_f1.pdf diff --git a/3432/CH7/EX7.24/Ex7_24.sce b/3432/CH7/EX7.24/Ex7_24.sce new file mode 100644 index 000000000..a816cd7c7 --- /dev/null +++ b/3432/CH7/EX7.24/Ex7_24.sce @@ -0,0 +1,108 @@ +//Example 7.24
+// LQR Design for a Tape Drive
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+// State space model for a Tape Drive
+F=[0 2 0 0 0;-0.10 -0.35 0.1 0.1 0.75; 0 0 0 2 0; 0.4 0.4 -0.4 -1.4 0; 0 -0.03 0 0 -1];
+G=[0 0 0 0 1]';
+H3=[0.5 0 0.5 0 0];
+//------------------------------------------------------------------
+// State feedback gain matrix via LQR (riccati equation)
+// (a) Continuous LQR for rho=1
+rho=1;
+R1=1;
+Q1=rho*H3'*H3;
+// Riccati equation
+P1=riccati(F, G*inv(R1)*G', Q1, 'c')
+K1=inv(R1)*G'*P1
+disp(K1,'K1')
+//------------------------------------------------------------------
+// State feedback gain matrix via LQR (riccati equation)
+// (a) Comparision in step response with rho=0.1,1,10.
+rho=0.1;
+R2=1;
+Q2=rho*H3'*H3;
+// Riccati equation
+P2=riccati(F, G*inv(R2)*G', Q2, 'c')
+K2=inv(R2)*G'*P2
+
+rho=10;
+R3=1;
+Q3=rho*H3'*H3;
+// Riccati equation
+P3=riccati(F, G*inv(R3)*G', Q3, 'c')
+K3=inv(R3)*G'*P3
+//------------------------------------------------------------------
+//input gains for step reference with rho=0.1,1,10.
+Ntilde1=-inv(H3*inv(F-G*K1)*G);
+Ntilde2=-inv(H3*inv(F-G*K2)*G);
+Ntilde3=-inv(H3*inv(F-G*K3)*G);
+
+//Closed loop system with rho=0.1,1,10.
+syscl1=syslin('c',(F-G*K1),G*Ntilde1,H3,0);
+syscl2=syslin('c',(F-G*K2),G*Ntilde2,H3,0);
+syscl3=syslin('c',(F-G*K3),G*Ntilde3,H3,0);
+
+//step response with rho=0.1,1,10.
+t=0:0.1:12;
+[y1 x1]=csim('step',t,syscl1); //closed loop response
+[y2 x2]=csim('step',t,syscl2); //closed loop response
+[y3 x3]=csim('step',t,syscl3); //closed loop response
+
+figure,
+a1=newaxes();
+a1.axes_bounds=[0,0,1.0,0.5];
+plot(t,y1);
+plot(t,y2,'r-.');
+plot(t,y3,'m:');
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('(a)Step response of step servo motor for LQR Design','fontsize',3);
+xlabel('Time t (sec.)','fontsize',2);
+ylabel(["Tape Position","$x_3$"],'fontsize',2);
+
+xstring(4.1,0.85,"$\rho=1$")
+xstring(5.5,0.75,"$\rho=0.1$")
+xstring(2.1,1.05,"$\rho=10$")
+//------------------------------------------------------------------
+//Tensions for the Tape
+//For tape output is Ht=[-0.2 -0.2 0.2 0.2 0];
+Ht=[-0.2 -0.2 0.2 0.2 0];
+H3=Ht;
+//input gains can not be computed because of singularity. so set it 1;
+Ntilde1=1;
+Ntilde2=1;
+Ntilde3=1;
+
+//Closed loop system with rho=0.1,1,10.
+syscl1=syslin('c',(F-G*K1),G*Ntilde1,H3,0);
+syscl2=syslin('c',(F-G*K2),G*Ntilde2,H3,0);
+syscl3=syslin('c',(F-G*K3),G*Ntilde3,H3,0);
+
+//step response with rho=0.1,1,10.
+t=0:0.1:12;
+[y1 x1]=csim('step',t,syscl1); //closed loop response
+[y2 x2]=csim('step',t,syscl2); //closed loop response
+[y3 x3]=csim('step',t,syscl3); //closed loop response
+
+a2=newaxes();
+a2.axes_bounds=[0,0.5,1.0,0.5];
+plot(t,y1);
+plot(t,y2,'r-.');
+plot(t,y3,'m:');
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('(b)Corresponding tension for Tape servomotor step response','fontsize',3);
+xlabel('Time t (sec.)','fontsize',2);
+ylabel(["Tape Tension","T"],'fontsize',2);
+
+
+xstring(4.3,-0.05,"$\rho=1$")
+xstring(6,-0.1,"$\rho=0.1$")
+xstring(1.5,-0.03,"$\rho=10$")
+//------------------------------------------------------------------
diff --git a/3432/CH7/EX7.24/Ex7_24_f0.pdf b/3432/CH7/EX7.24/Ex7_24_f0.pdf Binary files differnew file mode 100644 index 000000000..b91050fcc --- /dev/null +++ b/3432/CH7/EX7.24/Ex7_24_f0.pdf diff --git a/3432/CH7/EX7.25/Ex7_25.sce b/3432/CH7/EX7.25/Ex7_25.sce new file mode 100644 index 000000000..0128a2fa0 --- /dev/null +++ b/3432/CH7/EX7.25/Ex7_25.sce @@ -0,0 +1,52 @@ +//Example 7.25
+// An estimator design for a simple pendulum
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+// State space representation
+w0=1;
+F=[0 1; -w0^2 0];
+G=[0 1]';
+H=[1 0];
+J=0;
+n=sqrt(length(F));//order of the system
+// Desired estimator poles
+Pe=[-10*w0 -10*w0];
+// Observer gain matrix for system
+Lt=ppol(F',H',Pe);
+L=Lt';
+disp(L,"L=" );
+//------------------------------------------------------------------
+//simulation for closed loop system
+x0=[1 0]' //initial condition
+
+//State feedback control law u=-Kx; (from Ex7_15)
+K=[3*w0^2 4*w0];
+//------------------------------------------------------------------
+//Augmented plant and observer
+Faug=[F-G*K, zeros(n,n); L*H, F-L*H];
+Gaug=[0 0 0 0]';
+Haug=[H -H];
+Jaug=0;
+
+sys_aug=syslin('c',Faug,Gaug,Haug,Jaug);
+t=0:0.1:4;
+u=zeros(1,length(t));
+x0=[1 0 0 0]';
+[x z]=csim(u,t,sys_aug,x0); //closed loop response
+plot(t,z(1,:));
+plot(t,z(2,:),'m');
+plot(t,z(3,:),'b:');
+plot(t,z(4,:),'m:');
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title(['Initial condition response of oscillator showing',...
+'$\mathbf{x}$','and','$\hat{\mathbf{x}}$'],'fontsize',3)
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('Amplitude','fontsize',2)
+legend('$x_1$','$x_2$','$\hat{x}_1$','$\hat{x}_2$')
+xset('font size',2)
+//------------------------------------------------------------------
diff --git a/3432/CH7/EX7.25/Ex7_25_f0.pdf b/3432/CH7/EX7.25/Ex7_25_f0.pdf Binary files differnew file mode 100644 index 000000000..e24633f1a --- /dev/null +++ b/3432/CH7/EX7.25/Ex7_25_f0.pdf diff --git a/3432/CH7/EX7.26/Ex7_26.sce b/3432/CH7/EX7.26/Ex7_26.sce new file mode 100644 index 000000000..7485ee2b1 --- /dev/null +++ b/3432/CH7/EX7.26/Ex7_26.sce @@ -0,0 +1,55 @@ +//Example 7.26
+// A reduced order estimator design for pendulum
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+// State space representation
+w0=1;
+F=[0 1; -w0^2 0];
+G=[0 1]';
+H=[1 0];
+J=0;
+n=sqrt(length(F));//order of the system
+
+//partioned system
+Faa=F(1,1); Fab=F(1,2);
+Fba=F(2,1); Fbb=F(2,2);
+
+// Desired estimator poles
+Pe=[-10];
+// Observer gain matrix for system
+L=ppol(Fbb',Fab',Pe);
+L=L';
+disp(L,"L=" );
+//------------------------------------------------------------------
+//simulation for closed loop system
+x0=[1 0 10]' //initial condition
+
+//State feedback control law u=-Kx; (from Ex7_15)
+K=[3*w0^2 4*w0];
+//------------------------------------------------------------------
+//Augmented plant and observer
+Faug=[F-G*K, zeros(n,1); Fab, L*Fab, Fbb-L*Fab];
+Gaug=[0 0 0]';
+Haug=[H 0];
+J=0;
+
+sys_aug=syslin('c',Faug,Gaug,Haug,J);
+t=0:0.1:4;
+u=zeros(1,length(t));
+[x z]=csim(u,t,sys_aug,x0); //closed loop response
+plot(t,z(1,:),'b');
+plot(t,z(2,:),'r');
+plot(t,z(3,:),'r--');
+
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Initial condition response of the reduced order estimator','fontsize',3)
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('Amplitude','fontsize',2)
+legend('$x_1$','$x_2$','$\hat{x}_2$')
+xset('font size',2)
+//------------------------------------------------------------------
diff --git a/3432/CH7/EX7.26/Ex7_26_f0.pdf b/3432/CH7/EX7.26/Ex7_26_f0.pdf Binary files differnew file mode 100644 index 000000000..96d9f50aa --- /dev/null +++ b/3432/CH7/EX7.26/Ex7_26_f0.pdf diff --git a/3432/CH7/EX7.27/Ex7_27.sce b/3432/CH7/EX7.27/Ex7_27.sce new file mode 100644 index 000000000..8c3c51a9a --- /dev/null +++ b/3432/CH7/EX7.27/Ex7_27.sce @@ -0,0 +1,41 @@ +//Example 7.27
+// SRL estimator design for a simple pendulum
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+// State space representation
+F=[0 1; -1 0];
+G=[0 1]';
+H=[1 0];
+J=0;
+
+//Transfer function
+sys=syslin('c',F,G,H,J)
+sysGG=ss2tf(sys)
+
+//Symmetric root locus for the inverted pendulum estimator design
+//------------------------------------------------------------------
+//Root locus design
+evans(sysGG*sysGG)
+zoom_rect([-5 -5 5 5])
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+xset("color",2);
+h=legend('');
+h.visible = "off"
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Symmetric root locus for inverted the pendulum estimator design',...
+'fontsize',3);
+//------------------------------------------------------------------
+//pole locations for q=365; p=-3+-j3.18
+p=[-3+3.18*%i -3-3.18*%i]
+sig=real(p);
+omega=imag(p);
+plot(sig,omega,'ro')
+xstring(-4,1,["pole location at";"q=365"])
+xarrows([-3.5;-3.05],[2;3.1],-1.5,1)
+//------------------------------------------------------------------
diff --git a/3432/CH7/EX7.27/Ex7_27_f0.pdf b/3432/CH7/EX7.27/Ex7_27_f0.pdf Binary files differnew file mode 100644 index 000000000..ad30cd949 --- /dev/null +++ b/3432/CH7/EX7.27/Ex7_27_f0.pdf diff --git a/3432/CH7/EX7.28/Ex7_28.sce b/3432/CH7/EX7.28/Ex7_28.sce new file mode 100644 index 000000000..18d705b30 --- /dev/null +++ b/3432/CH7/EX7.28/Ex7_28.sce @@ -0,0 +1,61 @@ +//Example 7.28
+// Full order compensator design for satellite attitude control.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+
+// State space representation
+A=[0 1; 0 0];
+B=[0 1]';
+C=[1 0];
+D=0;
+n=sqrt(length(A));
+//Desired poles for the satellite attitude control system.
+Pc=[-0.707+0.707*%i -0.707-0.707*%i ]
+
+// State feedback gain
+K=ppol(A,B,Pc)
+disp(K,'K=',"State feedback gain")
+
+//Estimator - error roots are at
+Pe=[-2.5+4.3*%i -2.5-4.3*%i]
+L=ppol(A',C',Pe);
+L=L';
+disp(L,'L=',"Observer gain")
+//------------------------------------------------------------------
+//Compensator Design
+sys1=syslin('c',A,B,C,D);
+G=ss2tf(sys1);
+s=poly(0,'s');
+
+Ds=-K*inv(s*eye(n,n)-A+B*K+L*C)*L;
+
+exec('./zpk_dk.sci', -1);
+[pl,zr Kp]=zpk_dk(Ds);
+D=poly(zr,'s','roots')/poly(pl,'s','roots')
+
+evans(G*D)
+zoom_rect([-8 -6 8 6])
+
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+xset("color",2);
+h=legend('');
+h.visible = "off"
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script for setting figure properties
+title('Root locus for combined control and estimator,...
+ with process gain as the parameter','fontsize',3);
+//------------------------------------------------------------------
+//Frequnecy response for 1/s^2 and compensated
+
+figure,
+bode([-Ds*G;G],0.01/2/%pi,100/2/%pi,"rad");
+title(["Frequency response for","$G(s)=1/s^2$"],'fontsize',3)
+legend('Compensated','Uncompensated')
+exec .\fig_settings.sci; //custom script for setting figure properties
+//------------------------------------------------------------------
diff --git a/3432/CH7/EX7.28/Ex7_28_f0.pdf b/3432/CH7/EX7.28/Ex7_28_f0.pdf Binary files differnew file mode 100644 index 000000000..2f2a24476 --- /dev/null +++ b/3432/CH7/EX7.28/Ex7_28_f0.pdf diff --git a/3432/CH7/EX7.28/Ex7_28_f1.pdf b/3432/CH7/EX7.28/Ex7_28_f1.pdf Binary files differnew file mode 100644 index 000000000..8d6311069 --- /dev/null +++ b/3432/CH7/EX7.28/Ex7_28_f1.pdf diff --git a/3432/CH7/EX7.29/Ex7_29.sce b/3432/CH7/EX7.29/Ex7_29.sce new file mode 100644 index 000000000..a0c479432 --- /dev/null +++ b/3432/CH7/EX7.29/Ex7_29.sce @@ -0,0 +1,74 @@ +//Example 7.29
+// A reduced order compensator design for a satellite attitude control
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+// State space representation
+F=[0 1;0 0];
+G=[0 1]';
+H=[1 0];
+J=0;
+n=sqrt(length(F));//order of the system
+
+//partioned system
+Faa=F(1,1); Fab=F(1,2);
+Fba=F(2,1); Fbb=F(2,2);
+Ga=G(1);Gb=G(2);
+
+// Desired estimator poles
+Pe=[-5];
+// Observer gain matrix for system
+L=ppol(Fbb',Fab',Pe);
+L=L';
+disp(L,"L=" );
+//------------------------------------------------------------------
+//State feedback control law u=-Kx=-(K+[L*k2 0])[y xc]';
+k1=1; k2=sqrt(2);
+K=[k1 k2];
+Kc=K+[L*k2 0];
+//------------------------------------------------------------------
+//compensator differential equation
+//xc_dot=(Fbb-L*Fab)*xb_hat + (Fba - L*Faa)*y + (Gb - L*Ga)*u
+//xc_dot=((Fbb-L*Fab)-k2)*xc + [(Fba - L*Faa)-(Gb - L*Ga)*(k1+L*k2)+L*(Fbb-L*Fab)]*y
+Fc=(Fbb-L*Fab)-Gb*k2
+Fy=(Fba - L*Faa)-(Gb - L*Ga)*(k1+k2*L)+(Fbb-L*Fab)*L
+//compensator transfer function
+s=poly(0,'s');
+Gest=syslin('c',Fy/(s-Fc))//estimator transfer function
+Dcr=-[k1+L*k2+k2*Gest]
+disp(Dcr,'Dcr','compensator transfer function')
+//------------------------------------------------------------------
+//Root locus with reduced order compensator
+G=1/s^2;
+G=syslin('c',G);
+exec('./zpk_dk.sci', -1);
+[pl,zr Kp]=zpk_dk(Dcr);
+
+Dcr=poly(zr,'s','roots')/poly(pl,'s','roots')
+Dcr=syslin('c',Dcr);
+evans(G*Dcr)
+zoom_rect([-8 -4 2 4])
+
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+xset("color",2);
+h=legend('');
+h.visible = "off"
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(['Root locus of a reduced order controller and',"$1/s^2$",...
+ "process"],'fontsize',3);
+//------------------------------------------------------------------
+//Frequnecy response for 1/s^2 and compensated
+
+figure,
+bode([-Kp*G*Dcr;G],0.01/2/%pi,100/2/%pi,"rad");
+title(["Frequency response","$G(s)=1/s^2$", "with a reduced...
+ order estimator"],'fontsize',3)
+exec .\fig_settings.sci; //custom script for setting figure properties
+legend('Compensated','Uncompensated')
+//------------------------------------------------------------------
diff --git a/3432/CH7/EX7.29/Ex7_29_f0.pdf b/3432/CH7/EX7.29/Ex7_29_f0.pdf Binary files differnew file mode 100644 index 000000000..c2a23bbb2 --- /dev/null +++ b/3432/CH7/EX7.29/Ex7_29_f0.pdf diff --git a/3432/CH7/EX7.29/Ex7_29_f1.pdf b/3432/CH7/EX7.29/Ex7_29_f1.pdf Binary files differnew file mode 100644 index 000000000..5b330b97d --- /dev/null +++ b/3432/CH7/EX7.29/Ex7_29_f1.pdf diff --git a/3432/CH7/EX7.30/Ex7_30.sce b/3432/CH7/EX7.30/Ex7_30.sce new file mode 100644 index 000000000..99e6aaee4 --- /dev/null +++ b/3432/CH7/EX7.30/Ex7_30.sce @@ -0,0 +1,73 @@ +//Example 7.30
+// Full-Order Compensator Design for DC Servo.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+
+// State space representation
+//Transfer function model for DC Servo
+s=poly(0,'s');
+num=10;
+den=s*(s+2)*(s+8);
+Gs=syslin('c',num/den);
+
+// State space representation
+F=[-10 1 0;-16 0 1;0 0 0];
+G=[0 0 10]';
+H=[1 0 0];
+J=0;
+n=sqrt(length(F));
+//Desired poles for the DC Servo system.
+Pc=[-1.42 -1.04+2.14*%i -1.04-2.14*%i ]
+
+
+// State feedback gain
+K=ppol(F,G,Pc)
+disp(K,'K=',"State feedback gain")
+
+//Estimator - error roots are at
+Pe=[-4.25 -3.13+6.41*%i -3.13-6.41*%i]
+L=ppol(F',H',Pe);
+L=L';
+disp(L,'L=',"Observer gain")
+//------------------------------------------------------------------
+//Compensator Design
+DK=-K*inv(s*eye(n,n)-F+G*K+L*H)*L;
+
+exec('./zpk_dk.sci', -1);
+[p,z]=zpk_dk(DK);
+D=poly(z,'s','roots')/poly(p,'s','roots')
+
+evans(Gs*D)
+zoom_rect([-8 -9 3 9])
+
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+xset("color",2);
+h=legend('');
+h.visible = "off"
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Root locus for DC servo pole assignment','fontsize',3);
+//------------------------------------------------------------------
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/3432/CH7/EX7.30/Ex7_30_f0.pdf b/3432/CH7/EX7.30/Ex7_30_f0.pdf Binary files differnew file mode 100644 index 000000000..65b7d8541 --- /dev/null +++ b/3432/CH7/EX7.30/Ex7_30_f0.pdf diff --git a/3432/CH7/EX7.31/Ex7_31.sce b/3432/CH7/EX7.31/Ex7_31.sce new file mode 100644 index 000000000..7e5955621 --- /dev/null +++ b/3432/CH7/EX7.31/Ex7_31.sce @@ -0,0 +1,83 @@ +//Example 7.31
+// Reduced-Order Estimator Design for DC Servo.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+
+// State space representation
+//Transfer function model for DC Servo
+s=poly(0,'s');
+num=10;
+den=s*(s+2)*(s+8);
+Gs=syslin('c',num/den);
+// State space representation
+F=[-10 1 0;-16 0 1;0 0 0]
+G=[0 0 10]';
+H=[1 0 0];
+J=0;
+n=sqrt(length(F));
+//Desired poles for the DC Servo system.
+Pc=[-1.42 -1.04+2.14*%i -1.04-2.14*%i ]
+// State feedback gain
+K=ppol(F,G,Pc)
+disp(K,'K=',"State feedback gain")
+
+//------------------------------------------------------------------
+//Estimator - error roots are at
+//partioned system
+Faa=F(1,1); Fab=F(1,2:3);
+Fba=F(3,1); Fbb=F(2:3,2:3);
+Ga=G(1);Gb=G(2:3);
+
+Pe=[-4.24+4.24*%i, -4.24-4.24*%i]
+// Observer gain matrix for system
+L=ppol(Fbb',Fab',Pe);
+L=L';
+disp(L,"L=" );
+//------------------------------------------------------------------
+
+//State feedback control law u=-Kx=-(K+[L*k2 0])[y xc]';
+k1=K(1); k2=K(2:3);
+
+//------------------------------------------------------------------
+//compensator transfer function
+s=poly(0,'s');
+num=(-0.735+s)*(1.871+s);
+den=poly([-0.990 + 6.12* %i, -0.990 - 6.12* %i] ,'s','roots')
+Dcr=syslin('c',num/den);
+disp(Dcr,'Dcr','compensator transfer function')
+//------------------------------------------------------------------
+//Root locus with reduced order compensator
+evans(-Dcr*Gs)
+zoom_rect([-8 -9 3 9])
+
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+xset("color",2);
+h=legend('');
+h.visible = "off"
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Root locus for DC servo reduced order controller','fontsize',3);
+//------------------------------------------------------------------
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/3432/CH7/EX7.31/Ex7_31_f0.pdf b/3432/CH7/EX7.31/Ex7_31_f0.pdf Binary files differnew file mode 100644 index 000000000..98c3a4296 --- /dev/null +++ b/3432/CH7/EX7.31/Ex7_31_f0.pdf diff --git a/3432/CH7/EX7.32/Ex7_32.sce b/3432/CH7/EX7.32/Ex7_32.sce new file mode 100644 index 000000000..ca1184424 --- /dev/null +++ b/3432/CH7/EX7.32/Ex7_32.sce @@ -0,0 +1,122 @@ +//Example 7.32
+// Redesign of the Dc servo compensator using SRL
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+
+// State space representation
+//Transfer function model for DC Servo
+s=poly(0,'s');
+num=10;
+den=s*(s+2)*(s+8);
+Gs=syslin('c',num/den);
+
+// State space representation
+F=[-10 1 0;-16 0 1;0 0 0]
+G=[0 0 10]';
+H=[1 0 0];
+J=0;
+n=sqrt(length(F));
+//Desired poles for the DC Servo system.
+Pc=[-2+1.56*%i -2-1.56*%i -8.04]
+
+
+// State feedback gain
+K=ppol(F,G,Pc)
+disp(K,'K=',"State feedback gain")
+
+//Estimator - error roots are at
+Pe=[-4+4.49*%i -4-4.49*%i -9.169]
+exec .\acker_dk.sci;
+Lt=ppol(F',H',Pe);
+L=clean(Lt');
+disp(L,'L=',"Observer gain")
+//Error in book, Gain values are different in book.
+//------------------------------------------------------------------
+//Compensator Design
+DK=-K*inv(s*eye(n,n)-F+G*K+L*H)*L;
+DK=syslin('c',DK)
+exec('./zpk_dk.sci', -1);
+[pl,zr,Kp]=zpk_dk(DK);
+Dc=poly(zr,'s','roots')/poly(pl,'s','roots')
+//------------------------------------------------------------------
+//symmetric root locus
+G_s=horner(Gs,-s);
+evans(Gs*G_s)
+zoom_rect([-10 -5 10 5])
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+xset("color",2);
+h=legend('');
+h.visible = "off"
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script for setting figure properties
+title('Symmetric root locus','fontsize',3);
+//------------------------------------------------------------------
+//root locus
+figure,
+evans(Gs*Dc) //Correct root locus
+zoom_rect([-11 -6 1 6])
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+xset("color",2);
+h=legend('');
+h.visible = "off"
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Root locus for pole assignment from the SRL','fontsize',3);
+//------------------------------------------------------------------
+//Discrete-time controller
+nc=94.5*conv([7.98 1],[2.52 1])
+dc=conv([59.5348 8.56 1],[10.6 1])
+sysDc=poly(nc,'s','coeff')/poly(dc,'s','coeff');
+sysDc_ss=syslin('c',tf2ss(sysDc));
+ts=0.1;
+sysDd=dscr(sysDc_ss,ts)
+Gdz=ss2tf(sysDd);
+
+disp(sysDc,"Continuous-time compensator")
+disp(Gdz,"Discrete-time compensator")
+//------------------------------------------------------------------
+//step responses
+importXcosDiagram(".\Ex7_32_model.xcos")
+
+xcos_simulate(scs_m,4);
+scs_m.props.context
+figure,
+plot(yt.time,yt.values(:,1),2)
+plot(yt.time,yt.values(:,2),'r--')
+xlabel('Time (sec)');
+ylabel('y');
+title("Comaprison of step responses for continuous and discrete...
+ controllers",'fontsize',3)
+exec .\fig_settings.sci; //custom script for setting figure properties
+legend("continuous controller","digital controller",4)
+
+//Control inputs
+figure,
+plot(ut.time,ut.values(:,1),2)
+plot(ut.time,ut.values(:,2),'r--')
+xlabel('Time (sec)');
+ylabel('u');
+title("Comaprison of control signals for continuous and discrete...
+ controllers",'fontsize',3)
+exec .\fig_settings.sci; //custom script for setting figure properties
+legend("continuous controller","digital controller")
+//------------------------------------------------------------------
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/3432/CH7/EX7.32/Ex7_32_f0.pdf b/3432/CH7/EX7.32/Ex7_32_f0.pdf Binary files differnew file mode 100644 index 000000000..10af89212 --- /dev/null +++ b/3432/CH7/EX7.32/Ex7_32_f0.pdf diff --git a/3432/CH7/EX7.32/Ex7_32_f2.pdf b/3432/CH7/EX7.32/Ex7_32_f2.pdf Binary files differnew file mode 100644 index 000000000..0c39c3903 --- /dev/null +++ b/3432/CH7/EX7.32/Ex7_32_f2.pdf diff --git a/3432/CH7/EX7.32/Ex7_32_model.xcos b/3432/CH7/EX7.32/Ex7_32_model.xcos new file mode 100644 index 000000000..73d29da91 --- /dev/null +++ b/3432/CH7/EX7.32/Ex7_32_model.xcos @@ -0,0 +1 @@ +<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1" finalIntegrationTime="5.0" title="Ex7_32_model"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331 1318--><mxGraphModel as="model"><root><mxCell id="-2dd55334:14dcbdd0183:-7fd2"/><mxCell id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/><BasicBlock dependsOnT="1" id="-2dd55334:14dcbdd0183:-7f98" interfaceFunctionName="CLR" ordering="1" 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\ No newline at end of file diff --git a/3432/CH7/EX7.33/Ex7_33.sce b/3432/CH7/EX7.33/Ex7_33.sce new file mode 100644 index 000000000..46c2f6a57 --- /dev/null +++ b/3432/CH7/EX7.33/Ex7_33.sce @@ -0,0 +1,47 @@ +//Example 7.33
+// DC servo system redesign with modified with dominant second
+// order pole locations.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+
+// State space representation
+//Transfer function model for DC Servo
+s=poly(0,'s');
+num=10;
+den=s*(s+2)*(s+8);
+Gs=syslin('c',num/den);
+
+// State space representation
+F=[-10 1 0;-16 0 1;0 0 0]
+G=[0 0 10]';
+H=[1 0 0];
+J=0;
+n=sqrt(length(F));
+//Desired poles for the DC Servo system.
+Pc=[-1.41+1.41*%i -1.41-1.41*%i -8]
+
+
+// State feedback gain
+K=ppol(F,G,Pc)
+disp(K,'K=',"State feedback gain")
+
+//Estimator - error roots are at
+Pe=[-4.24+4.24*%i -4.24-4.24*%i -8]
+exec .\acker_dk.sci;
+Lt=ppol(F',H',Pe);
+L=clean(Lt');
+disp(L,'L=',"Observer gain")
+//Error in book, Gain values are different in book.
+//------------------------------------------------------------------
+//Compensator Design
+DK=-K*inv(s*eye(n,n)-F+G*K+L*H)*L;
+DK=syslin('c',DK)
+exec('./zpk_dk.sci', -1);
+[pl,zr,Kp]=zpk_dk(DK*10);
+disp(zr,"zeros",pl,"Poles",Kp*10,"Gain(includung system gain)")
+Dcs=poly(zr,'s','roots')/poly(pl,'s','roots')
+disp(Dcs,'Dcs=',"Compensator transfer function")
+//------------------------------------------------------------------
diff --git a/3432/CH7/EX7.34/Ex7_34.sce b/3432/CH7/EX7.34/Ex7_34.sce new file mode 100644 index 000000000..2e77ebe9f --- /dev/null +++ b/3432/CH7/EX7.34/Ex7_34.sce @@ -0,0 +1,110 @@ +//Example 7.34
+// Servomechanism, increasing the velocity constant through
+// zero assignment.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+
+// State space representation
+//Transfer function model for DC Servo
+s=poly(0,'s');
+num=1;
+den=s*(s+1);
+Gs=syslin('c',num/den);
+
+// State space representation
+F=[0 1;0 -1]
+G=[0 1]';
+H=[1 0];
+J=0;
+n=sqrt(length(F));
+//Desired poles for the DC Servo system.
+Pc=[-2 -2]
+
+// State feedback gain
+exec .\acker_dk.sci;
+K=acker_dk(F,G,Pc)//Gain computed in book is incorrect.
+disp(K,'K=',"State feedback gain")
+//------------------------------------------------------------------
+//Overall transfer function with reduced order estimator.
+Gred=8.32*(0.096+s)/(0.1 +s)/(8 + 4*s+s^2)
+Gred=syslin('c',Gred)
+disp(Gred,'Ys/Rs',"Overall transfer function with reduced...
+ order estimator")
+
+//Compensator
+D=(0.096+s)*(s+1)/(4.08 +s)/(0.0196+s)
+Ds=syslin('c',D*8.32)
+disp(Ds,'Ds=',"Compensator transfer function")
+//------------------------------------------------------------------
+//root locus
+figure(0)
+evans(D*Gs,100) //Correct root locus
+zoom_rect([-0.2 -0.1 0.1 0.1])
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+xset("color",2);
+h=legend('');
+h.visible = "off"
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Root locus of lag-lead compensation','fontsize',3);
+//------------------------------------------------------------------
+//Bode plot
+figure(1)
+bode(Ds*Gs,0.01/2/%pi,100/2/%pi,"rad") //Correct root locus
+
+f=gca();
+h=legend('');
+h.visible = "off"
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script for setting figure properties
+title('Frequency response of lag-lead compensation','fontsize',3);
+//------------------------------------------------------------------
+//step response of the system with lag compensation
+t=0:0.1:5;
+ylag=csim('step',t,8.32*Gs*D/(1+8.32*Gs*D));
+figure
+plot(t,ylag,2);
+xlabel('Time (sec)');
+ylabel('y');
+title("Step response of the system with lag compensation",'fontsize',3)
+exec .\fig_settings.sci; //custom script for setting figure properties
+//------------------------------------------------------------------
+//Discrete-time controller
+sysDc_ss=syslin('c',tf2ss(Ds));
+ts=0.1;
+sysDd=dscr(sysDc_ss,ts)
+Gdz=ss2tf(sysDd)
+
+disp(Gdz,"Discrete-time compensator")
+//------------------------------------------------------------------
+//step responses comparision
+importXcosDiagram(".\Ex7_34_model.xcos")
+
+xcos_simulate(scs_m,4);
+scs_m.props.context
+figure,
+plot(yt.time,yt.values(:,1),2)
+plot(yt.time,yt.values(:,2),'r--')
+xlabel('Time (sec)');
+ylabel('y');
+title("Comaprison of step responses for continuous and discrete...
+ controllers",'fontsize',3)
+exec .\fig_settings.sci; //custom script for setting figure properties
+legend("continuous controller","digital controller",4)
+
+//Control inputs
+figure,
+plot(ut.time,ut.values(:,1),2)
+plot(ut.time,ut.values(:,2),'r--')
+xlabel('Time (sec)');
+ylabel('u');
+title("Comaprison of control signals for continuous and discrete...
+ controllers",'fontsize',3)
+exec .\fig_settings.sci; //custom script for setting figure properties
+legend("continuous controller","digital controller")
+//------------------------------------------------------------------
diff --git a/3432/CH7/EX7.34/Ex7_34_f0.pdf b/3432/CH7/EX7.34/Ex7_34_f0.pdf Binary files differnew file mode 100644 index 000000000..d7b791b05 --- /dev/null +++ b/3432/CH7/EX7.34/Ex7_34_f0.pdf diff --git a/3432/CH7/EX7.34/Ex7_34_f4.pdf b/3432/CH7/EX7.34/Ex7_34_f4.pdf Binary files differnew file mode 100644 index 000000000..c76fc78a5 --- /dev/null +++ b/3432/CH7/EX7.34/Ex7_34_f4.pdf diff --git a/3432/CH7/EX7.34/Ex7_34_model.xcos b/3432/CH7/EX7.34/Ex7_34_model.xcos new file mode 100644 index 000000000..8ed169a3b --- /dev/null +++ b/3432/CH7/EX7.34/Ex7_34_model.xcos @@ -0,0 +1 @@ +<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1" finalIntegrationTime="5.0" title="Ex7_34_model"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331 1318--><mxGraphModel as="model"><root><mxCell id="-2dd55334:14dcbdd0183:-7fd2"/><mxCell id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/><BasicBlock dependsOnT="1" id="-2dd55334:14dcbdd0183:-7f98" interfaceFunctionName="CLR" ordering="1" 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\ No newline at end of file diff --git a/3432/CH7/EX7.35/Ex7_35.sce b/3432/CH7/EX7.35/Ex7_35.sce new file mode 100644 index 000000000..8bf65446b --- /dev/null +++ b/3432/CH7/EX7.35/Ex7_35.sce @@ -0,0 +1,82 @@ +//Example 7.35
+// Integral Control of a Motor Speed System
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+
+//Transfer function model
+num=1;
+s=poly(0,'s');
+den=(s+3);
+G=syslin('c',num/den);
+sys=tf2ss(G)
+
+// State space representation of augmented system
+F=[0 1; 0 -3];
+G=[0 1]'
+H=[1 0];
+J=0;
+
+//Desired poles for augmented system
+Pc=[-5 -5]
+
+// State feedback gain is
+K=ppol(F,G,Pc)
+disp(K,'K=')
+
+//Estimator
+Pe=[-10]
+L=ppol(sys.A',sys.C',Pe)
+disp(L','L=')
+
+//------------------------------------------------------------------
+//(c) Compare step reference and disturbance response.
+//step reference response switch r=1 and w=0;
+r=1;w=0;
+importXcosDiagram(".\Ex7_35_model.xcos")
+ //The diagram data structure
+xcos_simulate(scs_m,4);
+scs_m.props.context
+figure(0)
+plot(yt.time,yt.values)
+xlabel('time');
+ylabel('y');
+
+figure(1)
+plot(ut.time,ut.values)
+xlabel('time');
+ylabel('y');
+//------------------------------------------------------------------
+// Step disturbance response switch r=0 and w=1;
+w=1;r=0;
+importXcosDiagram(".\Ex7_35_model.xcos")
+ //The diagram data structure
+xcos_simulate(scs_m,4);
+scs_m.props.context
+
+scf(0)
+plot(yt.time,yt.values,'r--')
+xlabel('time');
+ylabel('y');
+title("step Response",'fontsize',3)
+exec .\fig_settings.sci; // custom script for setting figure properties
+legend("y1","y2")
+xset('font size',3);
+xstring(0.9,0.9,"$y_1$");
+xstring(0.25,0.12,"$y_2$");
+
+
+scf(1)
+plot(ut.time,ut.values,'r--')
+xlabel('time');
+ylabel('y');
+title("Control efforts",'fontsize',3)
+exec .\fig_settings.sci; // custom script for setting figure properties
+legend("u1","u2")
+xset('font size',3);
+xstring(0.25,2.5,"$u_1$");
+xstring(1,-1,"$u_2$");
+//------------------------------------------------------------------
+
diff --git a/3432/CH7/EX7.35/Ex7_35_f0.pdf b/3432/CH7/EX7.35/Ex7_35_f0.pdf Binary files differnew file mode 100644 index 000000000..5bdf20200 --- /dev/null +++ b/3432/CH7/EX7.35/Ex7_35_f0.pdf diff --git a/3432/CH7/EX7.35/Ex7_35_f1.pdf b/3432/CH7/EX7.35/Ex7_35_f1.pdf Binary files differnew file mode 100644 index 000000000..ef112fd12 --- /dev/null +++ b/3432/CH7/EX7.35/Ex7_35_f1.pdf diff --git a/3432/CH7/EX7.35/Ex7_35_model.xcos b/3432/CH7/EX7.35/Ex7_35_model.xcos new file mode 100644 index 000000000..bd27560af --- /dev/null +++ b/3432/CH7/EX7.35/Ex7_35_model.xcos @@ -0,0 +1 @@ +<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1" finalIntegrationTime="5.0" title="Ex7_35_model"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331 1318--><mxGraphModel as="model"><root><mxCell id="-2dd55334:14dcbdd0183:-7fd2"/><mxCell id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/><BasicBlock dependsOnT="1" id="-2dd55334:14dcbdd0183:-7f98" interfaceFunctionName="CLR" ordering="1" 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\ No newline at end of file diff --git a/3432/CH7/EX7.7/Ex7_7.sce b/3432/CH7/EX7.7/Ex7_7.sce new file mode 100644 index 000000000..71aeae4cb --- /dev/null +++ b/3432/CH7/EX7.7/Ex7_7.sce @@ -0,0 +1,29 @@ +//Example 7.7
+//Analog computer Implementation.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+// State space model of the given system
+F=[-6 -11 -6; 1 0 0; 0 1 0];
+G=[6; 0; 0];
+H=[0 0 1];
+J=0;
+sys_ss=syslin('c',F,G,H,J)
+disp(sys_ss)
+//------------------------------------------------------------------
+//Transfer function form
+[d,Ns,Ds]=ss2tf(sys_ss)
+Ns=clean(Ns);
+G=syslin('c',Ns/Ds);
+disp(G)
+//------------------------------------------------------------------
+// convert numerator - denominator to pole - zero form
+//gain (K) pole (P) and zeros (Z) of the system
+temp=polfact(Ns);
+Z=roots(Ns); //locations of zeros
+P=roots(Ds); //locations of poles
+K=temp(1); //first entry is always gain
+disp( K,"Gain", P, "Poles",Z,"Zeros",)
+//------------------------------------------------------------------
diff --git a/3432/CH7/EX7.8/Ex7_8.sce b/3432/CH7/EX7.8/Ex7_8.sce new file mode 100644 index 000000000..32d383597 --- /dev/null +++ b/3432/CH7/EX7.8/Ex7_8.sce @@ -0,0 +1,21 @@ +//Example 7.8 +//Time scaling an oscillator. + +xdel(winsid())//close all graphics Windows +clear; +clc; +//------------------------------------------------------------------ +// State space model of an oscillator +wn=15000 // rad/sec +F=[0 1;wn^2 0]; +G=[0;10^6]; +disp(G,"G",F,"F","Given system"); + +//------------------------------------------------------------------ +// State space model of the time-scaled system for +// a millisecond scale w0=1e3; +w0=1e3; //rad/sec +F1=F/w0; +G1=G/w0; +disp(G1,"G1",F1,"F1","Time scaled system in mm"); +//------------------------------------------------------------------ diff --git a/3432/CH7/EX7.9/Ex7_9.sce b/3432/CH7/EX7.9/Ex7_9.sce new file mode 100644 index 000000000..28a048851 --- /dev/null +++ b/3432/CH7/EX7.9/Ex7_9.sce @@ -0,0 +1,40 @@ +//Example 7.9
+//State Equations in Modal Canonical Form.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function
+s=poly(0,'s');
+g1=1/s^2;
+g2=-1/(s^2+2*s+4);
+Gs=g1+g2;
+//------------------------------------------------------------------
+// State space representation in modal canonical form
+sys1=tf2ss(g1);
+sys2=tf2ss(g2);
+[F1,G1,T1]=canon(sys1.A, sys1.B)
+H1=sys1.C*T1;
+
+[F2,G2,T2]=canon(sys2.A, sys2.B)
+H2=sys2.C*T2;
+
+F=[F1 zeros(2,2);zeros(2,2) F2];
+G=[G1;G2];
+H=[H1,H2];
+J=0;
+disp(J,"J",H,"H",G,"G",F,"F","System in modal canonical form")
+//------------------------------------------------------------------
+ //As Y=G*U; consatnts k1 and k2 are taken out from G1 and G2 will be
+ //multiplied to H1 and H2
+
+// So alternately, it can be reprsented as
+k1=-1;k2=-2;
+F=[F1 zeros(2,2);zeros(2,2) F2];
+G=[G1/k1;G2/k2];
+H=[H1*k1,H2*k2];
+J=0;
+disp(J,"J",H,"H",G,"G",F,"F","System in modal canonical form")
+//------------------------------------------------------------------
+
diff --git a/3432/CH8/EX8.1/Ex8_1.sce b/3432/CH8/EX8.1/Ex8_1.sce new file mode 100644 index 000000000..015f64896 --- /dev/null +++ b/3432/CH8/EX8.1/Ex8_1.sce @@ -0,0 +1,56 @@ +///Example 8.1 +// Digital Controller using tustin approximation. + +xdel(winsid())//close all graphics Windows +clear; +clc; +//------------------------------------------------------------------ +//Cntroller +s=poly(0,'s'); +numD=s/2+1; +denD=s/10+1; +D=10*numD/denD; +Ds=syslin('c',D); +//sampling freq. = 25 times bandwidth +Wbw=10; +Ws=25*Wbw; +fs=Ws/2/%pi; +T=1/fs; //sampling time +a=1;b=-1; +c=1;d=1; +//Digital controller +z=poly(0,'z'); +Dz=horner(Ds,2/T*(a*z+b)/(c*z+d)); +disp(Dz,'Digital Controller : ') + +//------------------------------------------------------------------ +//step response and control efforts. +figure(0); +importXcosDiagram(".\Ex8_1_model.xcos") + //The diagram data structure +xcos_simulate(scs_m,4); +scs_m.props.context +plot(yt.time,yt.values(:,1),'r--') +plot(yt.time,yt.values(:,2),2) + +xlabel('Time (sec.)'); +ylabel('Position, y'); +title(["Comparison between digital and continuous controller step... + response";"with a sample rate 25 times bandwidth";"(a) Position "],... + 'fontsize',3); +exec .\fig_settings.sci; // custom script for setting figure properties + +//control effort + +figure(1); +plot(ut.time,ut.values(:,1),'r--') +plot2d2(ut.time,ut.values(:,2),2) + +xlabel('Time (sec.)'); +ylabel('Control, u'); +title(["Comparison between digital and continuous controller step... + response";"with a sample rate 25 times bandwidth";"(b) Control "],... + 'fontsize',3); +exec .\fig_settings.sci; // custom script for setting figure properties +//------------------------------------------------------------------ + diff --git a/3432/CH8/EX8.1/Ex8_1_f0.pdf b/3432/CH8/EX8.1/Ex8_1_f0.pdf Binary files differnew file mode 100644 index 000000000..18b813926 --- /dev/null +++ b/3432/CH8/EX8.1/Ex8_1_f0.pdf diff --git a/3432/CH8/EX8.1/Ex8_1_f1.pdf b/3432/CH8/EX8.1/Ex8_1_f1.pdf 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\ No newline at end of file diff --git a/3432/CH8/EX8.2/Ex8_2.sce b/3432/CH8/EX8.2/Ex8_2.sce new file mode 100644 index 000000000..d5b21520e --- /dev/null +++ b/3432/CH8/EX8.2/Ex8_2.sce @@ -0,0 +1,65 @@ +//Example 8.2 +// Design of a Space Station Attitude Digital Controller using +// Discrete Equivalents + +xdel(winsid())//close all graphics Windows +clear; +clc; +//------------------------------------------------------------------ +// State space representation of continuous time system +s=poly(0,'s'); +num=1; +den=(s^2); +Gs=syslin('c',num/den); +Ds=0.81*(s+0.2)/(s+2); +Ds=syslin('c',Ds); +sysc=Gs*Ds; + +//Root locus +evans(sysc) +zoom_rect([-2 -0.4 0.5 0.4]) +f=gca(); +f.x_location = "origin" +f.y_location = "origin" +h=legend(''); +h.visible = "off" +exec .\fig_settings.sci; //custom script for setting figure properties +title('s-plane locus with respect to K','fontsize',3) +//------------------------------------------------------------------ +//Contonuous time response of the system +figure, +tc=0:0.1:30; +syscl=sysc/(1+sysc) +yc=csim("step",tc,syscl); +plot(tc,yc,'b') +//------------------------------------------------------------------ +// Discretization of the system at +z=poly(0,'z') +// sampling time Ts=1 sec +Ts=1; +Dz1=horner(Ds,2/Ts*(z-1)/(z+1)) +disp(Dz1,"Dz1=","Discrete-time controller with Ts=1 sec.") + +// sampling time Ts=0.5 sec +Ts2=0.5; +Dz2=horner(Ds,2/Ts2*(z-1)/(z+1)) +disp(Dz2,"Dz2=","Discrete-time controller with Ts=0.5 sec.") + +//discrete-time response of the system. + +importXcosDiagram(".\Ex8_2_model.xcos") + //The diagram data structure +xcos_simulate(scs_m,4); +//scs_m.props.context +plot(yt1.time,yt1.values,'m-.') //with Ts=1sec. +plot(yt2.time,yt2.values,'r--') //with Ts=0.5 sec. +//------------------------------------------------------------------------------ + +title('step responses of continous and digital implementations','fontsize',3) + +exec .\fig_settings.sci; // custom script for setting figure properties +xlabel('Time (sec)','fontsize',2) +ylabel('Plant output','fontsize',2) +legend("Continuous design","Discrete equivalent design, T=1 sec."... +,"Discrete equivalent design, T=0.5 sec.",4) +//------------------------------------------------------------------------------ diff --git a/3432/CH8/EX8.2/Ex8_2_f0.pdf b/3432/CH8/EX8.2/Ex8_2_f0.pdf Binary files differnew file mode 100644 index 000000000..58a1e2d85 --- /dev/null +++ b/3432/CH8/EX8.2/Ex8_2_f0.pdf diff --git a/3432/CH8/EX8.2/Ex8_2_f1.pdf b/3432/CH8/EX8.2/Ex8_2_f1.pdf Binary files differnew file mode 100644 index 000000000..614471a7f --- /dev/null +++ b/3432/CH8/EX8.2/Ex8_2_f1.pdf diff --git a/3432/CH8/EX8.2/Ex8_2_model.xcos b/3432/CH8/EX8.2/Ex8_2_model.xcos new file mode 100644 index 000000000..ec561ed0c --- /dev/null +++ b/3432/CH8/EX8.2/Ex8_2_model.xcos @@ -0,0 +1 @@ +<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1" finalIntegrationTime="30.0" title="Ex8_2_model"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331 1318--><mxGraphModel 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\ No newline at end of file diff --git a/3432/CH9/EX9.11/Ex9_11.sce b/3432/CH9/EX9.11/Ex9_11.sce new file mode 100644 index 000000000..cbb897559 --- /dev/null +++ b/3432/CH9/EX9.11/Ex9_11.sce @@ -0,0 +1,60 @@ +//Example 9.11
+//Describing Function for a relay with hysteresis nonlinearity.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//Response of the saturation noninearity to sinusoidal input
+figure;
+importXcosDiagram(".\Ex9_11_model.xcos")
+xcos_simulate(scs_m,4);
+scs_m.props.context
+plot(yt.time,yt.values(:,1),'r--')
+plot(yt.time,yt.values(:,2),'b')
+
+xlabel('Time (sec.)');
+ylabel('Amplitude');
+title("Relay with hysteresis nonlinearity output to sinusoidal...
+ input",'fontsize',3);
+exec .\fig_settings.sci; //custom script for setting figure properties
+zoom_rect([0 -1.2 5 1.2])
+//------------------------------------------------------------------
+////Describing Functin for relay with hysteresis nonlinearity.
+h=0.1;
+N=1;
+i=1;
+
+for a=0.1:0.025:1
+ if a<h then
+ Keq(i,1)=0;
+ ro(i,1)=0;
+ theta(i,1)=0
+ else
+ Keq(i,1)=4*N/(%pi*a)*(sqrt(1-(h/a)^2)-%i*h/a)
+ [r th]=polar(Keq(i,1));
+ ro(i,1)=r; //magnitude
+ theta(i,1)=clean(th); //angle in radians
+ end
+ i=i+1;
+end
+
+a=0.1:0.025:1
+a=a';
+figure,
+
+subplot(2,1,1), plot(a,ro)
+xlabel('$a$');
+ylabel(['Magnitude', '$|K_{eq}|$']);
+
+xset('font size',3);
+exec .\fig_settings.sci; //custom script for setting figure properties
+title("Describing Functin for relay with hysteresis nonlinearity...
+ with h=0.1 and N=1",'fontsize',3);
+
+subplot(2,1,2), plot(a,theta*180/%pi)
+xlabel('$a$');
+ylabel(['Phase', '$ \angle K_{eq}$','deg.']);
+xset('font size',3);
+exec .\fig_settings.sci; //custom script for setting figure properties
+//------------------------------------------------------------------
diff --git a/3432/CH9/EX9.11/Ex9_11_f0.pdf b/3432/CH9/EX9.11/Ex9_11_f0.pdf Binary files differnew file mode 100644 index 000000000..e1df85c5c --- /dev/null +++ b/3432/CH9/EX9.11/Ex9_11_f0.pdf diff --git a/3432/CH9/EX9.11/Ex9_11_f1.pdf b/3432/CH9/EX9.11/Ex9_11_f1.pdf Binary files differnew file mode 100644 index 000000000..ab8ab58c7 --- /dev/null +++ b/3432/CH9/EX9.11/Ex9_11_f1.pdf diff --git a/3432/CH9/EX9.11/Ex9_11_model.xcos b/3432/CH9/EX9.11/Ex9_11_model.xcos new file mode 100644 index 000000000..3fca2a069 --- /dev/null +++ b/3432/CH9/EX9.11/Ex9_11_model.xcos @@ -0,0 +1 @@ +<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1" finalIntegrationTime="5.0" title="Ex9_11_model"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331 1318--><mxGraphModel as="model"><root><mxCell id="-2dd55334:14dcbdd0183:-7fd2"/><mxCell id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/><BasicBlock blockType="h" id="-2dd55334:14dcbdd0183:-7e6e" interfaceFunctionName="CLOCK_c" 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\ No newline at end of file diff --git a/3432/CH9/EX9.12/Ex9_12.sce b/3432/CH9/EX9.12/Ex9_12.sce new file mode 100644 index 000000000..2457c730d --- /dev/null +++ b/3432/CH9/EX9.12/Ex9_12.sce @@ -0,0 +1,75 @@ +//Example 9.12
+//Conditionally stable system.
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function and its root locus
+
+s=poly(0,'s');
+num=0.1;
+den=(s^2+0.2*s+1)*(s);
+Gs=syslin('c',num/den)
+
+//Nyquist plot of the system
+nyquist(Gs,0.035,10)
+title("Nyquist plot and describing function to determine limit...
+ cycle",'fontsize',3);
+
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+h=legend('');
+h.visible = "off"
+xset("color",2);
+
+// Nyquist Plot of Describing Function for saturation nonlinearity.
+omegat=0.05:0.05:%pi;
+a=sin(omegat);
+N=0.1;
+k=1;
+
+Keq=2/%pi*(k*asin(N ./a /k)+N ./a .* sqrt(1-(N/k ./a) .^2));
+DF_nyq=-1 ./Keq;
+
+plot(DF_nyq,zeros(1,length(DF_nyq)),'m-.')
+exec .\fig_settings.sci; //custom script for setting figure properties
+zoom_rect([-0.8 -0.5 0.2 0.5])
+
+//limit cycle points
+plot(-0.5,0,'bo');
+
+xset('font size',3)
+xstring(-0.78,0.08,"limit cycle point");
+xarrows([-0.6;-0.52],[0.1;0.02],-1)
+xstring(-0.62,-0.22,"$-\frac{1}{K_{eq}$");
+xarrows([-0.55;-0.55],[-0.1;0],-1)
+//------------------------------------------------------------------
+//Describing Functin for saturation nonlinearity.
+Keq=[]
+i=1;
+
+for a=0:0.2:10
+ if k*a/N > 1 then
+ Keq(i,1)=2/%pi*(k*asin(N/a/k)+N/a*sqrt(1-(N/k/a)^2))
+ else
+ Keq(i,1)=k
+ end
+ i=i+1;
+end
+
+a=0:0.2:10;
+a=a';
+
+figure,
+plot(a,Keq)
+xlabel('$a$');
+ylabel('$K_{eq}$');
+
+xset('font size',3);
+title("Describing Function for a saturation nonlinearity...
+ with N=0.1 and k=1",'fontsize',3);
+exec .\fig_settings.sci; //custom script for setting figure properties
+zoom_rect([0 0 10 1.1])
+//------------------------------------------------------------------
+
diff --git a/3432/CH9/EX9.12/Ex9_12_f0.pdf b/3432/CH9/EX9.12/Ex9_12_f0.pdf Binary files differnew file mode 100644 index 000000000..dfc320ed0 --- /dev/null +++ b/3432/CH9/EX9.12/Ex9_12_f0.pdf diff --git a/3432/CH9/EX9.12/Ex9_12_f1.pdf b/3432/CH9/EX9.12/Ex9_12_f1.pdf Binary files differnew file mode 100644 index 000000000..465e69327 --- /dev/null +++ b/3432/CH9/EX9.12/Ex9_12_f1.pdf diff --git a/3432/CH9/EX9.13/Ex9_13.sce b/3432/CH9/EX9.13/Ex9_13.sce new file mode 100644 index 000000000..8857fc7be --- /dev/null +++ b/3432/CH9/EX9.13/Ex9_13.sce @@ -0,0 +1,54 @@ +//Example 9.13
+//Determination of stability with a hysteresis nonlinearity.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System Model
+s=poly(0,'s');
+num=1;
+den=(s^2+s);
+Gs=syslin('c',num/den);
+//------------------------------------------------------------------
+//Nyquist Plot of the system
+nyquist(Gs,0.25,3)
+
+// Nyquist Plot of Describing Function for hysteresis nonlinearity
+N=1;
+h=0.1;
+i=1;
+
+for omegat=0:0.05:%pi-0.1;
+ a=sin(omegat);
+ DF_nyq(i,1)=-%pi/4/N*(sqrt(a^2-h^2) + h * %i)
+ i=i+1;
+end
+
+plot(real(DF_nyq),imag(DF_nyq),'m-.')
+exec .\fig_settings.sci; // custom script for setting figure properties
+zoom_rect([-0.3 -0.3 0 0.3])
+title('Nyquist plot of system and describing function to...
+ determine limit cycle','fontsize',3)
+
+//limit cycle points
+plot(-0.1714,-0.0785,'ro');
+xstring(-0.25,0,"limit cycle point");
+xarrows([-0.2;-0.172],[0;-0.077],-1);
+
+//------------------------------------------------------------------
+//Response of the system
+K=2;
+r=1
+figure(1);
+importXcosDiagram(".\Ex9_13_model.xcos")
+xcos_simulate(scs_m,4);
+scs_m.props.context
+plot(yt.time,yt.values)
+
+xlabel('Time (sec.)');
+ylabel('Output, y');
+title("Step response displaying limit cycle oscillations",'fontsize',3);
+exec .\fig_settings.sci; //custom script for setting figure properties
+//------------------------------------------------------------------
+
diff --git a/3432/CH9/EX9.13/Ex9_13_f0.pdf b/3432/CH9/EX9.13/Ex9_13_f0.pdf Binary files differnew file mode 100644 index 000000000..ee72b27bd --- /dev/null +++ b/3432/CH9/EX9.13/Ex9_13_f0.pdf diff --git a/3432/CH9/EX9.13/Ex9_13_f1.pdf b/3432/CH9/EX9.13/Ex9_13_f1.pdf Binary files differnew file mode 100644 index 000000000..8fe98147c --- /dev/null +++ b/3432/CH9/EX9.13/Ex9_13_f1.pdf diff --git a/3432/CH9/EX9.13/Ex9_13_model.xcos b/3432/CH9/EX9.13/Ex9_13_model.xcos new file mode 100644 index 000000000..a6cfe91a0 --- /dev/null +++ b/3432/CH9/EX9.13/Ex9_13_model.xcos @@ -0,0 +1 @@ +<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1" finalIntegrationTime="50.0" title="Ex9_13_model"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331 1318--><mxGraphModel as="model"><root><mxCell id="-2dd55334:14dcbdd0183:-7fd2"/><mxCell id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/><BasicBlock dependsOnT="1" id="-2dd55334:14dcbdd0183:-7f98" interfaceFunctionName="CLR" ordering="1" 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\ No newline at end of file diff --git a/3432/CH9/EX9.5/Ex9_5.sce b/3432/CH9/EX9.5/Ex9_5.sce new file mode 100644 index 000000000..327b8ced4 --- /dev/null +++ b/3432/CH9/EX9.5/Ex9_5.sce @@ -0,0 +1,50 @@ +//Example 9.5
+//Changing Overshoot and Saturation nonlinearity.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function and its root locus
+
+s=poly(0,'s');
+num=(s+1)
+den=(s^2);
+Gs=syslin('c',num/den)
+
+//Root locus
+evans(Gs,5)
+title(["Root locus of", "$(s+1)/(s^2)$","with saturation removed"],...
+'fontsize',3);
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+h=legend('');
+h.visible = "off"
+exec .\fig_settings.sci; //custom script for setting figure properties
+//------------------------------------------------------------------
+// Step response
+K=1;
+i=[2 4 6 8 10 12];
+figure(1);
+importXcosDiagram(".\Ex9_5_model.xcos")
+
+for r=i
+xcos_simulate(scs_m,4);
+scs_m.props.context
+plot(yt.time,yt.values)
+end
+
+xlabel('time');
+ylabel('y');
+title("Step response of the system for various input sizes",'fontsize',3);
+exec .\fig_settings.sci; //custom script for setting figure properties
+
+xset('font size',3);
+xstring(4,2.5,"$r=2$");
+xstring(6,5.5,"$4$");
+xstring(8,8.7,"$6$");
+xstring(10,12.2,"$8$");
+xstring(12,15.4,"$10$");
+xstring(14,18.4,"$12$");
+//------------------------------------------------------------------
diff --git a/3432/CH9/EX9.5/Ex9_5_f0.pdf b/3432/CH9/EX9.5/Ex9_5_f0.pdf Binary files differnew file mode 100644 index 000000000..c385950a3 --- /dev/null +++ b/3432/CH9/EX9.5/Ex9_5_f0.pdf diff --git a/3432/CH9/EX9.5/Ex9_5_f1.pdf b/3432/CH9/EX9.5/Ex9_5_f1.pdf Binary files differnew file mode 100644 index 000000000..4bf4aea0b --- /dev/null +++ b/3432/CH9/EX9.5/Ex9_5_f1.pdf diff --git a/3432/CH9/EX9.5/Ex9_5_model.xcos b/3432/CH9/EX9.5/Ex9_5_model.xcos new file mode 100644 index 000000000..ee8ba7b01 --- /dev/null +++ b/3432/CH9/EX9.5/Ex9_5_model.xcos @@ -0,0 +1 @@ +<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1" finalIntegrationTime="30.0" title="Ex9_5_model"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331 1318--><mxGraphModel as="model"><root><mxCell id="-2dd55334:14dcbdd0183:-7fd2"/><mxCell id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/><BasicBlock dependsOnT="1" id="-2dd55334:14dcbdd0183:-7f98" interfaceFunctionName="CLR" ordering="1" 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\ No newline at end of file diff --git a/3432/CH9/EX9.6/Ex9_6.sce b/3432/CH9/EX9.6/Ex9_6.sce new file mode 100644 index 000000000..4e30f74c5 --- /dev/null +++ b/3432/CH9/EX9.6/Ex9_6.sce @@ -0,0 +1,47 @@ +//Example 9.6
+//Stability of conditionally stable system using root locus.
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function and its root locus
+
+s=poly(0,'s');
+num=(s+1)^2
+den=(s^3);
+Gs=syslin('c',num/den)
+//Root locus
+evans(Gs,7)
+title(["Root locus for", "$(s+1)^2/(s^3)$","for system"],...
+'fontsize',3);
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+h=legend('');
+h.visible = "off"
+exec .\fig_settings.sci; //custom script for setting figure properties
+//------------------------------------------------------------------
+//Response of the system
+K=2;
+i=[1 2 3 3.475];
+figure(1);
+
+importXcosDiagram(".\Ex9_6_model.xcos")
+
+for r=i
+xcos_simulate(scs_m,4);
+scs_m.props.context
+plot(yt.time,yt.values)
+end
+
+xlabel('Time (sec.)');
+ylabel('Amplitude');
+title("Step response of the system",'fontsize',3);
+
+exec .\fig_settings.sci; //custom script for setting figure properties
+xset('font size',3);
+xstring(3,6.5,"$r=3.475$");
+xstring(2.5,5.2,"$3$");
+xstring(2,3,"$2$");
+xstring(1,1.4,"$1$");
+//------------------------------------------------------------------
diff --git a/3432/CH9/EX9.6/Ex9_6_f0.pdf b/3432/CH9/EX9.6/Ex9_6_f0.pdf Binary files differnew file mode 100644 index 000000000..3e16ef4a3 --- /dev/null +++ b/3432/CH9/EX9.6/Ex9_6_f0.pdf diff --git a/3432/CH9/EX9.6/Ex9_6_f1.pdf b/3432/CH9/EX9.6/Ex9_6_f1.pdf Binary files differnew file mode 100644 index 000000000..b2bd90d44 --- /dev/null +++ b/3432/CH9/EX9.6/Ex9_6_f1.pdf diff --git a/3432/CH9/EX9.6/Ex9_6_model.xcos b/3432/CH9/EX9.6/Ex9_6_model.xcos new file mode 100644 index 000000000..51108cd4a --- /dev/null +++ b/3432/CH9/EX9.6/Ex9_6_model.xcos @@ -0,0 +1 @@ +<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1" finalIntegrationTime="20.0" title="Ex9_6_model"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331 1318--><mxGraphModel as="model"><root><mxCell id="-2dd55334:14dcbdd0183:-7fd2"/><mxCell id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/><BasicBlock dependsOnT="1" id="-2dd55334:14dcbdd0183:-7f98" interfaceFunctionName="CLR" ordering="1" 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\ No newline at end of file diff --git a/3432/CH9/EX9.7/Ex9_7.sce b/3432/CH9/EX9.7/Ex9_7.sce new file mode 100644 index 000000000..cfe5028dc --- /dev/null +++ b/3432/CH9/EX9.7/Ex9_7.sce @@ -0,0 +1,84 @@ +//Example 9.7
+//Analysis and design of the system with limit cycle using the root locus.
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function and its root locus
+
+s=poly(0,'s');
+num=0.1;
+den=(s^2+0.2*s+1)*(s);
+Gs=syslin('c',num/den);
+
+//Root locus
+evans(Gs,40)
+title(["Root locus of", "$(0.1/s(s^2+0.2*s+1)$"],'fontsize',3);
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+h=legend('');
+h.visible = "off"
+exec .\fig_settings.sci; // custom script for setting figure properties
+//------------------------------------------------------------------
+//Response of the system
+figure;
+//Response of the system
+K=0.5;
+i=[1 4 8];
+importXcosDiagram(".\Ex9_7_model.xcos")
+
+for r=i
+xcos_simulate(scs_m,4);
+scs_m.props.context
+plot(yt.time,yt.values)
+end
+
+xlabel('Time (sec.)');
+ylabel('Amplitude');
+title("Step response of the system",'fontsize',3);
+exec .\fig_settings.sci; // custom script for setting figure properties
+zoom_rect([0 0 150 9])
+
+xset('font size',3);
+xstring(80,1.6,"$r=1$");
+xstring(80,4.6,"$r=4$");
+xstring(80,8.2,"$r=8$");
+//------------------------------------------------------------------
+//System with notch compensation
+D=123*(s^2+0.18*s+0.81)/(s+10)^2;
+
+//Root locus
+figure,
+evans(Gs*D,40)
+title(["Root locus including notch compensation"],'fontsize',3);
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+h=legend('');
+h.visible = "off"
+exec .\fig_settings.sci; //custom script for setting figure properties
+zoom_rect([-14 -2 2 2])
+//------------------------------------------------------------------
+//Response of the system witth notch filter
+figure;
+K=0.5;
+i=[2 4];
+importXcosDiagram(".\Ex9_7_model_notch.xcos")
+
+for r=i
+xcos_simulate(scs_m,4);
+scs_m.props.context
+plot(yt.time,yt.values)
+end
+
+xlabel('Time (sec.)');
+ylabel('Amplitude');
+title("Step response of the system with notch filter",'fontsize',3);
+exec .\fig_settings.sci; //custom script for setting figure properties
+xset('font size',3);
+xstring(30,2.2,"$r=2$");
+xstring(34,3.75,"$r=4$");
+//------------------------------------------------------------------
+
+
diff --git a/3432/CH9/EX9.7/Ex9_7_f1.pdf b/3432/CH9/EX9.7/Ex9_7_f1.pdf Binary files differnew file mode 100644 index 000000000..c797e3271 --- /dev/null +++ b/3432/CH9/EX9.7/Ex9_7_f1.pdf diff --git a/3432/CH9/EX9.7/Ex9_7_f3.pdf b/3432/CH9/EX9.7/Ex9_7_f3.pdf Binary files differnew file mode 100644 index 000000000..28b108e20 --- /dev/null +++ b/3432/CH9/EX9.7/Ex9_7_f3.pdf diff --git a/3432/CH9/EX9.7/Ex9_7_model.xcos b/3432/CH9/EX9.7/Ex9_7_model.xcos new file mode 100644 index 000000000..475e6ce92 --- /dev/null +++ b/3432/CH9/EX9.7/Ex9_7_model.xcos @@ -0,0 +1 @@ +<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1" finalIntegrationTime="150.0" title="Ex9_7_model"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331 1318--><mxGraphModel as="model"><root><mxCell id="-2dd55334:14dcbdd0183:-7fd2"/><mxCell id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/><BasicBlock dependsOnT="1" id="-2dd55334:14dcbdd0183:-7f98" interfaceFunctionName="CLR" ordering="1" 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\ No newline at end of file diff --git a/3432/CH9/EX9.8/Ex9_8.sce b/3432/CH9/EX9.8/Ex9_8.sce new file mode 100644 index 000000000..159d2c456 --- /dev/null +++ b/3432/CH9/EX9.8/Ex9_8.sce @@ -0,0 +1,44 @@ +//Example 9.8
+//Antiwindup compensation for a PI controller.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System Model
+
+//Response of the system
+kp=2;
+ki=4;
+
+//Without antiwindup
+ka=0;
+importXcosDiagram(".\Ex9_8_model.xcos")
+xcos_simulate(scs_m,4);
+scs_m.props.context
+figure(0)
+plot(yt.time,yt.values,'m-.')
+figure(1)
+plot(ut.time,ut.values,'m-.')
+
+//With antiwindup
+ka=10;
+xcos_simulate(scs_m,4);
+scf(0)
+plot(yt.time,yt.values)
+exec .\fig_settings.sci; // custom script for setting figure properties
+xlabel('Time (sec.)');
+ylabel('Output');
+title("Integrator antiwindup (a) step response.",'fontsize',3);
+
+
+scf(1)
+plot(ut.time,ut.values);
+exec .\fig_settings.sci; // custom script for setting figure properties
+xlabel('Time (sec.)');
+ylabel('Control');
+title("Integrator antiwindup (b) Control effort.",'fontsize',3);
+zoom_rect([0 -1.2 10 1.2])
+
+//------------------------------------------------------------------
+
diff --git a/3432/CH9/EX9.8/Ex9_8_f0.pdf b/3432/CH9/EX9.8/Ex9_8_f0.pdf Binary files differnew file mode 100644 index 000000000..d60a27a89 --- /dev/null +++ b/3432/CH9/EX9.8/Ex9_8_f0.pdf diff --git a/3432/CH9/EX9.8/Ex9_8_f1.pdf b/3432/CH9/EX9.8/Ex9_8_f1.pdf Binary files differnew file mode 100644 index 000000000..0b10f8839 --- /dev/null +++ b/3432/CH9/EX9.8/Ex9_8_f1.pdf diff --git a/3432/CH9/EX9.8/Ex9_8_model.xcos b/3432/CH9/EX9.8/Ex9_8_model.xcos new file mode 100644 index 000000000..19ac5dd1e --- /dev/null +++ b/3432/CH9/EX9.8/Ex9_8_model.xcos @@ -0,0 +1 @@ +<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1" finalIntegrationTime="10.0" title="Ex9_8_model"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331 1318--><mxGraphModel as="model"><root><mxCell id="-2dd55334:14dcbdd0183:-7fd2"/><mxCell id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/><BasicBlock dependsOnT="1" id="-2dd55334:14dcbdd0183:-7f98" interfaceFunctionName="CLR" ordering="1" 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\ No newline at end of file diff --git a/3432/CH9/EX9.9/Ex9_9.sce b/3432/CH9/EX9.9/Ex9_9.sce new file mode 100644 index 000000000..977c213cc --- /dev/null +++ b/3432/CH9/EX9.9/Ex9_9.sce @@ -0,0 +1,49 @@ +//Example 9.9
+//Describing Function for a saturation nonlinearity.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//Response of the saturation nonlinearity to sinusoidal input
+figure;
+importXcosDiagram(".\Ex9_9_model.xcos")
+xcos_simulate(scs_m,4);
+scs_m.props.context
+plot(yt.time,yt.values(:,1),'r--')
+plot(yt.time,yt.values(:,2),'b')
+
+xlabel('Time (sec.)');
+ylabel('Amplitude');
+title("Saturation nonlinearity output to sinusoidal input",...
+'fontsize',3);
+exec .\fig_settings.sci; //custom script for setting figure properties
+//------------------------------------------------------------------
+//Describing Functin for saturation nonlinearity.
+k=1;
+N=1;
+i=1;
+Keq=[];
+
+for a=0:0.2:10
+ if k*a/N > 1 then
+ Keq(i,1)=2/%pi*(k*asin(N/a/k)+N/a*sqrt(1-(N/k/a)^2))
+ else
+ Keq(i,1)=k
+ end
+ i=i+1;
+end
+
+a=0:0.2:10;
+a=a';
+figure,
+plot(a,Keq)
+xlabel('$a$');
+ylabel('$K_{eq}}$');
+
+xset('font size',3);
+title("Describing Function for a saturation nonlinearity...
+ with k=N=1",'fontsize',3);
+exec .\fig_settings.sci; //custom script for setting figure properties
+zoom_rect([0 0 10 1.1])
+//------------------------------------------------------------------
diff --git a/3432/CH9/EX9.9/Ex9_9_f0.pdf b/3432/CH9/EX9.9/Ex9_9_f0.pdf Binary files differnew file mode 100644 index 000000000..1e81c3f5c --- /dev/null +++ b/3432/CH9/EX9.9/Ex9_9_f0.pdf diff --git a/3432/CH9/EX9.9/Ex9_9_f1.pdf b/3432/CH9/EX9.9/Ex9_9_f1.pdf Binary files differnew file mode 100644 index 000000000..2b7500dea --- /dev/null +++ b/3432/CH9/EX9.9/Ex9_9_f1.pdf diff --git a/3432/CH9/EX9.9/Ex9_9_model.xcos b/3432/CH9/EX9.9/Ex9_9_model.xcos new file mode 100644 index 000000000..a89bfe757 --- /dev/null +++ b/3432/CH9/EX9.9/Ex9_9_model.xcos @@ -0,0 +1 @@ +<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1" finalIntegrationTime="5.0" title="Ex9_9_model"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331 1318--><mxGraphModel as="model"><root><mxCell id="-2dd55334:14dcbdd0183:-7fd2"/><mxCell id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/><BasicBlock blockType="h" id="-2dd55334:14dcbdd0183:-7e6e" interfaceFunctionName="CLOCK_c" ordering="1" 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\ No newline at end of file diff --git a/3432/DEPENDENCIES/acker_dk.sci b/3432/DEPENDENCIES/acker_dk.sci new file mode 100644 index 000000000..3391d2454 --- /dev/null +++ b/3432/DEPENDENCIES/acker_dk.sci @@ -0,0 +1,73 @@ +//------------------------------------------------------------------ +//------------------------------------------------------------------ +//A function written by Deepti Khimani. +//Usage:- +//[K, lambda]=acker_dk(a, b, pl) +//K=acker_dk(a, b, pl) +//a:- System matrix. +//b:- input matrix. +//p:- Desired poles. +//K:-State feedback gain for the control law u=-Kx. +//lambda:- Eigen values of (a-b*k) +//------------------------------------------------------------------ +//------------------------------------------------------------------ + +function [K, lambda]=acker_dk(a, b, pl) + [lhs,rhs]=argn(0) + + if rhs == 0 then + disp(["K=acker_dk(a, b, pl)";"[K, lambda]=acker_dk(a, b, pl)"]); + disp(["a:- System matrix";"b:- input matrix";"p:- Desired poles"]); + disp(["K:-State feedback gain for the control law u=-Kx";... + "lambda:- Eigen values of (a-b*k)"]); + return; + end +[ra ca]=size(a); +[rb cb]=size(b); +l=length(pl); + +CO=cont_mat(a,b); + +if ra~=l then + error(["Dimension error:";"number of desired poles must equal... + to order of the system"]); +elseif ra~=ca then + error(["Dimension error:";"system matrix should be... + a sqaure matrix"]); +elseif rb~=ra then + error (["Dimension error:","Input matrix should have... + as many rows as a system matrix."]); +elseif rank(CO)<ra then + error("system is not controllable"); +end +//------------------------------------------------------------------ +//controllable canonical form +[Ac,Bc,T,ind]=canon(a,b); + +//CO=zeros(ra,cb); +for i=1:ra + CO(:,ra+1-i)=Ac^(i-1)*Bc; +end +//------------------------------------------------------------------ +chr_eq=poly(pl,'s'); +des_chr_coeff=coeff(chr_eq); + +des_chr_coeff=des_chr_coeff(1:ra); +alpha_c=Ac^ra; + +for k=1:ra + alpha_c=alpha_c + des_chr_coeff(k)*Ac^(k-1) +end +//------------------------------------------------------------------ +//State feedback gain +temp=zeros(1,ra); +temp(1)=1; +K=temp*inv(CO)*alpha_c; +K=K/T; +lambda=spec(a-b*K); +endfunction +//------------------------------------------------------------------ + + + + diff --git a/3432/DEPENDENCIES/fig_settings.sci b/3432/DEPENDENCIES/fig_settings.sci new file mode 100644 index 000000000..5d5e7d435 --- /dev/null +++ b/3432/DEPENDENCIES/fig_settings.sci @@ -0,0 +1,9 @@ +//------------------------------------------------------------------
+//figure handel settings
+f=get("current_figure"); //Current figure handle
+f.background=8; //make the figure window background white
+l=f.children(1);
+l.background=8 ;//make the text background white
+id=color('grey');
+xgrid(id);
+//------------------------------------------------------------------
diff --git a/3432/DEPENDENCIES/zpk_dk.sci b/3432/DEPENDENCIES/zpk_dk.sci new file mode 100644 index 000000000..95b4e6c13 --- /dev/null +++ b/3432/DEPENDENCIES/zpk_dk.sci @@ -0,0 +1,43 @@ +//------------------------------------------------------------------ +//------------------------------------------------------------------ +//A function written by Deepti Khimani. +//Usage:- +//p=zpk_dk(sl) +//[p, z]=zpk_dk(sl) +//[p, z, k]=zpk_dk(sl) +//p:- Poles of the system +//z:- zeros of the system +//k:- DC gain of the system +//------------------------------------------------------------------ +//------------------------------------------------------------------ + +function[pl,zr,k]=zpk_dk(sysmodel) + [lhs,rhs]=argn(0) + + if rhs == 0 then + disp(["p=zpk_dk(sl)";"[p, z]=zpk_dk(sl)";"[p, z, k]=zpk_dk(sl)"]); + disp(["p:- Poles of the system";"z:- zeros of the system"]); + disp("k:- DC gain of the system"); + return; + end + + if typeof(sysmodel)=="rational" then + sys=tf2ss(sysmodel); + pl=spec(sys.A); + zr=trzeros(sys); + temp1=poly(zr,'s','roots')/poly(pl,'s','roots'); + temp2=sysmodel/temp1; + temp3=tf2ss(temp2); + k=temp3.D; + elseif typeof(sysmodel)=="state-space" then + pl=spec(sysmodel.A); + zr=trzeros(sysmodel); + g=ss2tf(sysmodel); + temp1=poly(zr,'s','roots')/poly(pl,'s','roots'); + temp2=g/temp1; + temp3=tf2ss(temp2); + k=temp3.D + else + error("Wrong type of input argument.") + end +endfunction |