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| author | prashantsinalkar | 2017-10-10 12:27:19 +0530 |
|---|---|---|
| committer | prashantsinalkar | 2017-10-10 12:27:19 +0530 |
| commit | 7f60ea012dd2524dae921a2a35adbf7ef21f2bb6 (patch) | |
| tree | dbb9e3ddb5fc829e7c5c7e6be99b2c4ba356132c /257 | |
| parent | b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (diff) | |
| download | Scilab-TBC-Uploads-7f60ea012dd2524dae921a2a35adbf7ef21f2bb6.tar.gz Scilab-TBC-Uploads-7f60ea012dd2524dae921a2a35adbf7ef21f2bb6.tar.bz2 Scilab-TBC-Uploads-7f60ea012dd2524dae921a2a35adbf7ef21f2bb6.zip | |
initial commit / add all books
Diffstat (limited to '257')
265 files changed, 3850 insertions, 0 deletions
diff --git a/257/CH10/EX10.1/example_10_1.sce b/257/CH10/EX10.1/example_10_1.sce new file mode 100644 index 000000000..6f69e6e58 --- /dev/null +++ b/257/CH10/EX10.1/example_10_1.sce @@ -0,0 +1,32 @@ +s=%s
+Mr=2 //given
+omegaR=3 //given
+zeta=roots(16*s^4 - 16*s^2 + 1) //Mr=1/(2*zeta*sqrt(1-zeta^2))
+zeta(3,1)=0.933
+zeta(2,1)=0.0669
+disp(zeta)
+
+omegaN=omegaR/(sqrt(1-2*(0.2588)^2))
+disp(omegaN,"omegaN = ")
+
+TF= (omegaN^2)/poly([omegaN^2 2*0.2588*omegaN 1],'s',"coeff")
+disp(TF," transfer function = ")
+
+omegaD=omegaN*sqrt(1-(0.2588))
+Tr=(%pi-(atan(sqrt(1-(0.2588)^2)/0.2588)))/(omegaD)
+disp(Tr,"Tr = ")
+
+Tp=%pi/omegaD;
+disp(Tp,"Tp= ")
+
+Ts=4/(0.2588*omegaN)
+disp(Ts,"Ts = ")
+
+Tosc=2*%pi/omegaD
+disp(Tosc,"Tosc = ")
+
+N=Ts/Tosc;
+disp(N,"number of oscillations = ")
+
+Mp=%e^(-0.2588*%pi/(sqrt(1-(0.2588)^2)))
+disp(Mp,"Mp = ")
\ No newline at end of file diff --git a/257/CH10/EX10.2/example_10_2.sce b/257/CH10/EX10.2/example_10_2.sce new file mode 100644 index 000000000..ee36e843b --- /dev/null +++ b/257/CH10/EX10.2/example_10_2.sce @@ -0,0 +1,14 @@ +Mp=0.12 //given from table
+zeta=0.5594
+Tp=0.2
+
+omegaN=%pi/(Tp*sqrt(1-zeta^2));
+disp(omegaN,"omegaN = ")
+
+Mr=1/(2*zeta*sqrt(1-zeta^2))
+disp(Mr,"Mr = ")
+
+
+omegaR=omegaN*(sqrt(1-2*(zeta)^2))
+disp(omegaR," omegaR= ")
+
diff --git a/257/CH10/EX10.3/example_10_3.sce b/257/CH10/EX10.3/example_10_3.sce new file mode 100644 index 000000000..a5a181fec --- /dev/null +++ b/257/CH10/EX10.3/example_10_3.sce @@ -0,0 +1,10 @@ +
+s=%s;
+G=10/(s*(s+10))
+T=G/(1+G)
+disp(T,"T = ")
+
+//compare A*sin(w*t) and 10*sin(8*t)
+A=10;
+w=8;
+disp("c(t) = A*10/(sqrt((10-w^2)^2 + 100*w))*(sin(8*t-atan(10*w/(10-w^2))))")
diff --git a/257/CH10/EX10.4/example_10_4.sce b/257/CH10/EX10.4/example_10_4.sce new file mode 100644 index 000000000..1864171a2 --- /dev/null +++ b/257/CH10/EX10.4/example_10_4.sce @@ -0,0 +1,12 @@ +Mp=16.2
+Tp=%pi/(5*sqrt(3))
+zeta=0.5
+
+omegaD=%pi/Tp
+omegaN=omegaD/(sqrt(1-zeta^2))
+disp(omegaD,"omegaD = ")
+disp(omegaN,"omegaN = ")
+
+disp(omegaN*(sqrt(1-2*zeta^2)), " omegaR = ")
+disp(1/(2*zeta*sqrt(1-zeta^2))," Mr = ")
+
diff --git a/257/CH10/EX10.5/example_10_5.sce b/257/CH10/EX10.5/example_10_5.sce new file mode 100644 index 000000000..e2f1bae77 --- /dev/null +++ b/257/CH10/EX10.5/example_10_5.sce @@ -0,0 +1,14 @@ +s=poly(0,'s');
+omegaR=7
+
+zeta=abs(roots(poly([0.043766 0 -1 0 1],'s',"coeff")))
+disp(zeta)
+disp("but for zeta>0.7 , Mr does not exist, so neglect higher value")
+zeta=0.2141
+disp(zeta)
+
+omegaN=omegaR/(sqrt(1-2*(zeta)^2))
+disp(omegaN,"omegaN = ")
+
+disp(omegaN*sqrt(1-2*zeta^2 + sqrt(2-4*zeta^2+4*zeta^4))," B.W. = ")
+
diff --git a/257/CH10/EX10.6/example_10_6.sce b/257/CH10/EX10.6/example_10_6.sce new file mode 100644 index 000000000..2e164637f --- /dev/null +++ b/257/CH10/EX10.6/example_10_6.sce @@ -0,0 +1,14 @@ +Mr=1.1
+omegaR=11.2
+
+zeta=abs(roots(poly([0.2066 0 -1 0 1],'s',"coeff")))
+disp(zeta)
+disp("but for zeta>0.7 , Mr does not exist, so neglect higher value")
+zeta=0.54
+disp(zeta)
+
+omegaN=omegaR/(sqrt(1-2*(zeta)^2))
+disp(omegaN,"omegaN = ")
+
+TF=omegaN^2/(poly([0 2*zeta*omegaN 1],'s',"coeff"))
+disp(TF," TF = ")
\ No newline at end of file diff --git a/257/CH10/EX10.7/example_10_7.sce b/257/CH10/EX10.7/example_10_7.sce new file mode 100644 index 000000000..5f03883dc --- /dev/null +++ b/257/CH10/EX10.7/example_10_7.sce @@ -0,0 +1,15 @@ +s=%s
+
+//G=k/(s*(s*tau+1)) and T=G/(1+G)
+omegaN=12
+
+zeta=roots(poly([0.22225 0 -1 0 1],'s',"coeff"))
+disp("but for zeta>0.7 , Mr does not exist, so neglect higher value")
+zeta=0.578
+disp(zeta)
+
+tau=1/(2*sqrt(144)*zeta)
+disp(tau,"tau = ")
+k=144*tau;disp(k,"k = ")
+
+disp(omegaN*sqrt(1-2*zeta^2 + sqrt(2-4*zeta^2+4*zeta^4))," B.W. = ")
\ No newline at end of file diff --git a/257/CH10/EX10.8/example_10_8.sce b/257/CH10/EX10.8/example_10_8.sce new file mode 100644 index 000000000..4e5c422e8 --- /dev/null +++ b/257/CH10/EX10.8/example_10_8.sce @@ -0,0 +1,11 @@ +s=%s;
+G=100/(s*(s+8))
+T=G/(1+G)
+disp(T,"T = ")
+
+//compare denominator with s^2+2*zeta*omegaN + omegaN^2
+omegaN=10
+zeta=0.4;
+disp(1/(2*zeta*sqrt((1-zeta^2)))," Mr = ")
+disp(omegaN*sqrt(1-2*zeta^2)," omegaN = ")
+
diff --git a/257/CH10/EX10.9/example_10_9.sce b/257/CH10/EX10.9/example_10_9.sce new file mode 100644 index 000000000..f99a25731 --- /dev/null +++ b/257/CH10/EX10.9/example_10_9.sce @@ -0,0 +1,18 @@ +s=%s
+//G=k/(s*(s+a)) and T=G/(1+G)
+Mr=1.04
+omegaR=11.55
+
+disp("for zeta>0.7 , Mr does not exist, so neglect higher value")
+zeta=0.6021
+disp(zeta)
+
+omegaN=omegaR/(sqrt(1-2*(zeta)^2))
+disp(omegaN,"omegaN = ")
+
+
+k=omegaN^2
+disp(k,"k=")
+disp(2*zeta*omegaN," a = ")
+disp(omegaN*sqrt(1-2*zeta^2 + sqrt(2-4*zeta^2+4*zeta^4))," B.W. = ")
+disp(4/(zeta*omegaN)," Ts = ")
\ No newline at end of file diff --git a/257/CH11/EX11.1/example_11_1.sce b/257/CH11/EX11.1/example_11_1.sce new file mode 100644 index 000000000..b5496e387 --- /dev/null +++ b/257/CH11/EX11.1/example_11_1.sce @@ -0,0 +1,7 @@ +s=poly(0,'s');
+F=syslin('c',[20/((1+0.1*s)*s)])
+fmin=0.1; //Min freq in Hz
+fmax=20; //Max freq in Hz
+scf(1);clf;
+bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
+show_margins(F) //display gain and phase margin and associated crossover frequencies
diff --git a/257/CH11/EX11.10/example_11_10.sce b/257/CH11/EX11.10/example_11_10.sce new file mode 100644 index 000000000..bb07bfd75 --- /dev/null +++ b/257/CH11/EX11.10/example_11_10.sce @@ -0,0 +1,19 @@ +//there is a pole at the origin and contribution of gain k
+
+k=10^(14/20) //20*log(k)=14
+
+disp("equation of starting line is y=-20*log(w)+14")
+wc1=10^(0)
+disp(wc1,"hence at wc1, 14=-20*log(wc1)+14. that is wc1 = ")
+y1=poly([1 1/wc1],'s','coeff')
+
+disp("equation of next line is y=-40*log(w)+14")
+wc2=10^(40/40) //-40*log(wc2)=-40
+disp(wc2,"wc2=")
+y2=poly([1 1/wc2],'s','coeff')
+
+wc3=50 //given
+y3=poly([1 1/wc3],'s','coeff')
+
+TF= k*(y2)/((y1)*(y3))
+disp(TF,"transfer function = ")
diff --git a/257/CH11/EX11.11/example_11_11.sce b/257/CH11/EX11.11/example_11_11.sce new file mode 100644 index 000000000..cb661deb9 --- /dev/null +++ b/257/CH11/EX11.11/example_11_11.sce @@ -0,0 +1,31 @@ +s=poly(0,'s');
+F=syslin('c',[1/((1+s)*s*(0.1*s+1))]) //without k
+
+fmin=0.1; //Min freq in Hz
+fmax=20; //Max freq in Hz
+
+scf(1);clf;
+bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
+
+show_margins(F) //display gain and phase margin and associated crossover frequencies
+
+// TO FIND VALUE OF K
+
+// for GM=30 dB, the point on the plot without k is 10dB away from 0dB line.
+k1=10^(-10/20) // 20*log(k1)=-10
+disp(k1,"k for GM=30 is ")
+F1=syslin('c',[(k1)/((1+s)*s*(0.1*s+1))])
+
+[PhaseMargin,freqPM]=p_margin(F1)
+disp(freqPM*2*3.14,"corresponding omegaGC")
+disp(PhaseMargin,"PM=")
+
+// for PM=30degrees, the point on the magnitude plot without k is 6dB away from 0dB line.
+k2=10^(6/20) // 20*log(k1)= 6 dB
+disp(k2,"for PM=30degrees k is ")
+F2=syslin('c',[(k2)/((1+s)*s*(0.1*s+1))])
+
+[PhaseMargin,freqPM]=p_margin(F2)
+disp(freqPM*2*3.14,"corresponding omegaGC")
+[GainMargin,freqGM]=g_margin(F)
+disp(GainMargin,"GM=")
\ No newline at end of file diff --git a/257/CH11/EX11.12/ex_11_12.sce b/257/CH11/EX11.12/ex_11_12.sce new file mode 100644 index 000000000..078c2ebdd --- /dev/null +++ b/257/CH11/EX11.12/ex_11_12.sce @@ -0,0 +1,19 @@ +s=poly(0,'s');
+F=syslin('c',[(1+0.5*s)/((1+2*s)*s*(1+0.05*s+0.125*s^2))])
+
+fmin=0.1; //Min freq in Hz
+fmax=20; //Max freq in Hz
+
+scf(1);clf;
+bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
+
+[GainMargin,freqGM]=g_margin(F) //Calculates gain margin [dB] and corresponding frequency [Hz]
+disp(GainMargin,"GM=")
+disp(freqGM*2*(%pi),"omegaPC=")
+
+[PhaseMargin,freqPM]=p_margin(F) //Calculates phase [deg] and corresponding freq [Hz] of phase margin
+disp(PhaseMargin,"PM=")
+disp(freqPM*2*(%pi),"omegaGC")
+
+show_margins(F) //display gain and phase margin and associated crossover frequencies
+
diff --git a/257/CH11/EX11.13/example_11_13.sce b/257/CH11/EX11.13/example_11_13.sce new file mode 100644 index 000000000..737a1e969 --- /dev/null +++ b/257/CH11/EX11.13/example_11_13.sce @@ -0,0 +1,20 @@ +s=poly(0,'s');
+F=syslin('c',[(1+0.2*s)*(1+0.025*s)/((1+0.001*s)*s^(3)*(0.005*s+1))])
+
+fmin=0.1; //Min freq in Hz
+fmax=20; //Max freq in Hz
+
+scf(1);clf;
+bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
+
+[GainMargin,freqGM]=g_margin(F) //Calculates gain margin [dB] and corresponding frequency [Hz]
+disp(freqGM*2*3.14,"omegaPC=")
+show_margins(F) //display gain and phase margin and associated crossover frequencies
+
+//for omegaPC=16.54 ; the plot needs to be shifted by 64dB
+k1=10^(64/20)
+
+//for omegaPC =400 ; the plot needs to be shifted by 100dB
+k2=10^(100/20)
+
+disp(k1,k2,"the 2 values k lies between are")
diff --git a/257/CH11/EX11.14/ex_11_14.sce b/257/CH11/EX11.14/ex_11_14.sce new file mode 100644 index 000000000..9c08dec20 --- /dev/null +++ b/257/CH11/EX11.14/ex_11_14.sce @@ -0,0 +1,25 @@ +s=poly(0,'s');
+F=syslin('c',[1/((1+s)*s*(s+0.5))])
+
+fmin=0.1; //Min freq in Hz
+fmax=20; //Max freq in Hz
+
+scf(1);clf;
+bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
+
+[GainMargin,freqGM]=g_margin(F) //Calculates gain margin [dB] and corresponding frequency [Hz]
+disp(GainMargin,"GM=")
+//disp(freqGM*2*3.14,"omegaPC=")
+
+[PhaseMargin,freqPM]=p_margin(F) //Calculates phase [deg] and corresponding freq [Hz] of phase margin
+disp(PhaseMargin,"PM=")
+//disp(freqPM*2*3.14,"omegaGC")
+
+show_margins(F) //display gain and phase margin and associated crossover frequencies
+
+
+if(GainMargin>0 & PhaseMargin>0 )
+ disp("stable system")
+else
+ disp("unstable system")
+end
diff --git a/257/CH11/EX11.15/example_11_15.sce b/257/CH11/EX11.15/example_11_15.sce new file mode 100644 index 000000000..6d9352b52 --- /dev/null +++ b/257/CH11/EX11.15/example_11_15.sce @@ -0,0 +1,21 @@ +disp("equation of first straight line is y=-40*log(w)+c1")
+c1=poly([40*log10(40) 0],'s','coeff') //at w=40 , 0=-40*log(40)+c1
+disp(c1,"where c1 is ")
+A1=-40*log10(10)+c1
+disp(A1,"A1=")
+
+
+disp("equation of second straight line is y=-20*log(w)+c2")
+c2=poly([20*log10(40) 0],'s','coeff') //at w=40 , 0=-20*log(40)+c2
+disp(c2,"where c2 is ")
+wc1=10^( (-20-20*log10(40))/(-20)) // -20=-20*log(wc1)+c2
+disp(wc1,"hence wc1 = ")
+y2=poly([1 1/wc1],'s','coeff')
+A2=-20*log10(1000)+c2
+disp(A2,"A2 = ")
+
+disp("equation of third line is y=-40*log(w)+c3")
+c3= A2+ 40*log10(1000)
+disp(c3,"where c3 = ")
+wc2= 10^((-40-92.0411)/(-40))
+disp(wc2," wc2 = ")
diff --git a/257/CH11/EX11.16/example_11_16.sce b/257/CH11/EX11.16/example_11_16.sce new file mode 100644 index 000000000..41a70a55a --- /dev/null +++ b/257/CH11/EX11.16/example_11_16.sce @@ -0,0 +1,13 @@ +//solving the block diagram.. we have GH=k*(s+2)/s^2
+s=poly(0,'s');
+F=syslin('c',[k*(s+2)/(s^2)])
+
+x=2*tan(50*%pi/180) //50 = 180 + atan((x/2)) - 180
+disp(x,"omegaGC = ")
+
+k=(x^2)/sqrt(4+x^2) // |k|*sqrt(4+x^2)/(x^2) = 1
+disp(k,"for PM=50 K is ")
+
+[GainMargin,freqGM]=g_margin(F) //Calculates gain margin [dB] and corresponding frequency [Hz]
+disp(GainMargin,"GM=")
+
diff --git a/257/CH11/EX11.17/example_11_17.sce b/257/CH11/EX11.17/example_11_17.sce new file mode 100644 index 000000000..2e9f6a3bb --- /dev/null +++ b/257/CH11/EX11.17/example_11_17.sce @@ -0,0 +1,23 @@ +s=poly(0,'s');
+F=syslin('c',[10*(s*0.5+1)/((1+0.25*s)*s*(0.2*s+1))])
+
+fmin=0.1; //Min freq in Hz
+fmax=20; //Max freq in Hz
+scf(1);clf;
+bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
+
+[GainMargin,freqGM]=g_margin(F) //Calculates gain margin [dB] and corresponding frequency [Hz]
+disp(GainMargin,"GM=")
+disp(freqGM*2*3.14,"omegaPC=")
+
+[PhaseMargin,freqPM]=p_margin(F) //Calculates phase [deg] and corresponding freq [Hz] of phase margin
+disp(PhaseMargin,"PM=")
+disp(freqPM*2*3.14,"omegaGC")
+
+show_margins(F) //display gain and phase margin and associated crossover frequencies
+
+if(GainMargin>0 & PhaseMargin>0 )
+ disp("stable system")
+else
+ disp("unstable system")
+end
diff --git a/257/CH11/EX11.18/example_11_18.sce b/257/CH11/EX11.18/example_11_18.sce new file mode 100644 index 000000000..e53d295b6 --- /dev/null +++ b/257/CH11/EX11.18/example_11_18.sce @@ -0,0 +1,23 @@ +s=poly(0,'s');
+F=syslin('c',[4/((1+s)^3)])
+
+fmin=0.1; //Min freq in Hz
+fmax=20; //Max freq in Hz
+scf(1);clf;
+bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
+
+[GainMargin,freqGM]=g_margin(F) //Calculates gain margin [dB] and corresponding frequency [Hz]
+disp(GainMargin,"GM=")
+disp(freqGM*2*3.14,"omegaPC=")
+
+[PhaseMargin,freqPM]=p_margin(F) //Calculates phase [deg] and corresponding freq [Hz] of phase margin
+disp(PhaseMargin,"PM=")
+disp(freqPM*2*3.14,"omegaGC")
+
+show_margins(F) //display gain and phase margin and associated crossover frequencies
+
+if(GainMargin>0 & PhaseMargin>0 )
+ disp("stable system")
+else
+ disp("unstable system")
+end
diff --git a/257/CH11/EX11.19/example_11_19.sce b/257/CH11/EX11.19/example_11_19.sce new file mode 100644 index 000000000..4f72c3976 --- /dev/null +++ b/257/CH11/EX11.19/example_11_19.sce @@ -0,0 +1,26 @@ +//there exists one zero at the origin
+s=%s
+c=-20*log10(2) //at w=2, y=20*log(w)+c becomes this
+k=10.^(c/20)
+
+wc1=10.^((20-c)/20) //20=20*log10(wc1)-c
+y1=poly([1 1/wc1],'s','coeff')
+
+wc2=50
+y2=poly([1 1/wc2],'s','coeff')
+
+wc3=300
+y3=poly([1 1/wc3],'s','coeff')
+
+c2=20+20*log10(50) //equation b/w 50 and 300 is y=-20*log(w)+c2. this is at w=50.
+y=-20*log10(wc3)+c2
+
+c1=y-20*log10(wc3) // for slope with 20dB
+
+wc4=10.^((30-c1)/(20)) // 30=20*log(wc4)+c1
+y4=poly([1 1/wc4],'s','coeff')
+
+y5=poly([0 1],'s','coeff') //zero at origin
+
+TF= (k*(y5)*(y3^2))/((y1)*(y2)*(y4))
+disp(TF, "transfer fuction = ")
diff --git a/257/CH11/EX11.2/example_11_2.sce b/257/CH11/EX11.2/example_11_2.sce new file mode 100644 index 000000000..9311e38cf --- /dev/null +++ b/257/CH11/EX11.2/example_11_2.sce @@ -0,0 +1,24 @@ +s=poly(0,'s');
+F=syslin('c',[80/((2+s)*s*(s+20))])
+
+fmin=0.1; //Min freq in Hz
+fmax=20; //Max freq in Hz
+
+scf(1);clf;
+bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
+
+[GainMargin,freqGM]=g_margin(F) //Calculates gain margin [dB] and corresponding frequency [Hz]
+disp(GainMargin,"GM=")
+disp(freqGM*2*3.14,"omegaPC=")
+
+[PhaseMargin,freqPM]=p_margin(F) //Calculates phase [deg] and corresponding freq [Hz] of phase margin
+disp(PhaseMargin,"PM=")
+disp(freqPM*2*3.14,"omegaGC")
+
+show_margins(F) //display gain and phase margin and associated crossover frequencies
+
+if(GainMargin>0 & PhaseMargin>0 )
+ disp("stable system")
+else
+ disp("unstable system")
+end
diff --git a/257/CH11/EX11.20/example_11_20.sce b/257/CH11/EX11.20/example_11_20.sce new file mode 100644 index 000000000..23ff5493b --- /dev/null +++ b/257/CH11/EX11.20/example_11_20.sce @@ -0,0 +1,11 @@ +s=poly(0,'s');
+F=syslin('c',[200/((100+12*s+s^2)*s)])
+
+
+[GainMargin,freqGM]=g_margin(F) //Calculates gain margin [dB] and corresponding frequency [Hz]
+disp(GainMargin,"GM=")
+
+
+[PhaseMargin,freqPM]=p_margin(F) //Calculates phase [deg] and corresponding freq [Hz] of phase margin
+disp(PhaseMargin,"PM=")
+
diff --git a/257/CH11/EX11.21/example_11_21.sce b/257/CH11/EX11.21/example_11_21.sce new file mode 100644 index 000000000..897b351bd --- /dev/null +++ b/257/CH11/EX11.21/example_11_21.sce @@ -0,0 +1,24 @@ +s=poly(0,'s');
+F=syslin('c',[k/((1+0.2*s)*s*(0.05*s+1))]) //without k
+
+fmin=0.1; //Min freq in Hz
+fmax=20; //Max freq in Hz
+
+scf(1);clf;
+bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
+
+show_margins(F) //display gain and phase margin and associated crossover frequencies
+
+// TO FIND VALUE OF K
+
+k= 10^(26/20)
+disp(k,"k marginal = ")
+
+// for GM=10 dB, the point on the plot without k is 16dB away from 0dB line.
+k1=10^(16/20) // 20*log(k1)=-10
+disp(k1,"k for GM=10 is ")
+
+
+// for PM=40degrees, the point on the magnitude plot without k is 12dB away from 0dB line.
+k2=10^(12/20) // 20*log(k1)= 6 dB
+disp(k2,"for PM=40degrees k is ")
diff --git a/257/CH11/EX11.22/example_11_22.sce b/257/CH11/EX11.22/example_11_22.sce new file mode 100644 index 000000000..c7fbb67d6 --- /dev/null +++ b/257/CH11/EX11.22/example_11_22.sce @@ -0,0 +1,15 @@ +y=poly([0 1],'s','coeff') //pole at origin
+
+c=20+20*log10(5) //at w=5, y=20
+k=10.^(c/20) //at w=1, y=c
+
+wc1=5 //given
+y1=poly([1 1/wc1],'s','coeff')
+
+c1=20+40*log10(5) // second line is y=-40*log(w)+c1 . this is at w=5.
+
+wc2= 10.^((-40-c1)/(-40))
+y2=poly([1 1/wc2],'s','coeff')
+
+TF= k*y2/(y*y1)
+disp(TF,"transfer function = ")
\ No newline at end of file diff --git a/257/CH11/EX11.23/example_11_23.sce b/257/CH11/EX11.23/example_11_23.sce new file mode 100644 index 000000000..1f8344570 --- /dev/null +++ b/257/CH11/EX11.23/example_11_23.sce @@ -0,0 +1,20 @@ +s=poly(0,'s');
+F=syslin('c',[1/((1+s*0.02)*s*(0.05*s+1))]) //without k
+
+fmin=0.1; //Min freq in Hz
+fmax=20; //Max freq in Hz
+
+scf(1);clf;
+bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
+
+show_margins(F) //display gain and phase margin and associated crossover frequencies
+
+// TO FIND VALUE OF K
+
+// for GM=10 dB, the point on the plot without k is 26dB away from 0dB line.
+k1=10^(26/20) // 20*log(k1)=26
+disp(k1,"k for GM=30 is ")
+F1=syslin('c',[(k1)/((1+s*0.02)*s*(0.05*s+1))])
+
+[PhaseMargin,freqPM]=p_margin(F1)
+disp(PhaseMargin,"PM=")
diff --git a/257/CH11/EX11.24/example_11_24.sce b/257/CH11/EX11.24/example_11_24.sce new file mode 100644 index 000000000..9be2dedf9 --- /dev/null +++ b/257/CH11/EX11.24/example_11_24.sce @@ -0,0 +1,29 @@ +// 6dB/octave = 20dB/decade
+
+wc1=2
+y1=poly([1 1/wc1],'s','coeff')
+
+//to find k
+c1=60+40*log10(4) //y=-40*log(w)+c1
+Y2=-40*log10(2)+c1 //at w=2
+
+c2=Y2+20*log10(2) // y= -20*log(2)+c2
+Y1=-20*log10(1)+c2 //at w=1
+disp(Y1)
+k=10.^(Y1/20)
+
+wc2=10.^((36-c1)/(-40)) //from graph
+y2=poly([1 1/wc2],'s','coeff')
+
+c3=36+60*log10(wc2) //equation of line with sloe -60dB
+wc3=10.^((-18-c3)/(-60))
+y3=poly([1 1/wc3],'s','coeff')
+
+c4= -18+20*log10(wc3)
+wc4=10.^(-54-c4)/(-20)
+y4=poly([1 1/wc4],'s','coeff')
+y5=poly([0 1],'s','coeff') // pole at origin
+
+TF=(k*y3^2)/((y1)*(y2)*(y5)*(y4))
+disp(TF, "TF = ")
+
diff --git a/257/CH11/EX11.25/example_11_25.sce b/257/CH11/EX11.25/example_11_25.sce new file mode 100644 index 000000000..532d5db46 --- /dev/null +++ b/257/CH11/EX11.25/example_11_25.sce @@ -0,0 +1,20 @@ +s=poly(0,'s');
+F=syslin('c',[1/((1+0.001*s)*(s*0.1+1)*(0.25*s+1))]) //without k
+
+fmin=0.1; //Min freq in Hz
+fmax=20; //Max freq in Hz
+
+scf(1);clf;
+bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
+
+show_margins(F) //display gain and phase margin and associated crossover frequencies
+
+// TO FIND VALUE OF K
+
+// for PM=40degrees, the point on the magnitude plot without k is 8dB away from 0dB line.
+k2=10^(8/20) // 20*log(k1)= 8 dB
+disp(k2,"for PM=40degrees k is ")
+F2=syslin('c',[(k2)/((1+0.001*s)*(s*0.1+1)*(0.25*s+1))])
+
+[GainMargin,freqGM]=g_margin(F2)
+disp(GainMargin,"GM=")
\ No newline at end of file diff --git a/257/CH11/EX11.26/example_11_26.sce b/257/CH11/EX11.26/example_11_26.sce new file mode 100644 index 000000000..155a7d534 --- /dev/null +++ b/257/CH11/EX11.26/example_11_26.sce @@ -0,0 +1,19 @@ +s=poly(0,'s');
+F=syslin('c',[80000/((2+s)*s*(s+50)*(s+200))]) //without k
+
+fmin=0.1; //Min freq in Hz
+fmax=20; //Max freq in Hz
+
+scf(1);clf;
+bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
+
+[GainMargin,freqGM]=g_margin(F) //Calculates gain margin [dB] and corresponding frequency [Hz]
+disp(GainMargin,"GM=")
+
+
+[PhaseMargin,freqPM]=p_margin(F) //Calculates phase [deg] and corresponding freq [Hz] of phase margin
+disp(PhaseMargin,"PM=")
+
+
+show_margins(F) //display gain and phase margin and associated crossover frequencies
+
diff --git a/257/CH11/EX11.27/example_11_27.sce b/257/CH11/EX11.27/example_11_27.sce new file mode 100644 index 000000000..92fedf2f6 --- /dev/null +++ b/257/CH11/EX11.27/example_11_27.sce @@ -0,0 +1,21 @@ +s=poly(0,'s');
+F=syslin('c',[1/((121+13*s+s^2)*s)]) //without k
+
+fmin=0.1; //Min freq in Hz
+fmax=20; //Max freq in Hz
+
+scf(1);clf;
+bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
+
+show_margins(F) //display gain and phase margin and associated crossover frequencies
+
+// TO FIND VALUE OF K
+
+// for GM=12 dB, the point on the plot without k is 119.5dB away from 0dB line.
+k1=10^(52/20) // 20*log(k1)=52
+disp(k1,"k=")
+F1=syslin('c',[(k1)/((121+13*s+s^2)*s)])
+
+[PhaseMargin,freqPM]=p_margin(F1)
+disp(PhaseMargin,"PM=")
+
diff --git a/257/CH11/EX11.3/example_11_3.sce b/257/CH11/EX11.3/example_11_3.sce new file mode 100644 index 000000000..ab5e52ebf --- /dev/null +++ b/257/CH11/EX11.3/example_11_3.sce @@ -0,0 +1,21 @@ +//there is no pole or zero at the origin as the slope is initially 0
+
+wc1=1
+y1=poly([1 1 ],'s','coeff');
+
+// mag at wc2 is -20 and wc1 is 0. hence wc1 and wc2 are a decade apart.
+
+wc2=10
+y2=poly([1 1/wc2 ],'s','coeff');
+disp(y2)
+
+// mag at wc2 is -20 and at w=1000 is 0. hence wc2 and wc3 are decade apart.
+
+wc3=100
+y3=poly([1 1/wc3 ],'s','coeff');
+
+wc4=1000 //given
+y4=poly([1 1/wc4 ],'s','coeff');
+
+TF= (y2*y3)/(y1*y4)
+disp(TF,"transfer function = ")
diff --git a/257/CH11/EX11.4/example_11_4.sce b/257/CH11/EX11.4/example_11_4.sce new file mode 100644 index 000000000..11a67a367 --- /dev/null +++ b/257/CH11/EX11.4/example_11_4.sce @@ -0,0 +1,15 @@ +s=poly(0,'s');
+F=syslin('c',[242*(s+5)/((1+s)*s*(s^2+5*s+121))])
+fmin=0.1; //Min freq in Hz
+fmax=20; //Max freq in Hz
+scf(1);clf;
+bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
+show_margins(F) //display gain and phase margin and associated crossover frequencies
+
+[GainMargin,freqGM]=g_margin(F) //Calculates gain margin [dB] and corresponding frequency [Hz]
+disp(GainMargin,"GM=")
+disp(freqGM*2*3.14,"omegaPC=")
+
+[PhaseMargin,freqPM]=p_margin(F) //Calculates phase [deg] and corresponding freq [Hz] of phase margin
+disp(PhaseMargin,"PM=")
+disp(freqPM*2*3.14,"omegaGC")
diff --git a/257/CH11/EX11.5/example_11_5.sce b/257/CH11/EX11.5/example_11_5.sce new file mode 100644 index 000000000..979edfc80 --- /dev/null +++ b/257/CH11/EX11.5/example_11_5.sce @@ -0,0 +1,24 @@ +s=poly(0,'s');
+F=syslin('c',[1/((2+s)*s*(s+10))]) //without k
+
+fmin=0.1; //Min freq in Hz
+fmax=20; //Max freq in Hz
+
+scf(1);clf;
+bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
+
+[GainMargin,freqGM]=g_margin(F) //Calculates gain margin [dB] and corresponding frequency [Hz]
+disp(GainMargin,"GM=")
+disp(freqGM*2*3.14,"omegaPC=")
+
+[PhaseMargin,freqPM]=p_margin(F) //Calculates phase [deg] and corresponding freq [Hz] of phase margin
+disp(PhaseMargin,"PM=")
+disp(freqPM*2*3.14,"omegaGC")
+
+show_margins(F) //display gain and phase margin and associated crossover frequencies
+
+// TO FIND VALUE OF K
+
+//we have to make omegaPC=omegaGC. the required upward shift is 22dB
+k1=10^(22/20) // 20*log(k1)=22
+disp(20*k1,"k marginal = ")
diff --git a/257/CH11/EX11.6/example_11_6.sce b/257/CH11/EX11.6/example_11_6.sce new file mode 100644 index 000000000..c1c54a362 --- /dev/null +++ b/257/CH11/EX11.6/example_11_6.sce @@ -0,0 +1,28 @@ +//there is no pole or zero at the origin as the slope is initially 0
+
+w=1 //given
+y1=poly([1 1/w ],'s','coeff');
+
+disp("at wc1 equation is 15=20*log(wc1)") //at wc1, magnitude is 15
+wc1=10^(15/20)
+disp(wc1,"hence wc1=")
+y2=poly([1 1/wc1],'s','coeff')
+
+disp("equation of 2nd line is y= (-20*log(w))+c")
+
+k1=poly([-20*3 0],'c','coeff'); //at w=1000
+c=-k1
+disp(c, "where c is")
+wc2=10^(45/20)
+disp(wc2,"hence wc2 is")
+y3=poly([1 1/wc2],'s','coeff')
+
+wc3=1000 //given
+y4= poly([1 1/wc3],'s','coeff')
+
+TF=y1*y4/(y2*y3)
+disp(TF,"transfer function is")
+
+
+
+
diff --git a/257/CH11/EX11.7/example_11_7.sce b/257/CH11/EX11.7/example_11_7.sce new file mode 100644 index 000000000..858626f39 --- /dev/null +++ b/257/CH11/EX11.7/example_11_7.sce @@ -0,0 +1,28 @@ +s=poly(0,'s');
+F=syslin('c',[1/((1+0.5*s)*s*(s*0.2+1))])
+
+fmin=0.1; //Min freq in Hz
+fmax=20; //Max freq in Hz
+
+scf(1);clf;
+bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
+disp("without including k")
+[GainMargin,freqGM]=g_margin(F) //Calculates gain margin [dB] and corresponding frequency [Hz]
+disp(GainMargin,"GM=")
+disp(freqGM*2*3.14,"omegaPC=")
+
+[PhaseMargin,freqPM]=p_margin(F) //Calculates phase [deg] and corresponding freq [Hz] of phase margin
+disp(PhaseMargin,"PM=")
+disp(freqPM*2*3.14,"omegaGC")
+
+show_margins(F) //display gain and phase margin and associated crossover frequencies
+
+// TO FIND K FOR GM=6dB
+
+k= 10^(6/20) //20*logk=6
+disp(k,"k for GM=6 is")
+
+// TO FIND K FOR PM=25 degrees
+
+k= 10^(6/20) //20*logk=6
+disp(k,"k for PM=25 degrees is")
\ No newline at end of file diff --git a/257/CH11/EX11.8/example_11_8.sce b/257/CH11/EX11.8/example_11_8.sce new file mode 100644 index 000000000..b76badfe2 --- /dev/null +++ b/257/CH11/EX11.8/example_11_8.sce @@ -0,0 +1,51 @@ +// 6dB/octave=20 dB/decade
+
+y1=poly([0 0 1],'s','coeff'); //zero at origin for initial slope
+
+wc1=0.5
+y2=poly([1 1/wc1],'s','coeff')
+
+wc2=1
+y3=poly([1 1/wc2],'s','coeff')
+
+wc3=5
+y4=poly([1 1/wc3],'s','coeff')
+
+//to find k
+
+disp("equation at w=0.5 is y=20*Log(w)+c")
+k1=poly([32-20*log10(1) 0],'s','coeff') // at w=1 32=20*log(1)+c
+
+disp(k1,"where c is ")
+
+k=poly([32+20*log10(0.5) 0],'s','coeff') //magnitude at w=0.5
+
+disp("equation of initial line is y=40*(log(w)+c1)")
+k2=poly([26-40*log10(0.5) 0],'c','coeff') // at w=1 32=20*log(1)+c
+c1=k2
+disp(c1,"where c1 is ")
+
+//now the initial line must have magnitude zero at w=1 for k=1.but at w=1; magnitude is k3 as below, which is due to 'k'
+k3=poly([40*log10(1)+26-40*log10(0.5) 0],'c','coeff')
+
+k=10^((40*log10(1)+26-40*log10(0.5))/(20))
+
+TF= k*(y1)/((y2)*(y3)*(y4))
+disp(TF,"transfer function = ")
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/257/CH11/EX11.9/example_11_9.sce b/257/CH11/EX11.9/example_11_9.sce new file mode 100644 index 000000000..66e94c233 --- /dev/null +++ b/257/CH11/EX11.9/example_11_9.sce @@ -0,0 +1,24 @@ +s=poly(0,'s');
+F=syslin('c',[(s^2)/((1+0.2*s)*(0.02*s+1))]) //without k
+
+fmin=0.1; //Min freq in Hz
+fmax=20; //Max freq in Hz
+
+scf(1);clf;
+bode(F,fmin,fmax); //Plots frequency response of open-loop system in Bode diagram
+
+[GainMargin,freqGM]=g_margin(F) //Calculates gain margin [dB] and corresponding frequency [Hz]
+disp(GainMargin,"GM=")
+disp(freqGM*2*3.14,"omegaPC=")
+
+[PhaseMargin,freqPM]=p_margin(F) //Calculates phase [deg] and corresponding freq [Hz] of phase margin
+disp(PhaseMargin,"PM=")
+disp(freqPM*2*3.14,"omegaGC")
+
+show_margins(F) //display gain and phase margin and associated crossover frequencies
+
+// TO FIND VALUE OF K
+
+// at omega=5, the point on the plot without k 28dB away from 0dB line.
+k1=10^(-28/20) // 20*log(k1)=-28
+disp(k1,"k for omegaGC=5 is ")
diff --git a/257/CH12/EX12.1/eg_12_1.sce b/257/CH12/EX12.1/eg_12_1.sce new file mode 100644 index 000000000..3c14bb427 --- /dev/null +++ b/257/CH12/EX12.1/eg_12_1.sce @@ -0,0 +1,3 @@ +s=%s
+GH=syslin('c',10/s)
+nyquist(GH)
\ No newline at end of file diff --git a/257/CH12/EX12.11/example_12_11.sce b/257/CH12/EX12.11/example_12_11.sce new file mode 100644 index 000000000..04069765a --- /dev/null +++ b/257/CH12/EX12.11/example_12_11.sce @@ -0,0 +1,5 @@ +s=%s;
+sys1=syslin('c',10*(s+3)/((s-1)*(s)))
+nyquist(sys1)
+show_margins(sys1,'nyquist')
+
diff --git a/257/CH12/EX12.12/example_12_12.sce b/257/CH12/EX12.12/example_12_12.sce new file mode 100644 index 000000000..91bebd074 --- /dev/null +++ b/257/CH12/EX12.12/example_12_12.sce @@ -0,0 +1,4 @@ +s=%s;
+sys1=syslin('c',k*(0.05*s+1)*(1+s)/((10*s+1)*(s-1)))
+nyquist(sys1)
+show_margins(sys1,'nyquist')
diff --git a/257/CH12/EX12.13/example_12_13.sce b/257/CH12/EX12.13/example_12_13.sce new file mode 100644 index 000000000..316902f9f --- /dev/null +++ b/257/CH12/EX12.13/example_12_13.sce @@ -0,0 +1,4 @@ +s=%s;
+sys1=syslin('c',100*(1+5*s)/(s^4*(s+1)))
+nyquist(sys1)
+show_margins(sys1,'nyquist')
diff --git a/257/CH12/EX12.14/example_12_14.sce b/257/CH12/EX12.14/example_12_14.sce new file mode 100644 index 000000000..20c914ea9 --- /dev/null +++ b/257/CH12/EX12.14/example_12_14.sce @@ -0,0 +1,4 @@ +s=%s;
+sys1=syslin('c',k*(s+5)/(s*(s-2)))
+nyquist(sys1)
+//show_margins(sys1,'nyquist')
diff --git a/257/CH12/EX12.15/example_12_15.sce b/257/CH12/EX12.15/example_12_15.sce new file mode 100644 index 000000000..32a316e72 --- /dev/null +++ b/257/CH12/EX12.15/example_12_15.sce @@ -0,0 +1,4 @@ +s=%s;
+sys1=syslin('c',50/(s*(0.1*s+1)*(1+0.2*s)))
+nyquist(sys1)
+//show_margins(sys1,'nyquist')
diff --git a/257/CH12/EX12.16/example_12_16.sce b/257/CH12/EX12.16/example_12_16.sce new file mode 100644 index 000000000..7f270af0c --- /dev/null +++ b/257/CH12/EX12.16/example_12_16.sce @@ -0,0 +1,5 @@ +s=%s;
+sys1=syslin('c',10/(s^2*(0.25*s+1)*(1+0.5*s)))
+nyquist(sys1)
+//show_margins(sys1,'nyquist')
+
diff --git a/257/CH12/EX12.17/example_12_17.sce b/257/CH12/EX12.17/example_12_17.sce new file mode 100644 index 000000000..05429f32a --- /dev/null +++ b/257/CH12/EX12.17/example_12_17.sce @@ -0,0 +1,3 @@ +s=%s;
+sys1=syslin('c',k*(s+1)/((s-1)*(s)))
+nyquist(sys1)
\ No newline at end of file diff --git a/257/CH12/EX12.18/example_12_18.sce b/257/CH12/EX12.18/example_12_18.sce new file mode 100644 index 000000000..58e6a8ef6 --- /dev/null +++ b/257/CH12/EX12.18/example_12_18.sce @@ -0,0 +1,3 @@ +s=%s;
+sys1=syslin('c',5/((1-s)*(s)))
+nyquist(sys1)
\ No newline at end of file diff --git a/257/CH12/EX12.19/eg_12_19.sce b/257/CH12/EX12.19/eg_12_19.sce new file mode 100644 index 000000000..356ddd0c8 --- /dev/null +++ b/257/CH12/EX12.19/eg_12_19.sce @@ -0,0 +1,7 @@ +disp("as omega=0 point is on the positive real axis, so the plot for 0+ and 0- is the point itself")
+
+disp("no pole at origin. type=0")
+
+disp("two pole at origin. type=2")
+
+disp("system is stable as N=0. in fig12.49, system is unstable as N=4. z=4")
\ No newline at end of file diff --git a/257/CH12/EX12.2/eg_12_2.sce b/257/CH12/EX12.2/eg_12_2.sce new file mode 100644 index 000000000..fee17e60d --- /dev/null +++ b/257/CH12/EX12.2/eg_12_2.sce @@ -0,0 +1,6 @@ +//poles and zeroes
+s=%s
+sys=syslin('c',1/(k*s+1))
+plzr(sys)
+
+
diff --git a/257/CH12/EX12.20/eg_12_20.sce b/257/CH12/EX12.20/eg_12_20.sce new file mode 100644 index 000000000..c22cf13dd --- /dev/null +++ b/257/CH12/EX12.20/eg_12_20.sce @@ -0,0 +1,6 @@ +//poles and zeroes
+s=%s
+sys=syslin('c',1/((2*s+1)*(1+5*s)*(s)))
+plzr(sys)
+
+
diff --git a/257/CH12/EX12.21/example_12_21.sce b/257/CH12/EX12.21/example_12_21.sce new file mode 100644 index 000000000..935466e88 --- /dev/null +++ b/257/CH12/EX12.21/example_12_21.sce @@ -0,0 +1,3 @@ +s=%s;
+sys1=syslin('c',(s+1)/((s-4)*(s^2)))
+nyquist(sys1)
\ No newline at end of file diff --git a/257/CH12/EX12.23/example_12_23.sce b/257/CH12/EX12.23/example_12_23.sce new file mode 100644 index 000000000..3789ecaee --- /dev/null +++ b/257/CH12/EX12.23/example_12_23.sce @@ -0,0 +1,5 @@ +s=%s;
+sys1=syslin('c',(s+8)*(s+2)/((s^3)))
+nyquist(sys1)
+show_margins(sys1,'nyquist')
+
diff --git a/257/CH12/EX12.24/example_12_24.sce b/257/CH12/EX12.24/example_12_24.sce new file mode 100644 index 000000000..cd68c89c5 --- /dev/null +++ b/257/CH12/EX12.24/example_12_24.sce @@ -0,0 +1,3 @@ +s=%s;
+sys1=syslin('c',k*(s+2)^2/((s)^3))
+nyquist(sys1)
\ No newline at end of file diff --git a/257/CH12/EX12.26/eg_12_26.sce b/257/CH12/EX12.26/eg_12_26.sce new file mode 100644 index 000000000..7491dd97d --- /dev/null +++ b/257/CH12/EX12.26/eg_12_26.sce @@ -0,0 +1,4 @@ +
+s=%s
+sys=syslin('c',(12)/(s*(s+2)*(s+1)))
+plzr(sys)
diff --git a/257/CH12/EX12.27/eg_12_27.sce b/257/CH12/EX12.27/eg_12_27.sce new file mode 100644 index 000000000..3c14bb427 --- /dev/null +++ b/257/CH12/EX12.27/eg_12_27.sce @@ -0,0 +1,3 @@ +s=%s
+GH=syslin('c',10/s)
+nyquist(GH)
\ No newline at end of file diff --git a/257/CH12/EX12.28/example_12_28.sce b/257/CH12/EX12.28/example_12_28.sce new file mode 100644 index 000000000..e1020736f --- /dev/null +++ b/257/CH12/EX12.28/example_12_28.sce @@ -0,0 +1,3 @@ +s=%s;
+sys1=syslin('c',k/((s-1)*(s)*(s+4)))
+nyquist(sys1)
\ No newline at end of file diff --git a/257/CH12/EX12.29/eg_12_29.sce b/257/CH12/EX12.29/eg_12_29.sce new file mode 100644 index 000000000..f8c8a7aba --- /dev/null +++ b/257/CH12/EX12.29/eg_12_29.sce @@ -0,0 +1,5 @@ +s=%s;
+sys1=syslin('c',10000*(s+1)*(s+3)/(s*(s+2)*(s-4)))
+nyquist(sys1)
+show_margins(sys1,'nyquist')
+
diff --git a/257/CH12/EX12.3/eg_12_3.sce b/257/CH12/EX12.3/eg_12_3.sce new file mode 100644 index 000000000..384bbcdae --- /dev/null +++ b/257/CH12/EX12.3/eg_12_3.sce @@ -0,0 +1,6 @@ +//poles and zeroes
+s=%s
+sys=syslin('c',1/((k*s+1)*(s)))
+plzr(sys)
+
+
diff --git a/257/CH12/EX12.4/eg_12_4.sce b/257/CH12/EX12.4/eg_12_4.sce new file mode 100644 index 000000000..9c49ecc91 --- /dev/null +++ b/257/CH12/EX12.4/eg_12_4.sce @@ -0,0 +1,6 @@ +//poles and zeroes
+s=%s
+sys=syslin('c',1/((k*s+1)*(s^2)))
+plzr(sys)
+
+
diff --git a/257/CH12/EX12.6/eg_12_6.sce b/257/CH12/EX12.6/eg_12_6.sce new file mode 100644 index 000000000..3b1294ec3 --- /dev/null +++ b/257/CH12/EX12.6/eg_12_6.sce @@ -0,0 +1,3 @@ +s=%s
+GH=syslin('c',k/(s*(s+2)*(s+10)))
+nyquist(GH)
\ No newline at end of file diff --git a/257/CH12/EX12.7/eg_12_7.sce b/257/CH12/EX12.7/eg_12_7.sce new file mode 100644 index 000000000..369438a05 --- /dev/null +++ b/257/CH12/EX12.7/eg_12_7.sce @@ -0,0 +1,3 @@ +s=%s
+GH=syslin('c',40/((s+4)*(s^2+2*s+2)))
+nyquist(GH)
\ No newline at end of file diff --git a/257/CH12/EX12.8/eg_12_8.sce b/257/CH12/EX12.8/eg_12_8.sce new file mode 100644 index 000000000..cc71cf5a3 --- /dev/null +++ b/257/CH12/EX12.8/eg_12_8.sce @@ -0,0 +1,4 @@ +s=%s
+h=syslin('c',(1+0.5*s)/(1+0.1*s)*(1+0.02*s)*(s^2));
+nyquist(h)
+//show_margins(h,'nyquist')
diff --git a/257/CH12/EX12.9/eg_12_9.sce b/257/CH12/EX12.9/eg_12_9.sce new file mode 100644 index 000000000..93da42004 --- /dev/null +++ b/257/CH12/EX12.9/eg_12_9.sce @@ -0,0 +1,4 @@ +s=%s;
+sys=syslin('c',10/(s^2)*(s+2))
+nyquist(sys)
+show_margins(sys,'nyquist')
\ No newline at end of file diff --git a/257/CH13/EX13.10/Example_13_10.sce b/257/CH13/EX13.10/Example_13_10.sce new file mode 100644 index 000000000..db63a55b8 --- /dev/null +++ b/257/CH13/EX13.10/Example_13_10.sce @@ -0,0 +1,8 @@ +syms s U1 U2
+A=[0 3; -2 -5];
+B=[1 1 ; 1 1];
+C=[2 1; 1 0];
+D=[0 0 ; 0 0];
+U=[U1;U2]
+TM= C*inv(s*eye(2,2)-A) *B + D;
+disp(TM*U,"Y = ")
\ No newline at end of file diff --git a/257/CH13/EX13.11/Example_13_11.sce b/257/CH13/EX13.11/Example_13_11.sce new file mode 100644 index 000000000..62eb7c57d --- /dev/null +++ b/257/CH13/EX13.11/Example_13_11.sce @@ -0,0 +1,5 @@ +syms s t
+A=[0 -1; 2 -3]
+phi=inv(s*eye(2,2) - A)
+disp(phi,"phi(s) = ")
+x=ilaplace(phi,s,t) //state transition matrix
diff --git a/257/CH13/EX13.12/Example_13_12.sce b/257/CH13/EX13.12/Example_13_12.sce new file mode 100644 index 000000000..0830ddd45 --- /dev/null +++ b/257/CH13/EX13.12/Example_13_12.sce @@ -0,0 +1,9 @@ +T=(s^3+3*s^22+2*s)/(s^3+12*s^2+47*s+60);
+
+A=[-3 0 0; 0 -4 0; 0 0 -5]
+B=[1;1;1]
+C=[-3 24 -30]
+D=[1];
+disp("state modle is")
+disp(A*X+B,"[diff(X1);diff(X2);diff(X3)]=")
+disp(C*X+D,"and Y = ")
\ No newline at end of file diff --git a/257/CH13/EX13.13/Example_13_13.sce b/257/CH13/EX13.13/Example_13_13.sce new file mode 100644 index 000000000..3b837f428 --- /dev/null +++ b/257/CH13/EX13.13/Example_13_13.sce @@ -0,0 +1,9 @@ +syms R1 R2 L C U1 U2
+A=[-1/(R1*C) -1/C; 1/L -R2/L]
+B=[1/(C*R1) 0; 0 -R2/L]
+C=[-1/R1 0]
+D=[1/R1 0]
+U=[U1;U2]
+X=[X1;X2]
+disp(A*X+B*U,"[diff(X1);diff(X2)]=")
+disp(C*X+D*U,"and Y = ")
\ No newline at end of file diff --git a/257/CH13/EX13.14/Example_13_14.sce b/257/CH13/EX13.14/Example_13_14.sce new file mode 100644 index 000000000..53895229a --- /dev/null +++ b/257/CH13/EX13.14/Example_13_14.sce @@ -0,0 +1,7 @@ +s=%s;
+A=[-0 1;-2 -3]
+B=[1;0]
+C=[1 0]
+D=0;
+TF=C*inv(s*eye(2,2)-A) *B
+disp(TF,"transfer function = ")
\ No newline at end of file diff --git a/257/CH13/EX13.15/Example_13_15.sce b/257/CH13/EX13.15/Example_13_15.sce new file mode 100644 index 000000000..9596e0655 --- /dev/null +++ b/257/CH13/EX13.15/Example_13_15.sce @@ -0,0 +1,9 @@ +syms t a1 a2 a3 a4
+X=[%e^(-3*t); -3*%e^(-3*t)]
+X1=diff(X,t)
+
+x=[1;-3]
+x1=[-3;9]
+A=x1/x
+
+disp(A," A= ")
\ No newline at end of file diff --git a/257/CH13/EX13.16/Example_13_16.sce b/257/CH13/EX13.16/Example_13_16.sce new file mode 100644 index 000000000..998bacd2e --- /dev/null +++ b/257/CH13/EX13.16/Example_13_16.sce @@ -0,0 +1,13 @@ +syms s t
+A=[1 -2; 1 -4]
+X=[0.5 ; 1]
+phi=inv(s*eye(2,2)-A)
+disp(phi)
+
+a1=ilaplace(phi(1,1),s,t)
+a2=ilaplace(phi(1,2),s,t)
+a3=ilaplace(phi(2,1),s,t)
+a4=ilaplace(phi(2,2),s,t)
+
+S=[a1 a2;a3 a4]
+disp(S,"X(t) = ")
\ No newline at end of file diff --git a/257/CH13/EX13.17/Example_13_17.sce b/257/CH13/EX13.17/Example_13_17.sce new file mode 100644 index 000000000..93b302a3b --- /dev/null +++ b/257/CH13/EX13.17/Example_13_17.sce @@ -0,0 +1,11 @@ +A=[1 0;1 1 ]
+Xo=[1;0]
+phi=inv(s*eye(2,2)-A)
+
+a1=ilaplace(phi(1,1),s,t)
+a2=ilaplace(phi(1,2),s,t)
+a3=ilaplace(phi(2,1),s,t)
+a4=ilaplace(phi(2,2),s,t)
+
+S=[a1 a2;a3 a4]
+disp(S*Xo,"X(t) = ")
\ No newline at end of file diff --git a/257/CH13/EX13.18/Example_13_18.sce b/257/CH13/EX13.18/Example_13_18.sce new file mode 100644 index 000000000..622b7732c --- /dev/null +++ b/257/CH13/EX13.18/Example_13_18.sce @@ -0,0 +1,14 @@ +A=[1 0;1 1]
+B=[1;1]
+X=[1;0]
+U=[1/s]
+phi1=inv(s*eye(2,2)-A)
+
+phi=phi1*B*U
+
+a1=ilaplace(phi(1,1),s,t)
+a3=ilaplace(phi(2,1),s,t)
+
+
+S=[a1;a3]
+disp(S,"X(t) = ")
diff --git a/257/CH13/EX13.19/Example_13_19.sce b/257/CH13/EX13.19/Example_13_19.sce new file mode 100644 index 000000000..6785b98c2 --- /dev/null +++ b/257/CH13/EX13.19/Example_13_19.sce @@ -0,0 +1,24 @@ +A=[0 1; -2 -3]
+U=[1/s;1/(s+2)]
+B=[2 1; 0 1]
+phi=inv(s*eye(2,2)-A)
+X=[0;0]
+a1=ilaplace(phi(1,1),s,t)
+a2=ilaplace(phi(1,2),s,t)
+a3=ilaplace(phi(2,1),s,t)
+a4=ilaplace(phi(2,2),s,t)
+
+S=[a1 a2;a3 a4]
+disp(S,"%e^(A*t) = ")
+ZIR=S*X
+disp(ZIR," ZIR = ")
+
+k=phi*B*U
+b1=ilaplace(k(1,1),s,t)
+b3=ilaplace(k(2,1),s,t)
+
+ZSR=[b1;b3]
+disp(ZSR,"ZSR = ")
+
+X=ZIR+ZSR;
+
diff --git a/257/CH13/EX13.21/Example_13_21.sce b/257/CH13/EX13.21/Example_13_21.sce new file mode 100644 index 000000000..36cd80e80 --- /dev/null +++ b/257/CH13/EX13.21/Example_13_21.sce @@ -0,0 +1,11 @@ +syms s U
+T=(2*s^2+s+5)/(s^3+6*s^2+11*s+4)
+
+disp("state modle is")
+A=[0 1 0; 0 0 1; -4 -11 -6]
+B=[0;0;1]*U
+X=[X1;X2;X3]
+C=[5 1 2]
+D=0
+disp(A*X+B,"[diff(X1);diff(X2);diff(X3)]=")
+disp(C*X+D,"and Y = ")
\ No newline at end of file diff --git a/257/CH13/EX13.22/Example_13_22.sce b/257/CH13/EX13.22/Example_13_22.sce new file mode 100644 index 000000000..9c9d6f342 --- /dev/null +++ b/257/CH13/EX13.22/Example_13_22.sce @@ -0,0 +1,12 @@ +//takin laplace transform we get :
+
+T=(2*s^2+6*s+5)/(s^3+4*s^2+5*s+2)
+
+disp("state modle is")
+A=[0 1 0; 0 0 1; -2 -5 -4]
+B=[0;0;1]*U
+X=[X1;X2;X3]
+C=[5 6 2]
+D=0
+disp(A*X+B,"[diff(X1);diff(X2);diff(X3)]=")
+disp(C*X+D,"and Y = ")
\ No newline at end of file diff --git a/257/CH13/EX13.23/Example_13_23.sce b/257/CH13/EX13.23/Example_13_23.sce new file mode 100644 index 000000000..8639cee04 --- /dev/null +++ b/257/CH13/EX13.23/Example_13_23.sce @@ -0,0 +1,9 @@ +syms L1 L2 R1 C X1 X2 X3
+disp("state modle is")
+A=[0 0 -1/L1; 0 -R1/L2 1/L2; 1/C -1/C 0]
+B=[1/L1;0;1]*U
+X=[X1;X2;X3]
+C=[0 R1 0]
+D=0
+disp(A*X+B,"[diff(X1);diff(X2);diff(X3)]=")
+disp(C*X+D,"and Y = ")
\ No newline at end of file diff --git a/257/CH13/EX13.24/Example_13_24.sce b/257/CH13/EX13.24/Example_13_24.sce new file mode 100644 index 000000000..53eef0a5a --- /dev/null +++ b/257/CH13/EX13.24/Example_13_24.sce @@ -0,0 +1,24 @@ +A=[0 1; -2 -3]
+U=[1/s]
+B=[0; 1]
+phi=inv(s*eye(2,2)-A)
+X=[1;1]
+a1=ilaplace(phi(1,1),s,t)
+a2=ilaplace(phi(1,2),s,t)
+a3=ilaplace(phi(2,1),s,t)
+a4=ilaplace(phi(2,2),s,t)
+
+S=[a1 a2;a3 a4]
+disp(S,"%e^(A*t) = ")
+ZIR=S*X
+disp(ZIR," ZIR = ")
+
+k=phi*B*U
+b1=ilaplace(k(1,1),s,t)
+b3=ilaplace(k(2,1),s,t)
+
+ZSR=[b1;b3]
+disp(ZSR,"ZSR = ")
+
+X=ZIR+ZSR;
+disp(X," output = ")
diff --git a/257/CH13/EX13.3/Example_13_3.sce b/257/CH13/EX13.3/Example_13_3.sce new file mode 100644 index 000000000..80aa94300 --- /dev/null +++ b/257/CH13/EX13.3/Example_13_3.sce @@ -0,0 +1,13 @@ +syms Y t
+X1=Y;
+X2=diff(Y,t);
+X3=diff(X2,t);
+
+A=[0 1 0;0 0 1; -2 -7 -4]
+B=[0 ; 0 ; 5]
+
+disp("OUTPUT IS C*X + D*U WHERE ")
+C=[1 0 0 ];
+D=0;
+disp(C,"C=")
+disp(D,"D= ")
diff --git a/257/CH13/EX13.4/Example_13_4.sce b/257/CH13/EX13.4/Example_13_4.sce new file mode 100644 index 000000000..8171b3d47 --- /dev/null +++ b/257/CH13/EX13.4/Example_13_4.sce @@ -0,0 +1,19 @@ +syms s X1 X2 X3 U;
+
+T=(s^2+3*s+3)/(s^3+2*s^2+3*s+1)
+L1=-2/s;
+L2=-3/s^2
+L3=-1/s^3;
+T1=1/s;
+T2=3/s^2;
+T3=3/s^3;
+
+del1=1;
+del2=1;
+del3=1;
+
+disp("state modle is")
+A=[-2 1 0; -3 0 1; -1 0 0]
+B=[1;3;3]*U
+X=[X1;X2;X3]
+disp(A*X+B,"[diff(X1);diff(X2);diff(X3)]=")
\ No newline at end of file diff --git a/257/CH13/EX13.5/Example_13_5.sce b/257/CH13/EX13.5/Example_13_5.sce new file mode 100644 index 000000000..311f8ae2c --- /dev/null +++ b/257/CH13/EX13.5/Example_13_5.sce @@ -0,0 +1,12 @@ +syms s X1 X2 X3 U;
+
+T=(5*s^2+6*s+8)/(s^3+3*s^2+7*s+9)
+
+disp("state modle is")
+A=[0 1 0; 0 0 1; -9 -7 -3]
+B=[0;0;1]*U
+X=[X1;X2;X3]
+C=[8 6 5]
+D=0
+disp(A*X+B,"[diff(X1);diff(X2);diff(X3)]=")
+disp(C*X+D,"and Y = ")
\ No newline at end of file diff --git a/257/CH13/EX13.6/Example_13_6.sce b/257/CH13/EX13.6/Example_13_6.sce new file mode 100644 index 000000000..90a337d5c --- /dev/null +++ b/257/CH13/EX13.6/Example_13_6.sce @@ -0,0 +1,12 @@ +syms s X1 X2 X3 U;
+
+T=(s^2+4)/((s+1)*(s+2)*(s+3))
+
+disp("state modle is")
+A=[-1 0 0; -0 -2 0; 0 0 -3]
+B=[1;1;1]*U
+X=[X1;X2;X3]
+C=[2.5 -8 6.5];
+D=0;
+disp(A*X+B,"[diff(X1);diff(X2);diff(X3)]=")
+disp(C*X+D,"and Y = ")
\ No newline at end of file diff --git a/257/CH13/EX13.7/Example_13_7.sce b/257/CH13/EX13.7/Example_13_7.sce new file mode 100644 index 000000000..f7636b846 --- /dev/null +++ b/257/CH13/EX13.7/Example_13_7.sce @@ -0,0 +1,12 @@ +syms s X1 X2 X3 U;
+
+T=(1)/((s+2)^2*(s+1))
+
+disp("state modle is")
+A=[-2 1 0; -0 -2 0; 0 0 -1]
+B=[0;1;1]*U
+X=[X1;X2;X3]
+C=[-1 -1 1];
+D=0;
+disp(A*X+B,"[diff(X1);diff(X2);diff(X3)]=")
+disp(C*X+D,"and Y = ")
\ No newline at end of file diff --git a/257/CH13/EX13.8/Example_13_8.sce b/257/CH13/EX13.8/Example_13_8.sce new file mode 100644 index 000000000..87b57c18c --- /dev/null +++ b/257/CH13/EX13.8/Example_13_8.sce @@ -0,0 +1,12 @@ +syms s X1 X2 X3 U;
+
+T=(s+4)*(s+2)/((s)*(s+1)*(s+3))
+
+disp("state modle is")
+A=[0 1 1; -0 -3 1; 0 0 -1]
+B=[1;1;1]*U
+X=[X1;X2;X3]
+C=[1 0 0];
+D=0;
+disp(A*X+B,"[diff(X1);diff(X2);diff(X3)]=")
+disp(C*X+D,"and Y = ")
\ No newline at end of file diff --git a/257/CH13/EX13.9/Example_13_9.sce b/257/CH13/EX13.9/Example_13_9.sce new file mode 100644 index 000000000..1568e3a69 --- /dev/null +++ b/257/CH13/EX13.9/Example_13_9.sce @@ -0,0 +1,6 @@ +s=%s;
+A=[-2 -3;4 2]
+B=[3;5]
+C=[1 1]
+TF=C*inv(s*eye(2,2)-A) *B
+disp(TF,"transfer function = ")
\ No newline at end of file diff --git a/257/CH2/EX2.1/example_2_1.sce b/257/CH2/EX2.1/example_2_1.sce new file mode 100644 index 000000000..3a358f426 --- /dev/null +++ b/257/CH2/EX2.1/example_2_1.sce @@ -0,0 +1,4 @@ +//laplace transform of exponential function
+ syms t s;
+ y=laplace('%e^(-a*t)',t,s);
+ disp(y,"ans=")
diff --git a/257/CH2/EX2.2/example_2_2.sce b/257/CH2/EX2.2/example_2_2.sce new file mode 100644 index 000000000..bcccd9fc0 --- /dev/null +++ b/257/CH2/EX2.2/example_2_2.sce @@ -0,0 +1,3 @@ +syms t s w;
+y=laplace('sin(w*t)',t,s);
+disp(y,"ans=")
\ No newline at end of file diff --git a/257/CH2/EX2.3/example_2_3.sce b/257/CH2/EX2.3/example_2_3.sce new file mode 100644 index 000000000..5ff7fcc5e --- /dev/null +++ b/257/CH2/EX2.3/example_2_3.sce @@ -0,0 +1,7 @@ +s=%s;
+
+F=(s+2)/(s*(s+3)*(s+4))
+
+syms t s;
+y=ilaplace(F,s,t);
+disp(y,"f(t)=")
\ No newline at end of file diff --git a/257/CH2/EX2.4/example_2_4.sce b/257/CH2/EX2.4/example_2_4.sce new file mode 100644 index 000000000..8cc7341d8 --- /dev/null +++ b/257/CH2/EX2.4/example_2_4.sce @@ -0,0 +1,7 @@ +s=%s;
+
+F=(s-2)/(s*(s+1)^3);
+
+syms t s;
+y=ilaplace(F,s,t);
+disp(y,"f(t)=")
\ No newline at end of file diff --git a/257/CH2/EX2.5/example_2_5.sce b/257/CH2/EX2.5/example_2_5.sce new file mode 100644 index 000000000..e8fe1dbf7 --- /dev/null +++ b/257/CH2/EX2.5/example_2_5.sce @@ -0,0 +1,7 @@ +s=%s;
+
+F=(s^2+3)/((s^2+2*s+5)*(s+2));
+
+syms t s;
+y=ilaplace(F,s,t);
+disp(y,"f(t)=")
\ No newline at end of file diff --git a/257/CH2/EX2.6/example_2_6.sce b/257/CH2/EX2.6/example_2_6.sce new file mode 100644 index 000000000..d5f456b1b --- /dev/null +++ b/257/CH2/EX2.6/example_2_6.sce @@ -0,0 +1,9 @@ +//given d^2/dt(y(t)) + 6*d/dt(y(t)) + 8*y(t)
+
+s=%s;
+
+F= 16/((s+1)*(s^2+6*s+8));
+
+syms t s;
+y=ilaplace(F,s,t);
+disp(y,"f(t)=")
\ No newline at end of file diff --git a/257/CH2/EX2.7/example_2_7.sce b/257/CH2/EX2.7/example_2_7.sce new file mode 100644 index 000000000..d5f456b1b --- /dev/null +++ b/257/CH2/EX2.7/example_2_7.sce @@ -0,0 +1,9 @@ +//given d^2/dt(y(t)) + 6*d/dt(y(t)) + 8*y(t)
+
+s=%s;
+
+F= 16/((s+1)*(s^2+6*s+8));
+
+syms t s;
+y=ilaplace(F,s,t);
+disp(y,"f(t)=")
\ No newline at end of file diff --git a/257/CH2/EX2.8/example_2_8.sce b/257/CH2/EX2.8/example_2_8.sce new file mode 100644 index 000000000..b6b9161c0 --- /dev/null +++ b/257/CH2/EX2.8/example_2_8.sce @@ -0,0 +1,15 @@ +// using KVL we get i(t)*R + 1/C * int(i(t)) = v(t)
+
+// taking laplace transform V(s)= I(s)*R + 1/C * (I(s)/s)
+
+R=10^6
+C=10^-6
+
+s=%s;
+
+F=1/R*(1/(s + (1)/(R*C)));
+disp(F)
+
+syms t s;
+y=ilaplace(F,s,t);
+disp(y,"i(t)=")
\ No newline at end of file diff --git a/257/CH2/EX2.9/example_2_9.sce b/257/CH2/EX2.9/example_2_9.sce new file mode 100644 index 000000000..c815cab7d --- /dev/null +++ b/257/CH2/EX2.9/example_2_9.sce @@ -0,0 +1,13 @@ +// using KVL we have v(t)=i(t)*R+ L* d/dt(i(t))
+// taking laplace transform V(s)=I(s)*R + L*s*I(s)
+
+s=%s;
+
+R=10^3
+L=25*10^-3
+
+F=(50/s)/(R+s*L);
+
+syms t s;
+y=ilaplace(F,s,t);
+disp(y,"i(t)=")
diff --git a/257/CH3/EX3.1/example_3_1.sce b/257/CH3/EX3.1/example_3_1.sce new file mode 100644 index 000000000..25746735e --- /dev/null +++ b/257/CH3/EX3.1/example_3_1.sce @@ -0,0 +1,8 @@ +//applying KVL we have Vi(t) = R*i(t) + 1/C * int(i(t)) dt
+// Vo(t) = 1/C * int(i(t)) dt
+
+syms s R C I
+Vi= R*I + I/(s*C)
+Vo = I/(C*s)
+
+disp(Vo/Vi,"transfer function=")
\ No newline at end of file diff --git a/257/CH3/EX3.10/example_3_10.sce b/257/CH3/EX3.10/example_3_10.sce new file mode 100644 index 000000000..226c2ece3 --- /dev/null +++ b/257/CH3/EX3.10/example_3_10.sce @@ -0,0 +1,5 @@ +syms s t R C
+
+C=R*(1+2*%e^-s)/(2*s^2 + 2*s +1)
+
+disp(C/R,'transfer function=')
diff --git a/257/CH3/EX3.11/example_3_11.sce b/257/CH3/EX3.11/example_3_11.sce new file mode 100644 index 000000000..b9affc5fb --- /dev/null +++ b/257/CH3/EX3.11/example_3_11.sce @@ -0,0 +1,20 @@ +// given gain of buffer amplifier is 1
+s=%s
+I=1;
+R=10^6;
+C=10^-6
+C2=0.5*10^-6;
+
+Vi=1/(C*s)*I + R*I
+V1=R * I
+disp(V1/Vi,"V1/Vi is ")
+
+V2=I/(C2*s) + I*R
+Vo= I*R
+disp(Vo/V2,"Vo/V2 is ")
+
+V1=V2 //because gain=1
+(s/(s+1))*Vi == (s+2)/s * Vo //
+
+disp(s^2/((s+2)*(s+1)),"transfer function is")
+
diff --git a/257/CH3/EX3.12/example_3_12.sce b/257/CH3/EX3.12/example_3_12.sce new file mode 100644 index 000000000..548b5f395 --- /dev/null +++ b/257/CH3/EX3.12/example_3_12.sce @@ -0,0 +1,18 @@ +//given poles are -1, -2+%i , -2-%i and zero is s=-3
+
+num=poly([-3],'s','roots');
+den=poly([5 9 5 1 ],'s','coeff');
+G=k*num/den;
+disp(G,"G(s)=")
+
+//to find k
+//G(0)=10 given
+
+k=(10*(0+1)*(0+0+5))/3
+disp(k,"value of k is")
+
+disp(G,"transfer function is")
+
+
+
+
diff --git a/257/CH3/EX3.13/example_3_13.sce b/257/CH3/EX3.13/example_3_13.sce new file mode 100644 index 000000000..4dd64c9f1 --- /dev/null +++ b/257/CH3/EX3.13/example_3_13.sce @@ -0,0 +1,4 @@ +syms s t X
+Y=(s+4)/(s^2+2*s+5)*X
+y=ilaplace(Y,s,t)
+disp(y,'kj')
\ No newline at end of file diff --git a/257/CH3/EX3.14/example_3_14.sce b/257/CH3/EX3.14/example_3_14.sce new file mode 100644 index 000000000..377ac2a47 --- /dev/null +++ b/257/CH3/EX3.14/example_3_14.sce @@ -0,0 +1,8 @@ +s=%s
+syms Vi C1 R1 L C2 R2
+V1=Vi/(1+s*C1*R1)
+V2=I*(R2+s*L+(1/(s*C2)))
+V2=k*V1
+k*Vi/(1+s*C1*R1) == I*(R2 + s*L + (1/(s*C2)))
+
+disp((k*s*C2)/((1+s*C1*R1)*(1+s*C2*R2+(s^2)*L*C2)),'I/Vi=')
\ No newline at end of file diff --git a/257/CH3/EX3.15/example_3_15.sce b/257/CH3/EX3.15/example_3_15.sce new file mode 100644 index 000000000..70224bf28 --- /dev/null +++ b/257/CH3/EX3.15/example_3_15.sce @@ -0,0 +1,5 @@ +syms V2 I1 V1
+I1=V1
+V2=V1*((s+1)/(s^2+3*s+1))
+
+disp(((s+1)/(s^2+3*s+1)),'V2/V1=')
\ No newline at end of file diff --git a/257/CH3/EX3.2/example_3_2.sce b/257/CH3/EX3.2/example_3_2.sce new file mode 100644 index 000000000..a7f62daf7 --- /dev/null +++ b/257/CH3/EX3.2/example_3_2.sce @@ -0,0 +1,6 @@ +syms s t R L C
+
+Eo= I/(C*s)
+Ei= I*(R+s*L+1/(s*C))
+
+disp(Eo/Ei,'transfer function=')
diff --git a/257/CH3/EX3.3/example_3_3.sce b/257/CH3/EX3.3/example_3_3.sce new file mode 100644 index 000000000..e4ef1db88 --- /dev/null +++ b/257/CH3/EX3.3/example_3_3.sce @@ -0,0 +1,6 @@ +syms s t R L C
+
+Ei= I*L*s + I/(C*s) + R*I
+Eo= I*R
+
+disp(Eo/Ei,'transfer function=')
diff --git a/257/CH3/EX3.4/example_3_4.sce b/257/CH3/EX3.4/example_3_4.sce new file mode 100644 index 000000000..53a44d5c5 --- /dev/null +++ b/257/CH3/EX3.4/example_3_4.sce @@ -0,0 +1,5 @@ +//laplace transform of unit impulse response is transfer function
+syms s t
+
+y=laplace(%e^(-4*t),t,s)
+disp(y,"transfer function=")
\ No newline at end of file diff --git a/257/CH3/EX3.5/example_3_5.sce b/257/CH3/EX3.5/example_3_5.sce new file mode 100644 index 000000000..9d335ac23 --- /dev/null +++ b/257/CH3/EX3.5/example_3_5.sce @@ -0,0 +1,10 @@ +syms s t
+
+R=laplace(2,t,s)
+C=laplace(%e^(-5*t),t,s)
+
+TF=C/R
+
+c=ilaplace(2/(s*(s+5)),s,t) // as C= TF * R
+
+disp(c,"output is c(t)=")
\ No newline at end of file diff --git a/257/CH3/EX3.6/example_3_6.sce b/257/CH3/EX3.6/example_3_6.sce new file mode 100644 index 000000000..b51fe0f5b --- /dev/null +++ b/257/CH3/EX3.6/example_3_6.sce @@ -0,0 +1,18 @@ +s=%s;
+TF=syslin('c',(k*(s+6))/(s*(s+2)*(s+5)*(s^2+7*s+12)));
+disp(TF,"T(s)=")
+
+x=denom(TF);
+disp(x,"Characteristics equation=")
+
+y=roots(x);
+disp(y,"Poles of a system=")
+
+disp("zeroes of the system is -6")
+
+//pole zero plot
+
+p=poly([6 1],'s',"coeff")
+q=poly([0 120 154 71 14 1],'s',"coeff") //expanding the denominator
+V=syslin('c',p,q)
+plzr(V)
diff --git a/257/CH3/EX3.7/example_3_7.sce b/257/CH3/EX3.7/example_3_7.sce new file mode 100644 index 000000000..d04966cf0 --- /dev/null +++ b/257/CH3/EX3.7/example_3_7.sce @@ -0,0 +1,5 @@ +syms s t
+
+T=laplace(%e^(-t)*(1-cos(2*t)))
+
+disp(T,"transfer function=")
\ No newline at end of file diff --git a/257/CH3/EX3.8/example_3_8.sce b/257/CH3/EX3.8/example_3_8.sce new file mode 100644 index 000000000..43eb2df2e --- /dev/null +++ b/257/CH3/EX3.8/example_3_8.sce @@ -0,0 +1,6 @@ +syms R2 Z
+
+Eo= I*R2
+Ei= I*Z + I*R2 //where Z= R1/(1+s*R1*C)
+
+disp(Eo/Ei,'transfer function=')
diff --git a/257/CH3/EX3.9/example_3_9.sce b/257/CH3/EX3.9/example_3_9.sce new file mode 100644 index 000000000..0b26f5610 --- /dev/null +++ b/257/CH3/EX3.9/example_3_9.sce @@ -0,0 +1,6 @@ +syms R2 R1 C
+
+Eo= I*(1+R2*C*s)/(s*C)
+Ei= I*(R1+R2+(1/(s*C)))
+
+disp(Eo/Ei,'transfer function=')
diff --git a/257/CH4/EX4.1/example_4_1.sce b/257/CH4/EX4.1/example_4_1.sce new file mode 100644 index 000000000..11438e9ab --- /dev/null +++ b/257/CH4/EX4.1/example_4_1.sce @@ -0,0 +1,12 @@ +// F = M*s^2 +K*X + B*X*s
+syms s t V Q L C R I;
+//force-voltage method
+F=V;
+X=Q;
+M=L;
+K=1/C;
+B=R;
+
+V=I*(s*L + 1/(s*C) + R);
+
+disp("v = L*diff(i) + 1/C*int(i) + i*R")
\ No newline at end of file diff --git a/257/CH4/EX4.14/example_4_14.sce b/257/CH4/EX4.14/example_4_14.sce new file mode 100644 index 000000000..051e3f1c1 --- /dev/null +++ b/257/CH4/EX4.14/example_4_14.sce @@ -0,0 +1,17 @@ +syms M1 X1 B1 K X2 M2 B2 K3 K1 K2 C1 C2 C3 R1 R2 M3 X3 B3 I1 I2 I3 L3 L1 L2 R3
+
+F=M1*X1*s^2 + B1*s*X1 + K*X1 + B2*(X1-X2)*s
+zero=M2*X2*s^2 + B2*s*(X2-X1)+K3*X2+K2*(X2-X3)
+zro=K2*(X3-X2)+M3*s^2*X3+B3*s*X3
+disp(F)
+disp(zero," 0 =")
+disp(zro," 0 = ")
+
+disp("F-V equations are")
+
+V=L1*s*I1 + R1*I1 + R2*(I1-I2)+I1/(s*C1)
+zero=L2*s*I2 + I2/(s*C3) + R2*(I2-I1)+(I2-I3)/(s*C2)
+zro=(I3-I2)/(s*C2)+L3*s*I3+R3*I3
+disp(V)
+disp(zero)
+disp(zro)
\ No newline at end of file diff --git a/257/CH4/EX4.16/example_4_16.sce b/257/CH4/EX4.16/example_4_16.sce new file mode 100644 index 000000000..7767fceca --- /dev/null +++ b/257/CH4/EX4.16/example_4_16.sce @@ -0,0 +1,22 @@ +syms K1 K2 x1 x2 x3 B1 B2 M1 M2 V Q L C1 R i1 i2 i3 C2 L1 L2
+disp("equilibrium equations are")
+F=K1*(x1-x2)
+disp(F)
+zero=M1*s^2*x2+K1*(x2-x1)+B1*s*(x2-x3)
+disp(zero)
+zro=M2*s^2*x3+B2*s*x3+K2*x3+B1*s*(x3-x2)
+disp(zro)
+
+//force-voltage method
+F=V;
+X=Q;
+M=L;
+K=1/C;
+B=R;
+disp("F-V equations are")
+V=s*(i1-i2)/C1
+disp(V,"V = ")
+zero=L1*s*i2+(i2-i1)/(s*C)+R1*(i2-i3)
+disp(zero)
+zro=L2*s*i3+R2*i3+i3/(s*C2)+R1*(i3-i2)
+disp(zro)
\ No newline at end of file diff --git a/257/CH4/EX4.17/example_4_17.sce b/257/CH4/EX4.17/example_4_17.sce new file mode 100644 index 000000000..6c7ef98fb --- /dev/null +++ b/257/CH4/EX4.17/example_4_17.sce @@ -0,0 +1,7 @@ +syms xo D1 K1 D2 K2 x1 s C1 C2 R1 R2
+zero=xo*(s*D1+K1+D2*s+K2)-x1*(D1*s+K1)
+disp((D1*s+K1)/(s*D1+K1+D2*s+K2),"xo/x1 = ")
+
+E1=i1*(R1+1/(s*C1)+R2+1/(s*C2))
+Eo=i1*(R2+1/(s*C2))
+disp(Eo/E1,"Eo/E1 = ")
\ No newline at end of file diff --git a/257/CH4/EX4.18/example_4_18.sce b/257/CH4/EX4.18/example_4_18.sce new file mode 100644 index 000000000..2d4c44da9 --- /dev/null +++ b/257/CH4/EX4.18/example_4_18.sce @@ -0,0 +1,23 @@ +syms s t V q L C1 R K1 x1 x2 phi1 phi2 L1 R1 R2 L1 L2
+
+//F=K1*(x1-x2)
+//0=K1*(X2-X1) + M2*s^2*X2 + K2*X2 + B2*s*X2
+
+//F-V anolagy
+
+x1=q1;
+x2=q2;
+K1=1/C1;
+B=R;
+disp("V = 1/C1 * (q1-q2)")
+disp("0=1/C1*(q2-q1) + L2*s^2*q2 + q2/C2 + R2*s*q2")
+
+//F-I ANOLOGY
+
+M=C;
+B=1/R;
+K=1/L;
+
+disp("I=1/L1*(phi1-phi2)")
+disp("0=1/L1*(phi2-phi1) + C2*s^2*phi2 + 1/R2*s*phi2 + 1/L*phi2")
+
diff --git a/257/CH4/EX4.19/example_4_19.sce b/257/CH4/EX4.19/example_4_19.sce new file mode 100644 index 000000000..21d4919cf --- /dev/null +++ b/257/CH4/EX4.19/example_4_19.sce @@ -0,0 +1,6 @@ +syms B1 x1 x2 B2 K M s
+disp("differential equations are")
+F=B1*s*(x1-x2)
+disp(F)
+zero=B1*s*(x2-x1)+M*s^2*x2+K*x2+B2*s*x2
+disp(zero)
\ No newline at end of file diff --git a/257/CH4/EX4.2/example_4_2.sce b/257/CH4/EX4.2/example_4_2.sce new file mode 100644 index 000000000..74a256d4d --- /dev/null +++ b/257/CH4/EX4.2/example_4_2.sce @@ -0,0 +1,24 @@ +syms s t V q L C R L1 L2 X1 X2 q1 R1 R2 q2 X
+
+//F-V anolagy
+F=V;
+x=q;
+M=L;
+K=1/C;
+B=R;
+
+V=L1*q1*s^2 + R1*s*q1 + R2*s*(X1-X2)
+//0=L2*s^2*q2 + (1/C)*q2 + R2*s*(q2-q1)
+//REPLACING I/s=Q
+disp("V=L1*s*I1 + R1*I1 + R2*(I1-I2)") //LOOP 1
+disp("0=L2*s*I2 + 1/(s*C) + R2*(I2-I1)") //LOOP 2
+
+//F-I ANOLOGY
+
+phi=X;
+F=I;
+
+I=phi*(C*s^2 + 1/(R*s) + 1/L)
+//REPLACING phi=V/s
+I=V*(s*C + 1/R + 1/(s*L))
+disp("i(t)=c*diff(v) + v/R + 1/L*int(v)") //taking laplace inverse
diff --git a/257/CH4/EX4.20/example_4_20.sce b/257/CH4/EX4.20/example_4_20.sce new file mode 100644 index 000000000..e8619fdda --- /dev/null +++ b/257/CH4/EX4.20/example_4_20.sce @@ -0,0 +1,17 @@ +syms i1 i2 R1 R2 C s L x1 x2 B1 B2 M K R
+disp("loop equations are")
+V=i1*(R1+R2)+1/C*('i1-i2')/s-i2*R2
+disp(V)
+zero=L*s*i2+i2*R2-i1*R2+(i1-i2)/(C*s)
+disp(zero)
+
+//force-voltage method
+F=V;
+M=L;
+K=1/C;
+B=R;
+disp("F-V equtions are")
+F=s*x1*(B1+B2)+K*(x1-x2)-s*x2*B2
+disp(F)
+zero=M*s^2*x2+B2*(x2-x1)*s+K*(x2-x1)
+disp(zero)
\ No newline at end of file diff --git a/257/CH4/EX4.21/example_4_21.sce b/257/CH4/EX4.21/example_4_21.sce new file mode 100644 index 000000000..ef7ed077a --- /dev/null +++ b/257/CH4/EX4.21/example_4_21.sce @@ -0,0 +1,8 @@ +syms M1 X1 B1 K X2 M2 B2
+
+F=M1*X1*s^2 + B1*s*X1 + K*X1 + K1*(X1-X2)
+//M2*X2*s^2 + K1*(X2-X1)=0
+X2=X1*K1/(s^2*M2+K1)
+
+disp(X2/F,"X2/F = ")
+
diff --git a/257/CH4/EX4.3/example_4_3.sce b/257/CH4/EX4.3/example_4_3.sce new file mode 100644 index 000000000..2d4c44da9 --- /dev/null +++ b/257/CH4/EX4.3/example_4_3.sce @@ -0,0 +1,23 @@ +syms s t V q L C1 R K1 x1 x2 phi1 phi2 L1 R1 R2 L1 L2
+
+//F=K1*(x1-x2)
+//0=K1*(X2-X1) + M2*s^2*X2 + K2*X2 + B2*s*X2
+
+//F-V anolagy
+
+x1=q1;
+x2=q2;
+K1=1/C1;
+B=R;
+disp("V = 1/C1 * (q1-q2)")
+disp("0=1/C1*(q2-q1) + L2*s^2*q2 + q2/C2 + R2*s*q2")
+
+//F-I ANOLOGY
+
+M=C;
+B=1/R;
+K=1/L;
+
+disp("I=1/L1*(phi1-phi2)")
+disp("0=1/L1*(phi2-phi1) + C2*s^2*phi2 + 1/R2*s*phi2 + 1/L*phi2")
+
diff --git a/257/CH4/EX4.4/example_4_4.sce b/257/CH4/EX4.4/example_4_4.sce new file mode 100644 index 000000000..c5f4942a6 --- /dev/null +++ b/257/CH4/EX4.4/example_4_4.sce @@ -0,0 +1,17 @@ +syms V q L C R I phi
+
+//T=J diff(diff(theta,t),t) + K*theta + B*diff(theta,t)
+
+//F-V anolagy
+T=V;
+theta=q;
+J=L;
+K=1/C;
+B=R;
+disp("V= L*s*I + R*I + I/(s*C)")
+
+//F-C anology
+
+T=I;
+theta=phi
+disp("I= C*V*s + V/R + V/(s*L)")
diff --git a/257/CH4/EX4.5/example_4_5.sce b/257/CH4/EX4.5/example_4_5.sce new file mode 100644 index 000000000..54a05271e --- /dev/null +++ b/257/CH4/EX4.5/example_4_5.sce @@ -0,0 +1,22 @@ +syms V C1 q1 q2 L1 R1
+
+disp("equivalent systems equations")
+disp("T = K1 *(theta1-theta2)")
+disp("0=K1*(theta3-theta2) + J1*s^2*theta2 + B1*s*theta2 + K*(theta2-theta3) + B*s*(theta2-theta3) ")
+disp("0=K*(theta3-theta2) + B*s*(theta3-theta2) + J2*s^2*theta3 + B2*s*theta3 + K2*theta3")
+
+
+
+//F-V anology
+
+T=V;
+K1=1/C1;
+theta1=q1;
+theta2=q2;
+J1=L1;
+B1=R1;
+disp("FV analogy")
+disp(" V = 1/C1 *(q1-q2)")
+disp("0=1/C1*(q3-q2) + L1*s^22*q2 + R1*s*q2 + 1/C*(q2-q3) + R*s*(q2-q3) ")
+disp("0=1/C*(q3-q2) + R*s*(q3-q2) + L2*s^2*q3 + R2*s*q3 + 1/C2*q3")
+
diff --git a/257/CH4/EX4.6/example_4_6.sce b/257/CH4/EX4.6/example_4_6.sce new file mode 100644 index 000000000..79a65b3d3 --- /dev/null +++ b/257/CH4/EX4.6/example_4_6.sce @@ -0,0 +1,7 @@ +syms I R C s
+
+V1=I*(R+1/(s*C))
+V2=I*(1/(s*C))
+
+disp(V2/V1,"V2/V1 = ")
+
diff --git a/257/CH4/EX4.7/example_4_7.sce b/257/CH4/EX4.7/example_4_7.sce new file mode 100644 index 000000000..ef7ed077a --- /dev/null +++ b/257/CH4/EX4.7/example_4_7.sce @@ -0,0 +1,8 @@ +syms M1 X1 B1 K X2 M2 B2
+
+F=M1*X1*s^2 + B1*s*X1 + K*X1 + K1*(X1-X2)
+//M2*X2*s^2 + K1*(X2-X1)=0
+X2=X1*K1/(s^2*M2+K1)
+
+disp(X2/F,"X2/F = ")
+
diff --git a/257/CH5/EX5.1/example_5_1.sce b/257/CH5/EX5.1/example_5_1.sce new file mode 100644 index 000000000..439a1a740 --- /dev/null +++ b/257/CH5/EX5.1/example_5_1.sce @@ -0,0 +1,8 @@ +syms G1 G2 G3 G4 H1 H2
+
+a= G1*G4 //series
+b= (a)/(1-(a*H1)) //positive feedback
+c= (b*(G2+G3)) // G2 AND G3 are in parallel
+Y= c/(1+(c*H2)) // negetive feedback
+
+disp(Y,"C/R =")
\ No newline at end of file diff --git a/257/CH5/EX5.10/example_5_10.sce b/257/CH5/EX5.10/example_5_10.sce new file mode 100644 index 000000000..ea0af2ee5 --- /dev/null +++ b/257/CH5/EX5.10/example_5_10.sce @@ -0,0 +1,12 @@ +syms H G1 G2 G3
+
+//separating the two paths we get 1+1=2 in parallel combinations
+
+//shifting take off point after 2*G3 and then after 2*G2*G3
+
+a=(2*G2*G3)/(1+(2*G2*G3*H/(2*G3)))
+b=a/(1+(H*a))
+c=G1*b
+Y=c/(1+(c*(1/(2*G2*G3))))
+
+disp(Y,"C/R = ")
diff --git a/257/CH5/EX5.11/example_5_11.sce b/257/CH5/EX5.11/example_5_11.sce new file mode 100644 index 000000000..3ecb53645 --- /dev/null +++ b/257/CH5/EX5.11/example_5_11.sce @@ -0,0 +1,28 @@ +syms G1 G2 G3 G4
+
+//for C1/R1
+
+a=(-G2)*G3*G4
+Y=G1/(1+(G1*a))
+
+disp(Y," C1/R1 = ")
+
+// for C2/R1
+
+x=(-G1)*G2*G3
+O= (x)/(1+(x*G4))
+
+disp(O,"C2/R1 = ")
+
+//for C1/R2
+
+k=(-G1)*G2*G4
+K=k/(1+(k*G3))
+ disp(K,"C1/R2 = ")
+
+//for C2/R2
+
+f=(-G1)*G3*G4
+Z= G2/(1+(G2*f))
+disp(Z,"C2/R2 = ")
+
\ No newline at end of file diff --git a/257/CH5/EX5.12/example_5_12.sce b/257/CH5/EX5.12/example_5_12.sce new file mode 100644 index 000000000..f85438faa --- /dev/null +++ b/257/CH5/EX5.12/example_5_12.sce @@ -0,0 +1,8 @@ +syms G1 G2 G3 G4 G5 G6 G7 G8
+
+a= G8/(1+(G8*G6*G7)) //feedback
+b=a*G2*G5
+c=b/(1+(b*G4*G6))
+Y= G3*G1*c //series
+
+disp(Y,"C/R = ")
diff --git a/257/CH5/EX5.13/example_5_13.sce b/257/CH5/EX5.13/example_5_13.sce new file mode 100644 index 000000000..3fb1f028b --- /dev/null +++ b/257/CH5/EX5.13/example_5_13.sce @@ -0,0 +1,10 @@ +syms G1 G2 G3 G4 H1 H2
+
+// combining G1 and G3 andseparating the points linked by summing point in the feedback path
+
+a=(1+(G4*H2))
+b=G1*(G2+G3) //series
+c=b/(1+(b*H1*H2))
+Y=c*a
+
+disp(Y,"C/R = ")
\ No newline at end of file diff --git a/257/CH5/EX5.14/example_5_14.sce b/257/CH5/EX5.14/example_5_14.sce new file mode 100644 index 000000000..18d594fd7 --- /dev/null +++ b/257/CH5/EX5.14/example_5_14.sce @@ -0,0 +1,12 @@ +syms G1 G2 G3 G4 H1 H2
+
+//shifting take off point of G4 , after G2
+
+a=G4/G2
+b= a+G3
+c= G1*G2/(1+(G1*G2*H1))
+d=c*b
+e=d/(1+(d*H2/G1))
+Y=e/(1+(e*1))
+
+disp(Y,"C/R = ")
\ No newline at end of file diff --git a/257/CH5/EX5.15/example_5_15.sce b/257/CH5/EX5.15/example_5_15.sce new file mode 100644 index 000000000..3cf95c9c6 --- /dev/null +++ b/257/CH5/EX5.15/example_5_15.sce @@ -0,0 +1,28 @@ +s=%s
+
+ //to find C/E
+
+a=10/(s*(s+1))
+b=a/(1+(a*0.5*s))
+c=b*(s+4) //shifting the summer to the left
+
+//(s^2+6*s)/(10*(s+4)) * C == E + 3/(s+4)*(E+C)
+Y= 10*(s+7)/(s^2+6*s-30) //solving the above equation
+
+disp(Y,"C/E = ")
+
+// to find C/R
+
+d=c/(1+c*1) //using the associative law, exchange two summing points
+e=1+(3/(s+4))
+X= d*e
+
+disp(X," C/R = ")
+
+// to find C/N if r(s)=0
+
+x= (-0.5*s)-(s+4)
+k=10/(s*(s+1))
+f=k*x //removing the summing point
+V=1/(1-f)
+disp(V,"C/N = ")
diff --git a/257/CH5/EX5.16/example_5_16.sce b/257/CH5/EX5.16/example_5_16.sce new file mode 100644 index 000000000..fc17b2a36 --- /dev/null +++ b/257/CH5/EX5.16/example_5_16.sce @@ -0,0 +1,9 @@ +syms G1 G2 G3 H1 H2
+
+// combine the two summing points
+a= G3+G1
+b= G2/(1-(G2*H1))
+c= a*b
+Y=c/(1+c*H2)
+
+disp(Y,"C/R = ")
\ No newline at end of file diff --git a/257/CH5/EX5.17/example_5_17.sce b/257/CH5/EX5.17/example_5_17.sce new file mode 100644 index 000000000..f79ff5d45 --- /dev/null +++ b/257/CH5/EX5.17/example_5_17.sce @@ -0,0 +1,13 @@ +syms Ro Ra Rb Rc Rd
+
+//shifting summing points to left of 1/Ra and 1/Rb and combining the summing points
+a=((1/Ra)*Rc)/(1+(1/Ra)*Rc*1)
+b=(Rd/Rb)/(1+(Rd/Rb))
+//shift input summing points to the right and combine the three summing points
+c=(1/Ro)/(1+(1/Ro)*(Ra*Rc/(Ra+Rc)))
+
+d=c/(1-(b*Rb*c))
+e=a-b
+Y=e*d
+
+disp(Y,"Io/Vi = ")
\ No newline at end of file diff --git a/257/CH5/EX5.18/example_5_18.sce b/257/CH5/EX5.18/example_5_18.sce new file mode 100644 index 000000000..85e639146 --- /dev/null +++ b/257/CH5/EX5.18/example_5_18.sce @@ -0,0 +1,11 @@ +s=%s
+
+a=(1/(s+2))/(1+(1/(s+2)*4))
+b=a*(3*s/(s+4)) //shifting take off point to the right
+c=b/(1+(b*(5/s)))
+d=1+ ( (s/(s+3)) * ((s+4)/(3*s)) )
+Y=d*c
+
+disp(Y,"Y/R = ")
+
+disp((s+3)*(s^2+10*s+39))
\ No newline at end of file diff --git a/257/CH5/EX5.19/example_5_19.sce b/257/CH5/EX5.19/example_5_19.sce new file mode 100644 index 000000000..65d1cbb0b --- /dev/null +++ b/257/CH5/EX5.19/example_5_19.sce @@ -0,0 +1,11 @@ +syms G1 G2 G3 H1
+
+//shifting summing points to left
+//using accosiative law to exchange the summing points, redcusing minor feedback loop and reducing parallel combination of G3/G1 and 1
+
+a= (G3/G1)+1
+b=G1/(1+G1)
+c=a*b*G2
+Y=c/(1+(c*H1))
+
+disp(Y,"C/R = ")
\ No newline at end of file diff --git a/257/CH5/EX5.2/example_5_2.sce b/257/CH5/EX5.2/example_5_2.sce new file mode 100644 index 000000000..6972bf745 --- /dev/null +++ b/257/CH5/EX5.2/example_5_2.sce @@ -0,0 +1,21 @@ +syms G1 G2 G3 G4 G5 H5
+
+//with X(s)=0
+
+a= G2/(G2+1)
+b= a*G3*(G5/(1+G5*H5)) //G5 and H5 are in a loop
+c= b/(1+b) //unity feedback
+Y= G1*c
+
+disp(Y,"R/S=")
+
+//with R(s)=0
+
+x=G2/(1+G2)
+y=G5/(1+G5*H5)
+z=x*(-G3)
+Y2=y/(1-(z))
+
+disp(Y2,"X/C = ")
+
+
diff --git a/257/CH5/EX5.20/example_5_20.sce b/257/CH5/EX5.20/example_5_20.sce new file mode 100644 index 000000000..63df4f67c --- /dev/null +++ b/257/CH5/EX5.20/example_5_20.sce @@ -0,0 +1,13 @@ +syms M2 K2 M1 K1 B
+s=%s
+
+a=(K2/s)+B
+b=(1/(M1*s))/(1+((1/(M1*s)*(K1/s) )))
+//shifting summing point S2 before 1/m2*s and interchange positions of S1 and S2 using associative law
+c=(1/M2*s)*a
+d=c/(1+c)
+e=d*b
+f=e/(1+(e*M2*s))
+Y=f*(1/s)
+
+disp(Y," Y/R = ")
\ No newline at end of file diff --git a/257/CH5/EX5.21/example_5_21.sce b/257/CH5/EX5.21/example_5_21.sce new file mode 100644 index 000000000..65046d483 --- /dev/null +++ b/257/CH5/EX5.21/example_5_21.sce @@ -0,0 +1,14 @@ +s=%s;
+syms t s;
+
+F=(1- (3*%e^(-2*t)) + (2*%e^(-3*t)) );
+y=laplace(F,t,s);
+
+G=1
+x=laplace(G,t,s);
+
+disp((y/x),"closed loop transfer function is")
+
+T=y/x;
+
+disp((T/(1-T)) , "openloop transfer function is")
\ No newline at end of file diff --git a/257/CH5/EX5.22/example_5_22.sce b/257/CH5/EX5.22/example_5_22.sce new file mode 100644 index 000000000..65046d483 --- /dev/null +++ b/257/CH5/EX5.22/example_5_22.sce @@ -0,0 +1,14 @@ +s=%s;
+syms t s;
+
+F=(1- (3*%e^(-2*t)) + (2*%e^(-3*t)) );
+y=laplace(F,t,s);
+
+G=1
+x=laplace(G,t,s);
+
+disp((y/x),"closed loop transfer function is")
+
+T=y/x;
+
+disp((T/(1-T)) , "openloop transfer function is")
\ No newline at end of file diff --git a/257/CH5/EX5.23/example_5_23.sce b/257/CH5/EX5.23/example_5_23.sce new file mode 100644 index 000000000..3fb1f028b --- /dev/null +++ b/257/CH5/EX5.23/example_5_23.sce @@ -0,0 +1,10 @@ +syms G1 G2 G3 G4 H1 H2
+
+// combining G1 and G3 andseparating the points linked by summing point in the feedback path
+
+a=(1+(G4*H2))
+b=G1*(G2+G3) //series
+c=b/(1+(b*H1*H2))
+Y=c*a
+
+disp(Y,"C/R = ")
\ No newline at end of file diff --git a/257/CH5/EX5.24/example_5_24.sce b/257/CH5/EX5.24/example_5_24.sce new file mode 100644 index 000000000..c9d247081 --- /dev/null +++ b/257/CH5/EX5.24/example_5_24.sce @@ -0,0 +1,9 @@ +syms G1 G3 G4 H1 H2
+
+a=G1+G3
+b=G2/(1+(G2*H1))
+c= a*b
+d=c/(1+(c*H2))
+Y=d+G4
+
+disp(Y," C/R = ")
\ No newline at end of file diff --git a/257/CH5/EX5.3/example_5_3.sce b/257/CH5/EX5.3/example_5_3.sce new file mode 100644 index 000000000..0ce9d8903 --- /dev/null +++ b/257/CH5/EX5.3/example_5_3.sce @@ -0,0 +1,9 @@ +syms G1 G2 H1 H2
+
+a=G2/(1+(G2*H2))
+b= G1*a
+c= H1*(1+G2*H2)/G2 //shifting the take off point
+d= b/(1+b)
+Y= d/(1+(d*c))
+
+disp(Y," R/C = ")
\ No newline at end of file diff --git a/257/CH5/EX5.4/example_5_4.sce b/257/CH5/EX5.4/example_5_4.sce new file mode 100644 index 000000000..0ce9d8903 --- /dev/null +++ b/257/CH5/EX5.4/example_5_4.sce @@ -0,0 +1,9 @@ +syms G1 G2 H1 H2
+
+a=G2/(1+(G2*H2))
+b= G1*a
+c= H1*(1+G2*H2)/G2 //shifting the take off point
+d= b/(1+b)
+Y= d/(1+(d*c))
+
+disp(Y," R/C = ")
\ No newline at end of file diff --git a/257/CH5/EX5.5/example_5_5.sce b/257/CH5/EX5.5/example_5_5.sce new file mode 100644 index 000000000..4ddf21dfa --- /dev/null +++ b/257/CH5/EX5.5/example_5_5.sce @@ -0,0 +1,8 @@ +syms G1 G2 G3 G4 H1 H2
+
+a= G1*G2 //shifting the take off point
+b= a/(1+(a*H2))
+c=(1+(G3/G2))
+Y= b*c*(G4/(1+G4*H1))
+
+disp(Y,"C/R = ")
\ No newline at end of file diff --git a/257/CH5/EX5.6/example_5_6.sce b/257/CH5/EX5.6/example_5_6.sce new file mode 100644 index 000000000..3d1888017 --- /dev/null +++ b/257/CH5/EX5.6/example_5_6.sce @@ -0,0 +1,10 @@ +syms G1 G2 G3 H1 H2
+
+a=G2/(1+G2)
+b=1+G3
+c= b*a //shifting the take off point
+d= (1/(1+G3))+(H2)
+e= d*H1
+Y= a*b/e
+
+disp(Y,"R/C = ")
\ No newline at end of file diff --git a/257/CH5/EX5.7/example_5_7.sce b/257/CH5/EX5.7/example_5_7.sce new file mode 100644 index 000000000..ab618e626 --- /dev/null +++ b/257/CH5/EX5.7/example_5_7.sce @@ -0,0 +1,8 @@ +syms G1 G2 G3 H1 H2 H3
+
+a= G3/(1+G3*H1*H2) //feedback
+b=G2*a/(1+(G2*a))
+c=G1*b
+Y=c/(1+c*H1*H2*H3)
+
+disp(Y,"C/R = ")
diff --git a/257/CH5/EX5.8/example_5_8.sce b/257/CH5/EX5.8/example_5_8.sce new file mode 100644 index 000000000..38d5c0bb6 --- /dev/null +++ b/257/CH5/EX5.8/example_5_8.sce @@ -0,0 +1,12 @@ +syms G1 G2 G3 H1 H2
+
+//shifting the taake off points twice to the left
+a=G1/(1+G1*H1*G2)
+b=(1+(G3/G2))
+c=a*b
+d=G2/(1+(G2*H2))
+e=c*d
+f=(-H1)*G2*H2
+Y=e/1+(e*f)
+
+disp(Y,"C/R = ")
diff --git a/257/CH5/EX5.9/example_5_9.sce b/257/CH5/EX5.9/example_5_9.sce new file mode 100644 index 000000000..07c6d9880 --- /dev/null +++ b/257/CH5/EX5.9/example_5_9.sce @@ -0,0 +1,11 @@ +syms H1 H2 H3 G1 G2 G3 G4
+
+//shifting summing points before G1 and take off points after G4
+
+a= G1*G2/(1+(G1*G2*H1))
+b= G3*G4/(1+(G3*G4*H2))
+c=a*b
+Y= c/(1+(c*(H3/(G1*G4))))
+
+disp(Y,"C/R = ")
+
diff --git a/257/CH6/EX6.1/example6_1.sce b/257/CH6/EX6.1/example6_1.sce new file mode 100644 index 000000000..0f74a72dd --- /dev/null +++ b/257/CH6/EX6.1/example6_1.sce @@ -0,0 +1,17 @@ +syms G1 G2 G3 G4 G5 G6 H1 H2;
+
+T1=G1*G3*G4*G5*G6;
+T2=G1*G2*G6;
+
+L1=-G4*H1;
+L2=-G3*G4*G5*H2;
+L3=-G2*H2;
+
+delta=1-(L1+L2+L3)+(L1*L3)
+del1=1;
+del2=1-L1
+
+TF=(T1*del1 + T2*del2)/delta ;
+disp(TF,"tf=")
+
+
diff --git a/257/CH6/EX6.10/example6_10.sce b/257/CH6/EX6.10/example6_10.sce new file mode 100644 index 000000000..a691657a1 --- /dev/null +++ b/257/CH6/EX6.10/example6_10.sce @@ -0,0 +1,19 @@ +syms R C Vi s Vo;
+
+T1=(s*R*C)
+T2=1/(s*R*C);
+T3=1
+
+L1=-(s*R*C)
+L2=-1/(s*R*C);
+L3=-1;
+
+delta=1-(L1+L2+L3)+(L1*L2)
+del1=1;
+del2=1-L1
+del3=1
+
+TF=(T1*del1 + T2*del2 + T3*del3)/delta ;
+disp(TF,"Vo/VI = ")
+
+
diff --git a/257/CH6/EX6.11/example6_11.sce b/257/CH6/EX6.11/example6_11.sce new file mode 100644 index 000000000..c2008fa92 --- /dev/null +++ b/257/CH6/EX6.11/example6_11.sce @@ -0,0 +1,18 @@ +syms r1 r2 r3 r4 a ;
+
+T1=(r3*r4)/(r1*r2)
+T2=(a*r4)/(r1);
+
+L1=-(r3/r1)
+L2=-r3/(r2);
+L3=-r4/r2;
+L4=a*r3/r1
+
+delta=1-(L1+L2+L3+L4)+(L1*L3)
+del1=1;
+del2=1;
+
+TF=(T1*del1 + T2*del2)/delta ;
+disp(TF,"Vo/VI = ")
+
+
diff --git a/257/CH6/EX6.12/example6_12.sce b/257/CH6/EX6.12/example6_12.sce new file mode 100644 index 000000000..d89430e9a --- /dev/null +++ b/257/CH6/EX6.12/example6_12.sce @@ -0,0 +1,17 @@ +syms G1 G2 G3 G4 H1 H2;
+
+T1=G1*G3*G2;
+T2=G1*G2*G4;
+
+L1=-G1*G2*H1;
+L2=G1*G2*G3*H2;
+L3=G2*G1*G4*H2;
+
+delta=1-(L1+L2+L3)
+del1=1;
+del2=1;
+
+TF=(T1*del1 + T2*del2)/delta ;
+disp(TF,"C/R = ")
+
+
diff --git a/257/CH6/EX6.13/example6_13.sce b/257/CH6/EX6.13/example6_13.sce new file mode 100644 index 000000000..33414d576 --- /dev/null +++ b/257/CH6/EX6.13/example6_13.sce @@ -0,0 +1,25 @@ +syms G1 G2 G3 G4 G5 G6 G7 G8 H1 H2;
+
+T1=G1*G2*G3;
+T2=G4*G5*G6;
+T3=G1*G7*G6;
+T4=G4*G8*G3;
+T5=G4*G8*(-H2)*G7*G6;
+T6=G1*G7*(-H1)*G8*G3;
+
+L1=-G5*H1;
+L2=-G2*H2;
+L3=G7*G8*H1*H2;
+
+delta=1-(L1+L2+L3)+(L1*L2)
+del1=1-L1;
+del2=1-L2;
+del3=1
+del4=1
+del5=1
+del6=1
+
+TF=(T1*del1 + T2*del2 + T3*del3 + T4*del4 + T5*del5 + T6*del6)/delta ;
+disp(TF,"C/R = ")
+
+
diff --git a/257/CH6/EX6.14/example6_14.sce b/257/CH6/EX6.14/example6_14.sce new file mode 100644 index 000000000..2e09c17ae --- /dev/null +++ b/257/CH6/EX6.14/example6_14.sce @@ -0,0 +1,8 @@ +syms R1 s C1 R2 C2 Vi Vo I;
+
+Z= (R1/(s*C1))/(R1+(1/(s*C1)))
+
+Ei= Z*I + R2*I + I/(s*C2)
+Eo= I*(R2 + 1/(s*C2))
+
+disp(Eo/Ei, " Eo/Ei = ")
\ No newline at end of file diff --git a/257/CH6/EX6.15/example6_15.sce b/257/CH6/EX6.15/example6_15.sce new file mode 100644 index 000000000..ccc300bde --- /dev/null +++ b/257/CH6/EX6.15/example6_15.sce @@ -0,0 +1,19 @@ +syms G1 G2 G3 G4 H1 H2 ;
+
+T1=G1*G3*G2;
+T2=G1*G4;
+
+L1=-G1*G2*H1;
+L2=-G3*G2*H2;
+L3=-G4*H2;
+L4=G5*G3*G2
+L5=-G1*G4
+
+delta=1-(L1+L2+L3+L4+L5)
+del1=1;
+del2=1;
+
+TF=(T1*del1 + T2*del2)/delta ;
+disp(TF,"C/R = ")
+
+
diff --git a/257/CH6/EX6.16/example6_16.sce b/257/CH6/EX6.16/example6_16.sce new file mode 100644 index 000000000..39fa3e4bc --- /dev/null +++ b/257/CH6/EX6.16/example6_16.sce @@ -0,0 +1,16 @@ +T1=1*5*10*1;
+T2=1*10*1;
+
+L1=10*(-1);
+L2=1*(-2);
+L3=5*10*1*(-1);
+L4=10*1*(-1)
+
+delta=1-(L1+L2+L3+L4)+(L1*L4)
+del1=1;
+del2=1-L1;
+
+TF=(T1*del1 + T2*del2)/delta ;
+disp(TF,"C/R = ")
+
+
diff --git a/257/CH6/EX6.17/example6_17.sce b/257/CH6/EX6.17/example6_17.sce new file mode 100644 index 000000000..368c6944a --- /dev/null +++ b/257/CH6/EX6.17/example6_17.sce @@ -0,0 +1,21 @@ +s=%s
+
+R1=100*10^3
+R2=10^6
+C1=10*10^-6
+C2=10^-6
+
+
+T1=(1/R1)*(1/(s*C1))*(1/R2)*(1/(s*C2))
+
+L1=-1/(s*C1*R1);
+L2=-1/(s*R2*C1);
+L3=-1/(s*C2*R2);
+
+delta=1-(L1+L2+L3)+(L1*L3)
+del1=1;
+
+TF=(T1*del1)/delta ;
+disp(TF,"C/R = ")
+
+
diff --git a/257/CH6/EX6.18/example6_18.sce b/257/CH6/EX6.18/example6_18.sce new file mode 100644 index 000000000..df442e946 --- /dev/null +++ b/257/CH6/EX6.18/example6_18.sce @@ -0,0 +1,17 @@ +syms G1 G2 G3 H1 H2;
+
+T1=G1*G2;
+T2=G3*G2;
+
+L1=-G1*H2*G2;
+L2=-G3*H2*G2;
+L3=-G2*H1;
+
+delta=1-(L1+L2+L3)
+del1=1;
+del2=1;
+
+TF=(T1*del1 + T2*del2)/delta ;
+disp(TF,"C/R = ")
+
+
diff --git a/257/CH6/EX6.19/example6_19.sce b/257/CH6/EX6.19/example6_19.sce new file mode 100644 index 000000000..8a3fc45d8 --- /dev/null +++ b/257/CH6/EX6.19/example6_19.sce @@ -0,0 +1,19 @@ +syms G1 G2 G3 G4 H1 H2;
+
+T1=G1*G3*G2;
+T2=G4;
+
+L1=-G1*H1*G2;
+L2=-G3*H2*G2;
+L3=-G2*G1*G3;
+L4=-G4;
+L5=-G2*G4*H1*H2;
+
+delta=1-(L1+L2+L3+L4+L5)
+del1=1;
+del2=1
+
+TF=(T1*del1 + T2*del2)/delta ;
+disp(TF,"C/R = ")
+
+
diff --git a/257/CH6/EX6.2/example6_2.sce b/257/CH6/EX6.2/example6_2.sce new file mode 100644 index 000000000..f8a3033fe --- /dev/null +++ b/257/CH6/EX6.2/example6_2.sce @@ -0,0 +1,15 @@ +syms R1 R2 I1 I2 C V1 VI L s Vo;
+
+T1=L/(R1*R2*C)
+
+L1=-1/(s*R1*C);
+L2=-1/(s*R2*C);
+L3=-(s*L)/R2;
+
+delta=1-(L1+L2+L3)+(L1*L3)
+del1=1;
+
+TF=(T1*del1)/delta ;
+disp(TF,"Vo/VI = ")
+
+
diff --git a/257/CH6/EX6.20/example6_20.sce b/257/CH6/EX6.20/example6_20.sce new file mode 100644 index 000000000..bc412f8fd --- /dev/null +++ b/257/CH6/EX6.20/example6_20.sce @@ -0,0 +1,18 @@ +syms R1 Ro;
+
+T1=1/(R1)*(R1*2)*(1/Ro);
+T2=(1/R1)*(R1)*(-1/Ro);
+
+L1=-2*R1/(R1);
+L2=-2*R1/(Ro);
+L3=-1;
+L4=-(R1/Ro)
+
+delta=1-(L1+L2+L3+L4)+(L1*L3 + L1*L4 + L2*L3)
+del1=1-L3;
+del2=1-L1;
+
+TF=(T1*del1 + T2*del2)/delta ;
+disp(TF,"Io/Vi = ")
+
+
diff --git a/257/CH6/EX6.21/example6_21.sce b/257/CH6/EX6.21/example6_21.sce new file mode 100644 index 000000000..4a21ae988 --- /dev/null +++ b/257/CH6/EX6.21/example6_21.sce @@ -0,0 +1,17 @@ +syms R1 R2 R3 C1 C2 C3 L1 L2 s;
+
+T1=1/(R3*(R1+s*L1)*(R2+s*L2)*C1*C2*C3*s^3)
+
+L1=-1/(s*(R1+s*L1)*C1);
+L2=-1/(s*(R2+s*L2)*C1);
+L3=1/(-(s*L2+R2)*s*C2);
+L4=1/(-s*R3*C2)
+L5=-1/(s*R3*C3)
+
+delta=1-(L1+L2+L3+L4+L5)+(L1*L3 + L1*L4 + L1*L5 + L2*L4 + L2*L5 + L3*L5)-(L1*L3*L5)
+del1=1;
+
+TF=(T1*del1)/delta ;
+disp(TF,"Vo/VI = ")
+
+
diff --git a/257/CH6/EX6.22/example6_22.sce b/257/CH6/EX6.22/example6_22.sce new file mode 100644 index 000000000..e1a326884 --- /dev/null +++ b/257/CH6/EX6.22/example6_22.sce @@ -0,0 +1,19 @@ +syms a12 a23 a34 a45 a32 a43 a25 a24 a44
+
+T1= a12*a23*a34*a45;
+T2=a24*a12*a45;
+T3=a12*a25;
+
+L1=a23*a32;
+L2=a34*a43;
+L3=a44;
+L4=a24*a43*a32;
+
+delta=1-(L1+L2+L3+L4)+(L1*L3)
+del1=1;
+del2=1;
+del3=1-(L2+L3)
+
+TF=(T1*del1 + T2*del2 + T3*del3)/delta ;
+disp(TF,"C/R = ")
+
diff --git a/257/CH6/EX6.23/example6_23.sce b/257/CH6/EX6.23/example6_23.sce new file mode 100644 index 000000000..79370d2e9 --- /dev/null +++ b/257/CH6/EX6.23/example6_23.sce @@ -0,0 +1,23 @@ +syms G1 G2 G3 G4 G5 G6 H1 H2;
+
+T1=G1*G2;
+T2=G3*G4;
+T3=G1*G6*G4;
+T4=G2*G3*G5
+
+L1=-G2*H1;
+L2=-G3*H2;
+L3=G5*G6;
+L4=-G4*H1*G6;
+L5=-G1*G6*H2
+
+delta=1-(L1+L2+L3+L4+L5)+(L1*L2)
+del1=1;
+del2=1;
+del3=1
+del4=1;
+
+TF=(T1*del1 + T2*del2 + T3*del3 + T4*del4)/delta ;
+disp(TF,"C/R = ")
+
+
diff --git a/257/CH6/EX6.24/example6_24.sce b/257/CH6/EX6.24/example6_24.sce new file mode 100644 index 000000000..3c51b182e --- /dev/null +++ b/257/CH6/EX6.24/example6_24.sce @@ -0,0 +1,19 @@ +s=%s
+
+T1=1*3*6*1
+T3=1*2*5*1
+T2=1*4*7*1
+T4=1*2*(1/(s+1))*1*6
+T5=1*2*(1/(s+1))*(1/(s+1))*7*1
+T6=1*3*(1/(s+1))*7*1
+
+delta=1
+del1=1
+del2=1
+del3=1
+del4=1
+del5=1
+del6=1
+
+TF=(T1*del1 + T2*del2 + T3*del3 + T4*del4 + T5*del5 + T6*del6)/delta
+disp(TF,"Y/R = ")
diff --git a/257/CH6/EX6.25/example6_25.sce b/257/CH6/EX6.25/example6_25.sce new file mode 100644 index 000000000..a9ff30b86 --- /dev/null +++ b/257/CH6/EX6.25/example6_25.sce @@ -0,0 +1,25 @@ +syms G1 G2 G3 G4 G5 H2 H3;
+
+T1=G1*G3*G2;
+T2=G1*G3*G5;
+T3=G4*G2*G3;
+T4=-G4*G2*G5*G3*H2
+
+L1=-G2*H3;
+L2=-G3*H3;
+L3=-G5*H2*H3*G3;
+L4=-G1*G2*G3;
+L5=-G1*G3*G5;
+L6=-G2*G3*G4;
+L7=G2*G3*G4*G5*H2;
+
+delta=1-(L1+L2+L3+L4+L5+L6+L7)
+del1=1;
+del2=1;
+del3=1
+del4=1;
+
+TF=(T1*del1 + T2*del2 + T3*del3 + T4*del4)/delta ;
+disp(TF,"C/R = ")
+
+
diff --git a/257/CH6/EX6.26/example6_26.sce b/257/CH6/EX6.26/example6_26.sce new file mode 100644 index 000000000..0c176fe4b --- /dev/null +++ b/257/CH6/EX6.26/example6_26.sce @@ -0,0 +1,15 @@ +syms R1 R2 R3 C1 C2 s;
+
+T1=1/(R1*R2*R3*C1*C2*s^2)
+
+L1=-1/(s*R1*C1);
+L2=-1/(s*R2*C1);
+L3=-1/(s*R2*C2);
+
+delta=1-(L1+L2+L3+L4)+(L1*L3 + L1*L4)
+del1=1;
+
+TF=(T1*del1)/delta ;
+disp(TF,"Vo/VI = ")
+
+
diff --git a/257/CH6/EX6.27/example6_27.sce b/257/CH6/EX6.27/example6_27.sce new file mode 100644 index 000000000..2b0acbee7 --- /dev/null +++ b/257/CH6/EX6.27/example6_27.sce @@ -0,0 +1,25 @@ +syms G1 G2 G3 G4 G5 H1 H2 H3 H4 H5 H6;
+
+T1=G1*G3*G2*G4*G5;
+T2=G1*G3*G5*G4;
+T3=G4*G2*G1*G5;
+T4=-G4*G2*G5*G1*H2
+
+L1=-G2*H2;
+L2=-G4*H4;
+L3=-G5*H5;
+L4=-G4*G5*H6*G2*G3;
+L5=-G2*G4*G5*H6;
+L6=-H1;
+L7=-H3;
+
+delta=1-(L1+L2+L3+L4+L5+L6+L7)+(L1*L2+L1*L3+L6*L2+L6*L3+L7*L2+L7*L3+L6*L7)-(L6*L7*L2+L6*L7*L3)
+del1=1;
+del2=1-L6;
+del3=1-L7;
+del4=1;
+
+TF=(T1*del1 + T2*del2 + T3*del3 + T4*del4)/delta ;
+disp(TF,"C/R = ")
+
+
diff --git a/257/CH6/EX6.4/example6_4.sce b/257/CH6/EX6.4/example6_4.sce new file mode 100644 index 000000000..79370d2e9 --- /dev/null +++ b/257/CH6/EX6.4/example6_4.sce @@ -0,0 +1,23 @@ +syms G1 G2 G3 G4 G5 G6 H1 H2;
+
+T1=G1*G2;
+T2=G3*G4;
+T3=G1*G6*G4;
+T4=G2*G3*G5
+
+L1=-G2*H1;
+L2=-G3*H2;
+L3=G5*G6;
+L4=-G4*H1*G6;
+L5=-G1*G6*H2
+
+delta=1-(L1+L2+L3+L4+L5)+(L1*L2)
+del1=1;
+del2=1;
+del3=1
+del4=1;
+
+TF=(T1*del1 + T2*del2 + T3*del3 + T4*del4)/delta ;
+disp(TF,"C/R = ")
+
+
diff --git a/257/CH6/EX6.5/example6_5.sce b/257/CH6/EX6.5/example6_5.sce new file mode 100644 index 000000000..b778ada31 --- /dev/null +++ b/257/CH6/EX6.5/example6_5.sce @@ -0,0 +1,17 @@ +syms G1 G2 G3 G4 G5 H1 H2;
+
+T1=G1*G3*G4*G2;
+T2=G4*G5;
+
+L1=-G2*H1;
+L2=-G3*G1*G4*G2*H2;
+L3=-G4*G5*H2;
+
+delta=1-(L1+L2+L3)+(L1*L3)
+del1=1;
+del2=1-L1
+
+TF=(T1*del1 + T2*del2)/delta ;
+disp(TF,"C/R = ")
+
+
diff --git a/257/CH6/EX6.6/example6_6.sce b/257/CH6/EX6.6/example6_6.sce new file mode 100644 index 000000000..539f0ae84 --- /dev/null +++ b/257/CH6/EX6.6/example6_6.sce @@ -0,0 +1,17 @@ +syms G1 G2 G3 G4 G5 H1 H2 H3 H4 H5;
+
+T1=G1*G3*G4*G5*G2;
+
+L1=-G1*H1;
+L2=-G3*H3;
+L3=-G2*H2*G1*G3;
+L4=-G4*H4;
+L5=-G5*H5;
+
+delta=1-(L1+L2+L3+L4+L5)+(L1*L2+L1*L5+L1*L4+L2*L5+L3*L5)-(L1*L2*L5)
+del1=1;
+
+TF=(T1*del1)/delta ;
+disp(TF,"C/R = ")
+
+
diff --git a/257/CH6/EX6.8/example6_8.sce b/257/CH6/EX6.8/example6_8.sce new file mode 100644 index 000000000..8e44a943c --- /dev/null +++ b/257/CH6/EX6.8/example6_8.sce @@ -0,0 +1,16 @@ +syms G1 G2 G3 G4 G5 G6 G7 G8;
+
+T1=G1*G8*G7*G5*G6;
+T2=G1*G2*G3*G4*G8;
+
+L1=-G6*H5;
+L2=-G3*H3;
+
+delta=1-(L1+L2)+(L1*L2)
+del1=1-L2;
+del2=1-L1;
+
+TF=(T1*del1 + T2*del2)/delta ;
+disp(TF,"C/R = ")
+
+
diff --git a/257/CH6/EX6.9/example6_9.sce b/257/CH6/EX6.9/example6_9.sce new file mode 100644 index 000000000..8109e1816 --- /dev/null +++ b/257/CH6/EX6.9/example6_9.sce @@ -0,0 +1,24 @@ +syms G1 G2 G3 G4 G5 G6 G7 G8 H1 H2 H3 H4;
+
+T1=G1*G2*G3*G5*G6*G4;
+T2=G1*G2*G7*G6;
+T3=G1*G2*G3*G4*G8
+
+L1=-G4*H4;
+L2=-G5*G6*H1;
+L3=-G2*G3*G4*G5*H2
+L4=-G2*G7*H2
+L5=-G1*G2*G3*G4*G5*G6*H3
+L6=-G1*G2*G6*G7*H3
+L7=-G1*G2*G3*G4*G8*H3
+L8=-G8*H1
+
+delta=1-(L1+L2+L3+L4+L5+L6+L7+L8)+(L1*L4+L4*L8+L1*L6)
+del1=1;
+del2=1-L1;
+del3=1
+
+TF=(T1*del1 + T2*del2 + T3*del3)/delta ;
+disp(TF,"C/R = ")
+
+
diff --git a/257/CH7/EX7.1/example_7_1.sce b/257/CH7/EX7.1/example_7_1.sce new file mode 100644 index 000000000..95a3a2983 --- /dev/null +++ b/257/CH7/EX7.1/example_7_1.sce @@ -0,0 +1,19 @@ +p=poly([2 1],'s','coeff');
+q=poly([0 4 5 1],'s','coeff');
+G=40*p/q //gain FACTOR=40
+H=1
+y=G*H //type 1
+
+syms s
+Kp=limit(s*y/s,s,0) //Kp= position error coefficient
+Kv=limit(s*G*H,s,0) //Kv= velocity error coefficient
+Ka=limit(s^2*G*H,s,0) //Ka= accelaration error coefficient
+
+disp(Ka ,"Ka = ")
+disp(Kv ,"Kv = ")
+disp(Kp ,"Kp = ")
+
+Ess=4/Kv
+disp(Ess, "Ess = ")
+
+
diff --git a/257/CH7/EX7.10/example_7_10.sce b/257/CH7/EX7.10/example_7_10.sce new file mode 100644 index 000000000..2da8f6dcf --- /dev/null +++ b/257/CH7/EX7.10/example_7_10.sce @@ -0,0 +1,13 @@ +syms k1 k2 s
+T= k1/(s^s+k1*k2*s+k1)
+
+Mp=25 //given
+zeta=0.4037
+Tp=4
+
+omegaN=%pi/(Tp*(sqrt(1-zeta^2)))
+disp(omegaN,"omegaN = ")
+k1=omegaN^2
+disp(k1," k1 = ")
+k2=2*zeta/(sqrt(k1))
+disp(k2," k2 = ")
diff --git a/257/CH7/EX7.11/example_7_11.sce b/257/CH7/EX7.11/example_7_11.sce new file mode 100644 index 000000000..8d59e1fe4 --- /dev/null +++ b/257/CH7/EX7.11/example_7_11.sce @@ -0,0 +1,15 @@ +syms s
+TF=8/(s^2+4*s+8)
+
+Mp=25 //given
+
+omegaN=sqrt(8)
+disp(omegaN,"omegaN = ")
+zeta=4/(2*omegaN)
+disp(zeta,"zeta = ")
+omegaD=omegaN*(sqrt(1-zeta^2))
+Tp=%pi/omegaD
+disp(Tp," Tp = ")
+disp(%e^(-%pi*zeta/sqrt(1-zeta^2))," Mp = ")
+disp(4/(zeta*omegaN)," Ts = ")
+
diff --git a/257/CH7/EX7.12/example_7_12.sce b/257/CH7/EX7.12/example_7_12.sce new file mode 100644 index 000000000..5046b66b4 --- /dev/null +++ b/257/CH7/EX7.12/example_7_12.sce @@ -0,0 +1,20 @@ +T=15/(s^2+4*s+18)
+
+omegaN=sqrt(18)
+zeta=4/(2*omegaN)
+disp(omegaN,"omegaN = ")
+disp(zeta,"zeta = ")
+omegaD=omegaN*sqrt(1-zeta^2)
+for(n=1:3)
+ t=n*%pi/omegaD
+ if(n==2)
+ T=t
+ disp(t,"t for 1st undershoot = ")
+ disp(T,"time period for oscillations = ")
+ end
+
+end
+
+disp(4/(zeta*omegaN),"Ts = ")
+disp(Ts/T,"total number of cycles = ")
+disp(1/T," frequency of damped oscillations = ")
\ No newline at end of file diff --git a/257/CH7/EX7.13/example_7_13.sce b/257/CH7/EX7.13/example_7_13.sce new file mode 100644 index 000000000..b0d6586e5 --- /dev/null +++ b/257/CH7/EX7.13/example_7_13.sce @@ -0,0 +1,18 @@ +syms f J K s t
+
+T=1/(J*(s^2+(f/J)*s+(K/J))) //Q/I
+
+omegaN=sqrt(K/J)
+Mp=6 //given
+zeta=0.667
+
+omegaD=omegaN*sqrt(1-zeta^2)
+Tp=%pi/omegaD
+disp(Tp," Tp = ")
+
+I=laplace('10',t,s)
+Q=I*T
+x=limit(s*Q,s,0);
+disp(10/0.5," K = ")
+disp(K/omegaN^2," J= ")
+disp(zeta*(2*sqrt(K*J))," f = ")
diff --git a/257/CH7/EX7.14/example_7_14.sce b/257/CH7/EX7.14/example_7_14.sce new file mode 100644 index 000000000..3a71f7bb8 --- /dev/null +++ b/257/CH7/EX7.14/example_7_14.sce @@ -0,0 +1,11 @@ +s=%s;
+T=20/(s+10)
+
+syms t s;
+y=ilaplace(T,s,t);
+
+T1=20/((s+10)*s)
+c1=ilaplace(T1,s,t)
+
+T2=20/((s+10)*s^2)
+c2=ilaplace(T2,s,t)
diff --git a/257/CH7/EX7.15/example_7_15.sce b/257/CH7/EX7.15/example_7_15.sce new file mode 100644 index 000000000..08d365f5e --- /dev/null +++ b/257/CH7/EX7.15/example_7_15.sce @@ -0,0 +1,17 @@ +syms A s t
+
+G=(A)/(s+A);
+R=1/s; //unit step input
+C=G*R;
+c=ilaplace(C,s,t);
+disp(c," c(t) = ")
+
+A=-log(1-0.95)/60 //system attains 95% of final value at t=60
+disp(A," A = ")
+
+
+
+
+
+
+
diff --git a/257/CH7/EX7.16/example_7_16.sce b/257/CH7/EX7.16/example_7_16.sce new file mode 100644 index 000000000..f648c5c5e --- /dev/null +++ b/257/CH7/EX7.16/example_7_16.sce @@ -0,0 +1,24 @@ +q=poly([0 200 4 1],'s','coeff');
+G=k/q //gain FACTOR=k
+H=1
+y=G*H //type 1
+
+syms s
+Kp=limit(s*y/s,s,0) //Kp= position error coefficient
+Kv=limit(s*G*H,s,0) //Kv= velocity error coefficient
+Ka=limit(s^2*G*H,s,0) //Ka= accelaration error coefficient
+
+disp(Ka ,"Ka = ")
+disp(Kv ,"Kv = ")
+disp(Kp ,"Kp = ")
+
+//for unit step input
+A=1
+Ess=A/(Kp + 1)
+disp(Ess, "Ess for unit step input is ")
+
+disp(A/Kv, "Ess for unit ramp input is ")
+
+
+
+
diff --git a/257/CH7/EX7.18/example_7_18.sce b/257/CH7/EX7.18/example_7_18.sce new file mode 100644 index 000000000..122592c50 --- /dev/null +++ b/257/CH7/EX7.18/example_7_18.sce @@ -0,0 +1,21 @@ +q=poly([0 1 2],'s','coeff');
+G=1/q //gain FACTOR=1
+H=1
+F=1/(1+G*H)
+
+syms t s;
+Ko=limit(s*F/s,s,0) //Ko=Lt s->0 (1/(1+G(s)H(S))
+d=diff(s*F/s,s);
+K1=limit(diff(s*F/s,s),s,0) //K1=Lt s->0 (dF(s)/ds)
+K2=limit(diff(d,s),s,0) //K2=Lt s->0 (d2F(s)/ds)
+dd=diff(d,s)
+K3=limit(diff(dd,s),s,0)
+disp(K3)
+
+a=(2+4*t+6*(t^2)+2*(t^3))
+b=diff( a,t)
+c=diff(b,t)
+d=diff(c,t)
+e=(Ko*a)+(K1*b)+(K2*c)+(K3*d) //error by dynamic coefficient method
+disp(e,"error")
+
diff --git a/257/CH7/EX7.19/example_7_19.sce b/257/CH7/EX7.19/example_7_19.sce new file mode 100644 index 000000000..3c923811e --- /dev/null +++ b/257/CH7/EX7.19/example_7_19.sce @@ -0,0 +1,21 @@ +q=poly([0 20 1],'s','coeff');
+G=400/q //gain FACTOR=k
+H=1
+T=G/(1+G*H)
+
+omegaN=sqrt(400)
+zeta=20/(2*omegaN)
+disp(omegaN,"omegaN = ")
+disp(zeta,"zeta = ")
+omegaD=omegaN*sqrt(1-zeta^2)
+theta= atan(sqrt(1-zeta^2)/zeta)
+disp(theta,"theta = ")
+
+syms s t
+c=(1-(%e^(-zeta*omegaN*t))/sqrt(1-zeta^2)*sin(omegaD*t+theta))
+disp(c, " c = ")
+
+Kv=limit(s*G*H,s,0)
+disp(Kv, " Kv = ")
+Ess=1/Kv
+disp(Ess, " Ess = ")
diff --git a/257/CH7/EX7.2/example_7_2.sce b/257/CH7/EX7.2/example_7_2.sce new file mode 100644 index 000000000..39caa5edd --- /dev/null +++ b/257/CH7/EX7.2/example_7_2.sce @@ -0,0 +1,22 @@ +p=poly([6 5 1],'s','coeff');
+q=poly([0 20 29 10 1],'s','coeff');
+G=10*p/q //gain FACTOR=10
+H=1
+y=G*H //type 1
+
+syms s
+Kp=limit(s*y/s,s,0) //Kp= position error coefficient
+Kv=limit(s*G*H,s,0) //Kv= velocity error coefficient
+Ka=limit(s^2*G*H,s,0) //Ka= accelaration error coefficient
+
+disp(Ka ,"Ka = ")
+disp(Kv ,"Kv = ")
+disp(Kp ,"Kp = ")
+
+Ess1=3/(1+Kp)
+disp(Ess1, "Ess1 = ")
+Ess2=1/(Kv)
+disp(Ess2, "Ess2 = ")
+
+disp("Ess3=2/(Ka) = infinity")
+
diff --git a/257/CH7/EX7.20/example_7_20.sce b/257/CH7/EX7.20/example_7_20.sce new file mode 100644 index 000000000..6046eda15 --- /dev/null +++ b/257/CH7/EX7.20/example_7_20.sce @@ -0,0 +1,14 @@ +syms k T s
+T= k/(s^2+k*T*s+k)
+
+Mp=20 //given
+zeta=0.4559
+Tp=2
+
+omegaN=%pi/(Tp*(sqrt(1-zeta^2)))
+disp(omegaN,"omegaN = ")
+k=omegaN^2
+disp(k," k = ")
+T=2*zeta*omegaN/k
+disp(T," T = ")
+
diff --git a/257/CH7/EX7.21/example_7_21.sce b/257/CH7/EX7.21/example_7_21.sce new file mode 100644 index 000000000..b6b0e5227 --- /dev/null +++ b/257/CH7/EX7.21/example_7_21.sce @@ -0,0 +1,18 @@ +Mp=30 //given
+Ts=5
+zeta=0.358
+
+omegaN=4/(zeta*Ts)
+disp(omegaN,"omegaN = ")
+
+omegaD=omegaN*(sqrt(1-zeta^2))
+Tp=%pi/omegaD
+disp(Tp," Tp = ")
+
+TF=omegaN^2/(s^2+2*zeta*omegaN*s+omegaN^2)
+disp(TF, "transfer function = ")
+
+theta=atan(sqrt(1-zeta^2)/zeta)
+disp(theta," theta = ")
+c=(((1-(%e^(-zeta*omegaN*t))/sqrt(1-zeta^2)*sin(omegaD*t+theta))))
+disp(c," c = ")
\ No newline at end of file diff --git a/257/CH7/EX7.22/example_7_22.sce b/257/CH7/EX7.22/example_7_22.sce new file mode 100644 index 000000000..d52d32235 --- /dev/null +++ b/257/CH7/EX7.22/example_7_22.sce @@ -0,0 +1,8 @@ +syms t s
+p=poly([1 2],'s','coeff');
+q=poly([0 1 2 1],'s','coeff');
+T=p/q //gain FACTOR=40
+R=1/s;
+C=R*T;
+c=ilaplace(C,s,t)
+disp(c," c = ")
\ No newline at end of file diff --git a/257/CH7/EX7.23/example_7_23.sce b/257/CH7/EX7.23/example_7_23.sce new file mode 100644 index 000000000..c84912b9d --- /dev/null +++ b/257/CH7/EX7.23/example_7_23.sce @@ -0,0 +1,17 @@ +q=poly([0 10 1],'s','coeff');
+G=k/q
+H=1
+T=G/(1+G*H)
+
+zeta=0.5
+k=100/(4*zeta^2)
+disp(k," k = ")
+
+omegaN=sqrt(k)
+disp(omegaN,"omegaN = ")
+Ts=4/(zeta*omegaN)
+disp(Ts," Ts = ")
+omegaD=omegaN*(sqrt(1-zeta^2))
+Tp=%pi/omegaD
+disp(Tp," Tp = ")
+disp(%e^(-%pi*zeta/sqrt(1-zeta^2))," Mp = ")
\ No newline at end of file diff --git a/257/CH7/EX7.24/example_7_24.sce b/257/CH7/EX7.24/example_7_24.sce new file mode 100644 index 000000000..1e7a70a3e --- /dev/null +++ b/257/CH7/EX7.24/example_7_24.sce @@ -0,0 +1,10 @@ +syms s T k
+T=k/(T*s^2+s+k)
+
+disp(sqrt(k/T)," omegaN = ")
+disp(1/(2*sqrt(k*T))," zeta = ")
+
+disp("in case1 we have k2=1/16*k1")
+disp("in case2 we have 4=T2/T1")
+
+disp("so T must be multiplied by 4 to reduce zeta from 0.6 to 0.3")
diff --git a/257/CH7/EX7.25/example_7_25.sce b/257/CH7/EX7.25/example_7_25.sce new file mode 100644 index 000000000..d096d58f5 --- /dev/null +++ b/257/CH7/EX7.25/example_7_25.sce @@ -0,0 +1,25 @@ +syms s t
+q=poly([1 0.4],'s','coeff');
+q=poly([0 0.6 1],'s','coeff');
+G=p/q //gain FACTOR=k
+H=1
+T=1/(1+G*H)
+R=1/s
+C=R*T;
+disp(C)
+c=ilaplace(C,s,t)
+disp(c, " c = ")
+
+omegaN=sqrt(1) //comparing denominator with standard form
+disp(omegaN,"omegaN = ")
+zeta=1/(2*omegaN)
+disp(zeta,"zeta=")
+omegaD=omegaN*sqrt(1-zeta^2)
+disp(omegaD,"omegaD = ")
+theta=atan(sqrt(1-zeta^2)/zeta)
+
+disp((%pi-theta)/omegaD," Tr = ")
+Tp=%pi/omegaD
+disp(Tp," Tp = ")
+disp(%e^(-%pi*zeta/sqrt(1-zeta^2))," Mp = ")
+disp(4/(zeta*omegaN)," Ts = ")
diff --git a/257/CH7/EX7.26/example_7_26.sce b/257/CH7/EX7.26/example_7_26.sce new file mode 100644 index 000000000..ddff1c556 --- /dev/null +++ b/257/CH7/EX7.26/example_7_26.sce @@ -0,0 +1,28 @@ +syms s;
+G=k/((s+2)*s*(s^2+2*s+5))
+H=1;
+
+Kv=limit(s*G*H,s,0) //Kv= velocity error coefficient
+A=1 //magnitude of unit ramp
+Ess=A/Kv
+disp("Ess is less than 0.2 ") //10/k < 0.2
+disp("k lies between 50 and infinity")
+
+Kp=limit(s*y/s,s,0) //Kp= position error coefficient
+Ka=limit(s^2*G*H,s,0) //Ka= accelaration error coefficient
+
+disp(Ka ,"Ka = ")
+disp(Kv ,"Kv = ")
+disp(Kp ,"Kp = ")
+
+Ess1=2/(1+Kp)
+disp(Ess1, "Ess1 = ")
+Ess2=4/(Kv)
+disp(Ess2, "Ess2 = ")
+//Ess3=1/(Ka)
+//disp(Ess3, "Ess3 = ")
+
+disp(" e =Ess1+Ess2+Ess3 = infinity")
+
+
+
diff --git a/257/CH7/EX7.27/example_7_27.sce b/257/CH7/EX7.27/example_7_27.sce new file mode 100644 index 000000000..8616a1efc --- /dev/null +++ b/257/CH7/EX7.27/example_7_27.sce @@ -0,0 +1,15 @@ +syms s
+G= 100/(s^2*(s+2)*(s+5))
+
+syms s
+Kp=limit(s*y/s,s,0) //Kp= position error coefficient
+Kv=limit(s*G*H,s,0) //Kv= velocity error coefficient
+Ka=limit(s^2*G*H,s,0) //Ka= accelaration error coefficient
+
+disp(Ka ,"Ka = ")
+disp(Kv ,"Kv = ")
+disp(Kp ,"Kp = ")
+
+Ess=1/(1+Kp) + (1/Kv) + (4/Ka)
+disp(Ess, "Ess = ")
+
diff --git a/257/CH7/EX7.28/example_7_28.sce b/257/CH7/EX7.28/example_7_28.sce new file mode 100644 index 000000000..6d40eb32d --- /dev/null +++ b/257/CH7/EX7.28/example_7_28.sce @@ -0,0 +1,15 @@ +q=poly([0 2 1],'s','coeff');
+G=8/q
+H=1
+
+omegaN=sqrt(8)
+zeta=2/(2*omegaN)
+disp(omegaN,"omegaN = ")
+disp(zeta,"zeta = ")
+
+syms s a
+T=8/(s^2+s*(2+8*a)+8)
+disp((0.7*2*sqrt(8)-2)/8, " a for zeta=0.7 is ")
+disp(%e^(-%pi*zeta/sqrt(1-zeta^2))," Mp for zeta=0.3535 is ")
+
+
diff --git a/257/CH7/EX7.3/example_7_3.sce b/257/CH7/EX7.3/example_7_3.sce new file mode 100644 index 000000000..10eaa8a71 --- /dev/null +++ b/257/CH7/EX7.3/example_7_3.sce @@ -0,0 +1,21 @@ +p=3/5
+q=poly([10 7 1],'s','coeff');
+G=p/q
+H=1
+y=G*H
+F1=1/(1+y)
+
+F=1/(1+y);
+disp(F,"1/(1+G(s)H(s))=")
+syms t s;
+Ko=limit(s*F/s,s,0) //Ko=Lt s->0 (1/(1+G(s)H(S))
+d=diff(s*F/s,s);
+K1=limit(diff(s*F/s,s),s,0) //K1=Lt s->0 (dF(s)/ds)
+K2=limit(diff(d,s),s,0) //K2=Lt s->0 (d2F(s)/ds)
+
+a=(6+5*t+6*(t^2)/2)
+b=diff((6+5*t+6*(t^2)/2) ,t)
+c=diff(b,t)
+e=Ko*a+K1*b+K2*c //error by dynamic coefficient method
+disp(e,"e = ")
+
diff --git a/257/CH7/EX7.30/example_7_30.sce b/257/CH7/EX7.30/example_7_30.sce new file mode 100644 index 000000000..8f667abfb --- /dev/null +++ b/257/CH7/EX7.30/example_7_30.sce @@ -0,0 +1,10 @@ +q=poly([0 1 1],'s','coeff');
+G=k/q //gain FACTOR=k
+H=1
+T=G/(1+G*H)
+
+zeta=0.5911; //given
+Tp=0.5;
+omegaN=%pi/(Tp*(sqrt(1-zeta^2)))
+disp(omegaN,"omegaN = ")
+disp(omegaN^2," k = ")
\ No newline at end of file diff --git a/257/CH7/EX7.31/example_7_31.sce b/257/CH7/EX7.31/example_7_31.sce new file mode 100644 index 000000000..a805531fa --- /dev/null +++ b/257/CH7/EX7.31/example_7_31.sce @@ -0,0 +1,9 @@ +syms k1 k2 s k t
+T= s/(s+k1*k2+k1*k) //solving the block diagram
+
+T1=k1/(s*(s+2*k1))
+y=ilaplace(T1,s,t)
+disp(y, " y = ")
+
+
+
diff --git a/257/CH7/EX7.32/example_7_32.sce b/257/CH7/EX7.32/example_7_32.sce new file mode 100644 index 000000000..f99f5f541 --- /dev/null +++ b/257/CH7/EX7.32/example_7_32.sce @@ -0,0 +1,18 @@ +syms G M U Q ;
+
+T1=U*Q*G;
+T2=M*G;
+
+L1=-G*Q;
+
+delta=1-(L1)
+del1=1;
+del2=1;
+
+TF=(T1*del1 + T2*del2)/delta ;
+disp(TF,"T = ")
+
+disp("sensitivity T wrt G is 1/(1+Q*G)")
+
+
+
diff --git a/257/CH7/EX7.33/example_7_33.sce b/257/CH7/EX7.33/example_7_33.sce new file mode 100644 index 000000000..a50eba5d6 --- /dev/null +++ b/257/CH7/EX7.33/example_7_33.sce @@ -0,0 +1,10 @@ +syms s t
+p=poly([8 1],'s','coeff');
+q=poly([0 4 1],'s','coeff');
+G=2*p/q //gain FACTOR=2
+H=1
+T=G/(1+G*H)
+R=1/s;
+C=T*R
+c=ilaplace(C,s,t)
+disp(c,"c = ")
\ No newline at end of file diff --git a/257/CH7/EX7.34/example_7_34.sce b/257/CH7/EX7.34/example_7_34.sce new file mode 100644 index 000000000..a04cdfd7f --- /dev/null +++ b/257/CH7/EX7.34/example_7_34.sce @@ -0,0 +1,16 @@ +syms s k
+q=poly([0 0 1],'s','coeff');
+G=100/q //gain FACTOR=100
+H=1+k*s
+y=G*H
+
+T=G/(1+G*H)
+
+omegaN=sqrt(100) //comparing denominator with standard form
+disp(omegaN,"omegaN = ")
+zeta=100*k/(2*omegaN)
+disp(zeta,"zeta=")
+
+Mp=4.32;
+zeta=0.7071;
+disp(zeta/5," k = ")
\ No newline at end of file diff --git a/257/CH7/EX7.35/example_7_35.sce b/257/CH7/EX7.35/example_7_35.sce new file mode 100644 index 000000000..ac81e2b0e --- /dev/null +++ b/257/CH7/EX7.35/example_7_35.sce @@ -0,0 +1,16 @@ +K=33;
+B=15;
+M=3
+
+T=1/(M*s^2+B*s+K)
+
+omegaN=sqrt(11) //comparing denominator with standard form
+disp(omegaN,"omegaN = ")
+zeta=5/(2*omegaN)
+disp(zeta,"zeta=")
+disp(%e^(-%pi*zeta/sqrt(1-zeta^2))," Mp = ")
+omegaD=omegaN*(sqrt(1-zeta^2))
+Tp=%pi/omegaD
+disp(Tp," Tp = ")
+disp(4/(zeta*omegaN)," Ts = ")
+
diff --git a/257/CH7/EX7.36/example_7_36.sce b/257/CH7/EX7.36/example_7_36.sce new file mode 100644 index 000000000..16f41fe51 --- /dev/null +++ b/257/CH7/EX7.36/example_7_36.sce @@ -0,0 +1,20 @@ +ss=%s
+G=64/(s*(s+9.6))
+H=1
+T=G/(1+G*H)
+
+omegaN=sqrt(64)
+disp(omegaN,"omegaN = ")
+zeta=9.6/(2*omegaN)
+disp(zeta,"zeta = ")
+omegaD=omegaN*(sqrt(1-zeta^2))
+theta=atan(sqrt(1-zeta^2)/zeta)
+disp(theta," theta = ")
+
+c=((1-(%e^(-zeta*omegaN*t))/sqrt(1-zeta^2)*sin(omegaD*t+theta)))
+disp(c, "c = ")
+
+Tp=%pi/omegaD
+disp(Tp," Tp = ")
+disp(4/(zeta*omegaN)," Ts = ")
+
diff --git a/257/CH7/EX7.37/example_7_37.sce b/257/CH7/EX7.37/example_7_37.sce new file mode 100644 index 000000000..450e6044b --- /dev/null +++ b/257/CH7/EX7.37/example_7_37.sce @@ -0,0 +1,32 @@ +syms s
+
+T1=12/((s+3)*(s+4));
+T2=-3/(s+4);
+
+L1=-24/((s+3)*(s+4)*(s+5));
+
+delta=1-(L1)
+del1=1;
+del2=1;
+
+T=(T1*del1 + T2*del2)/delta ;
+disp(T,"T = ")
+
+G=T/(1-T)
+disp(G," G=")
+H=1
+
+Kp=limit(s*G*H/s,s,0) //Kp= position error coefficient
+Kv=limit(s*G*H,s,0) //Kv= velocity error coefficient
+disp(Kv ,"Kv = ")
+disp(Kp ,"Kp = ")
+
+Ess=1/(1+Kp)
+disp(Ess, "Ess for step input is = ")
+disp(" for ramp input e=infinity")
+
+
+
+
+
+
diff --git a/257/CH7/EX7.38/example_7_38.sce b/257/CH7/EX7.38/example_7_38.sce new file mode 100644 index 000000000..152db1bf6 --- /dev/null +++ b/257/CH7/EX7.38/example_7_38.sce @@ -0,0 +1,14 @@ +Mp=0.5/2 *100;
+zeta=0.4036;
+
+for(n=0:3)
+ T=n*%pi/omegaD
+ if(n==2)
+ T=0.2
+ omegaN=2*%pi/(T*(sqrt(1-zeta^2)))
+ disp(omegaN," omegaN = ")
+ end
+end
+
+
+
\ No newline at end of file diff --git a/257/CH7/EX7.39/example_7_39.sce b/257/CH7/EX7.39/example_7_39.sce new file mode 100644 index 000000000..e0bfedad2 --- /dev/null +++ b/257/CH7/EX7.39/example_7_39.sce @@ -0,0 +1,19 @@ +syms s
+
+G=10/(s^2*(s^2+s+10))
+H=s;
+T=G/(1+G*H)
+
+Kp=limit(s*T/s,s,0) //Kp= position error coefficient
+Kv=limit(s*T,s,0) //Kv= velocity error coefficient
+Ka=limit(s^2*T,s,0) //Ka= accelaration error coefficient
+
+disp(Ka ,"Ka = ")
+disp(Kv ,"Kv = ")
+disp(Kp ,"Kp = ")
+
+R=10/s
+T1=T/(1+T)
+C=R*T1;
+Css=limit(s*C,s,0)
+disp(Css," Css = ")
\ No newline at end of file diff --git a/257/CH7/EX7.4/example_7_4.sce b/257/CH7/EX7.4/example_7_4.sce new file mode 100644 index 000000000..10eaa8a71 --- /dev/null +++ b/257/CH7/EX7.4/example_7_4.sce @@ -0,0 +1,21 @@ +p=3/5
+q=poly([10 7 1],'s','coeff');
+G=p/q
+H=1
+y=G*H
+F1=1/(1+y)
+
+F=1/(1+y);
+disp(F,"1/(1+G(s)H(s))=")
+syms t s;
+Ko=limit(s*F/s,s,0) //Ko=Lt s->0 (1/(1+G(s)H(S))
+d=diff(s*F/s,s);
+K1=limit(diff(s*F/s,s),s,0) //K1=Lt s->0 (dF(s)/ds)
+K2=limit(diff(d,s),s,0) //K2=Lt s->0 (d2F(s)/ds)
+
+a=(6+5*t+6*(t^2)/2)
+b=diff((6+5*t+6*(t^2)/2) ,t)
+c=diff(b,t)
+e=Ko*a+K1*b+K2*c //error by dynamic coefficient method
+disp(e,"e = ")
+
diff --git a/257/CH7/EX7.5/example_7_5.sce b/257/CH7/EX7.5/example_7_5.sce new file mode 100644 index 000000000..03acf2645 --- /dev/null +++ b/257/CH7/EX7.5/example_7_5.sce @@ -0,0 +1,17 @@ +q=poly([0 1 1],'s','coeff');
+G=10/q //gain FACTOR=10
+H=1
+T=G/(1+G*H)
+
+Stg=(1/(1+G*H))
+Stg= (-1+ %i*1)/(49+%i*1) //at s= %i*w where w=1
+disp(abs(Stg),"sensitivity at w=1 is ")
+
+//sensitivity wrt H
+T=-G*H/(1+G*H)
+Sth=-50/(49+%i*1) //at s= %i*w where w=1
+disp(abs(Sth),"sensitivity wrt H at w=1 is ")
+
+
+
+
diff --git a/257/CH7/EX7.6/example_7_6.sce b/257/CH7/EX7.6/example_7_6.sce new file mode 100644 index 000000000..d22f9f087 --- /dev/null +++ b/257/CH7/EX7.6/example_7_6.sce @@ -0,0 +1,14 @@ +syms s Td
+G=(1+s*Td)/(s*(s+1.6))
+H=1
+T=G/(1+G*H)
+
+omegaN=2; //comparing the denominator with standard form
+zeta=1 //zeta=(1.6+4*Td)/(4)
+Td=(4-1.6)/4
+disp(Td,"Td = ")
+Ts=4/(zeta*omegaN)
+disp(Ts," Ts = ")
+
+
+
diff --git a/257/CH7/EX7.7/example_7_7.sce b/257/CH7/EX7.7/example_7_7.sce new file mode 100644 index 000000000..bfb158cc8 --- /dev/null +++ b/257/CH7/EX7.7/example_7_7.sce @@ -0,0 +1,26 @@ +q=poly([0 0 6 5 1],'s','coeff');
+G=1/q //gain FACTOR=k
+H=1
+y=G*H
+disp(y)
+
+syms s
+Kp=limit(s*y/s,s,0) //Kp= position error coefficient
+Kv=limit(s*G*H,s,0) //Kv= velocity error coefficient
+Ka=limit(s^2*G*H,s,0) //Ka= accelaration error coefficient
+
+disp(Ka ,"Ka = ")
+disp(Kv ,"Kv = ")
+disp(Kp ,"Kp = ")
+
+Ess1=1/(1+Kp)
+disp(Ess1, "Ess1 = ")
+Ess2=10/(Kv)
+disp(Ess2, "Ess2 = ")
+Ess3=40/(Ka)
+disp(Ess3, "Ess3 = ")
+
+Ess=Ess1+Ess2+Ess3 //Ess=10 given
+k=Ess/10
+disp(k, "k = ")
+
diff --git a/257/CH7/EX7.8/example_7_8.sce b/257/CH7/EX7.8/example_7_8.sce new file mode 100644 index 000000000..668ac6dc5 --- /dev/null +++ b/257/CH7/EX7.8/example_7_8.sce @@ -0,0 +1,12 @@ +q=poly([1 1.105 0.1055 0.0005],'s','coeff');
+G=20000/q //gain FACTOR=20000
+H=1
+y=G*H
+p=poly([0 1],'s','coeff');
+R=1000/p
+
+Kp=limit(s*y/s,s,0)
+Ess=1000/(1+Kp)
+
+Css=1000-Ess
+disp(Css," Css = ")
diff --git a/257/CH7/EX7.9/example_7_9.sce b/257/CH7/EX7.9/example_7_9.sce new file mode 100644 index 000000000..c98cafa1f --- /dev/null +++ b/257/CH7/EX7.9/example_7_9.sce @@ -0,0 +1,14 @@ +q=poly([24 5 1],'s','coeff');
+G=20/q
+H=1
+y=G*H
+
+omegaN=sqrt(24) //comparing denominator with standard form
+disp(omegaN,"omegaN = ")
+zeta=5/(2*omegaN)
+disp(zeta,"zeta=")
+omegaD=omegaN*sqrt(1-zeta^2)
+disp(omegaD,"omegaD = ")
+syms t
+theta=atan(sqrt(1-zeta^2)/zeta)
+disp(20/24*((1-(%e^(-zeta*omegaN*t))/sqrt(1-zeta^2)*sin(omegaD*t+theta))))
\ No newline at end of file diff --git a/257/CH8/EX8.10/example_8_10.sce b/257/CH8/EX8.10/example_8_10.sce new file mode 100644 index 000000000..c5a1af4c4 --- /dev/null +++ b/257/CH8/EX8.10/example_8_10.sce @@ -0,0 +1,21 @@ +s=%s
+P=s^4+2*s^2+1
+disp(routh_t(P))
+r=coeff(P)
+routh=routh_t(P)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+end
+ if(c>=1)
+ printf("system is unstable")
+ else printf("no sign changes, so no roots in RHS")
+ end
+ disp("s^2 is")
+ k=roots(routh(1,:))
+ disp(k)
+
+ disp("since, s^2 is negetive, s is purely imaginary. hence the 4 roots are on the imaginary axis")
\ No newline at end of file diff --git a/257/CH8/EX8.12/example_8_12.sce b/257/CH8/EX8.12/example_8_12.sce new file mode 100644 index 000000000..ca0e2964c --- /dev/null +++ b/257/CH8/EX8.12/example_8_12.sce @@ -0,0 +1,40 @@ +s=%s
+F=s^3+4*s^2+13*s+50
+
+disp(routh_t(F))
+r=coeff(F)
+routh=routh_t(F)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("system is unstable")
+ else printf("there are no roots on RHS")
+ end
+syms s k
+G=5*k/(s*(1+s/3)*(1+s/6)*18)
+H=1
+Kv=limit(s*G*H,s,0)
+disp(Kv, " Kv = ")
+
+s=%s
+F=s^3+9*s^2+18*s+180
+
+disp(routh_t(F))
+r=coeff(F)
+routh=routh_t(F)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("system is unstable")
+ else printf("there are no roots on RHS")
+ end
diff --git a/257/CH8/EX8.14/example_8_14.sce b/257/CH8/EX8.14/example_8_14.sce new file mode 100644 index 000000000..fc06620a1 --- /dev/null +++ b/257/CH8/EX8.14/example_8_14.sce @@ -0,0 +1,24 @@ +s=%s
+F=s^6+2*s^5+8*s^4+12*s^3+20*s^2+16*s+16
+
+disp(routh_t(F))
+r=coeff(F)
+routh=routh_t(F)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("system is unstable")
+ else printf("there are no roots on RHS")
+ end
+
+
+R=sqrt(roots(routh(3,:)))
+disp(R)
+
+disp("non repeated roots on imaginary axis. hence system is marginally stable")
+
diff --git a/257/CH8/EX8.15/example_8_15.sce b/257/CH8/EX8.15/example_8_15.sce new file mode 100644 index 000000000..53f97fd04 --- /dev/null +++ b/257/CH8/EX8.15/example_8_15.sce @@ -0,0 +1,18 @@ +s=%s
+F=2*s^5+s^4+6*s^3+s+1
+
+disp(routh_t(F))
+r=coeff(F)
+routh=routh_t(F)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("system is unstable")
+ else printf("there are no roots on RHS")
+ end
+
diff --git a/257/CH8/EX8.16/example_8_16.sce b/257/CH8/EX8.16/example_8_16.sce new file mode 100644 index 000000000..424a2bd5d --- /dev/null +++ b/257/CH8/EX8.16/example_8_16.sce @@ -0,0 +1,24 @@ +//determining critical value of K
+s=%s
+syms K
+m=s^3+3*(K)*s^2+(K+2)*s+4
+cof_a_0 = coeffs(m,'s',0);
+cof_a_1 = coeffs(m,'s',1);
+cof_a_2 = coeffs(m,'s',2);
+cof_a_3 = coeffs(m,'s',3);
+
+r=[cof_a_0 cof_a_1 cof_a_2 cof_a_3]
+
+n=length(r);
+routh=[r([4,2]);r([3,1])];
+routh=[routh;-det(routh)/routh(2,1),0];
+t=routh(2:3,1:2); //extracting the square sub block of routh matrix
+routh=[routh;-det(t)/t(2,1),0]
+disp(routh,"rouths tabulation=")
+routh(3,1)=0 //For marginaly stable system
+
+
+
+
+
+
diff --git a/257/CH8/EX8.17/example_8_17.sce b/257/CH8/EX8.17/example_8_17.sce new file mode 100644 index 000000000..179904bfb --- /dev/null +++ b/257/CH8/EX8.17/example_8_17.sce @@ -0,0 +1,39 @@ +//determining critical value of K
+s=%s
+syms K
+m=s^3+10*s^2+(K+21)*s+13*K
+cof_a_0 = coeffs(m,'s',0);
+cof_a_1 = coeffs(m,'s',1);
+cof_a_2 = coeffs(m,'s',2);
+cof_a_3 = coeffs(m,'s',3);
+
+r=[cof_a_0 cof_a_1 cof_a_2 cof_a_3]
+
+n=length(r);
+routh=[r([4,2]);r([3,1])];
+routh=[routh;-det(routh)/routh(2,1),0];
+t=routh(2:3,1:2); //extracting the square sub block of routh matrix
+routh=[routh;-det(t)/t(2,1),0]
+disp(routh,"rouths tabulation=")
+routh(3,1)=0 //For marginaly stable system
+
+disp("for its closed loop poles more negetive than -1")
+s=%s
+syms K
+m=s^3+7*s^2+(K+4)*s+12*K-12
+cof_a_0 = coeffs(m,'s',0);
+cof_a_1 = coeffs(m,'s',1);
+cof_a_2 = coeffs(m,'s',2);
+cof_a_3 = coeffs(m,'s',3);
+
+r=[cof_a_0 cof_a_1 cof_a_2 cof_a_3]
+
+n=length(r);
+routh=[r([4,2]);r([3,1])];
+routh=[routh;-det(routh)/routh(2,1),0];
+t=routh(2:3,1:2); //extracting the square sub block of routh matrix
+routh=[routh;-det(t)/t(2,1),0]
+disp(routh,"rouths tabulation=")
+routh(3,1)=0 //For marginaly stable system
+
+
diff --git a/257/CH8/EX8.18/example_8_18.sce b/257/CH8/EX8.18/example_8_18.sce new file mode 100644 index 000000000..84b2438de --- /dev/null +++ b/257/CH8/EX8.18/example_8_18.sce @@ -0,0 +1,17 @@ +s=%s
+// C=s^4+10*s^3+36*s^2+70*s+75 characteristic equation//
+F=(s-2)^4+10*(s-2)^3+36*(s-2)^2+70*(s-2)+75 //shifting the origin with respect to s=-2//
+disp(routh_t(F))
+r=coeff(F)
+routh=routh_t(F)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+end
+ if(c>=1)
+ printf("there are %d roots to the right of s=-2 line",c+1)
+ else printf("system is stable")
+ end
diff --git a/257/CH8/EX8.19/example_8_19.sce b/257/CH8/EX8.19/example_8_19.sce new file mode 100644 index 000000000..f3b367aea --- /dev/null +++ b/257/CH8/EX8.19/example_8_19.sce @@ -0,0 +1,23 @@ +s=%s
+F=s^6+2*s^5+5*s^4+8*s^3+8*s^2+8*s+4
+
+disp(routh_t(F))
+r=coeff(F)
+routh=routh_t(F)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("system is unstable")
+ else
+ disp("s^2 is")
+ k=(roots(routh(3,:)))
+ disp(k)
+end
+
+if(k(2,1)==k(3,1))
+ printf("repeated roots on imaginary axis. hence unstable system")
\ No newline at end of file diff --git a/257/CH8/EX8.2/example_8_2.sce b/257/CH8/EX8.2/example_8_2.sce new file mode 100644 index 000000000..1dd56abae --- /dev/null +++ b/257/CH8/EX8.2/example_8_2.sce @@ -0,0 +1,16 @@ +s=%s;
+P=s^3+6*s^2+11*s+6;
+routh=routh_t(P)
+disp(routh)
+r=coeff(P)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("system is unstable")
+ else printf("system is stable")
+ end
\ No newline at end of file diff --git a/257/CH8/EX8.20/example_8_20.sce b/257/CH8/EX8.20/example_8_20.sce new file mode 100644 index 000000000..794126e0a --- /dev/null +++ b/257/CH8/EX8.20/example_8_20.sce @@ -0,0 +1,36 @@ +s=%s
+syms K
+m=s^4+6*s^3+30*s^2+60*s+K
+cof_a_0 = coeffs(m,'s',0);
+cof_a_1 = coeffs(m,'s',1);
+cof_a_2 = coeffs(m,'s',2);
+cof_a_3 = coeffs(m,'s',3);
+
+r=[cof_a_0 cof_a_1 cof_a_2 cof_a_3]
+
+n=length(r);
+routh=[r([4,2]);r([3,1])];
+routh=[routh;-det(routh)/routh(2,1),0];
+t=routh(2:3,1:2); //extracting the square sub block of routh matrix
+routh=[routh;-det(t)/t(2,1),0]
+disp(routh,"rouths tabulation=")
+routh(3,1)=0 //For marginaly stable system
+
+disp("for all closed loop poles to left of -1")
+s=%s
+syms K
+m=s^4+2*s^3+18*s^2+14*s+K-35
+cof_a_0 = coeffs(m,'s',0);
+cof_a_1 = coeffs(m,'s',1);
+cof_a_2 = coeffs(m,'s',2);
+cof_a_3 = coeffs(m,'s',3);
+
+r=[cof_a_0 cof_a_1 cof_a_2 cof_a_3]
+
+n=length(r);
+routh=[r([4,2]);r([3,1])];
+routh=[routh;-det(routh)/routh(2,1),0];
+t=routh(2:3,1:2); //extracting the square sub block of routh matrix
+routh=[routh;-det(t)/t(2,1),0]
+disp(routh,"rouths tabulation=")
+routh(3,1)=0 //For marginaly stable system
\ No newline at end of file diff --git a/257/CH8/EX8.21/example_8_21.sce b/257/CH8/EX8.21/example_8_21.sce new file mode 100644 index 000000000..5d16fc8d4 --- /dev/null +++ b/257/CH8/EX8.21/example_8_21.sce @@ -0,0 +1,30 @@ +s=%s
+P=s^6+s^5+5*s^4+s^3+2*s^2-2*s-8
+routh=routh_t(P)
+disp(routh)
+r=coeff(P)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("system has %d roots in RHS",c)
+ else printf("no roots in RHS")
+ end
+ k=0
+
+R=(sqrt(roots(routh(3,:)))) //real part of the roots//
+disp("s is")
+disp(R)
+for(i=1:3)
+ if(real(R(i,1)) == 0)
+ k=k+1
+ end
+end
+
+ printf("%d is in the imaginary axis and ",k) //conjugate pairs//
+ printf(" %d roots are in LHS",6-k-c) //out of 6 roots//
+
\ No newline at end of file diff --git a/257/CH8/EX8.22/ex_8_22.sce b/257/CH8/EX8.22/ex_8_22.sce new file mode 100644 index 000000000..36729e0ff --- /dev/null +++ b/257/CH8/EX8.22/ex_8_22.sce @@ -0,0 +1,20 @@ +//terms in a row become infinite//
+s=%s;
+//P=s^5+2*s^4+3*s^3+6*s^2+2*s+1;//
+//replace 's' by '1/z' to get F//
+z=%z;
+F=z^5+2*z^4+6*z^3+3*z^2+2*z+1
+disp(routh_t(F))
+r=coeff(F)
+routh=routh_t(F)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("system is unstable")
+ else printf("system is stable")
+ end
\ No newline at end of file diff --git a/257/CH8/EX8.23/example_8_23.sce b/257/CH8/EX8.23/example_8_23.sce new file mode 100644 index 000000000..17abb700e --- /dev/null +++ b/257/CH8/EX8.23/example_8_23.sce @@ -0,0 +1,27 @@ +s=%s
+P=s^6+2*s^5+9*s^4+16*s^3+24*s^2+32*s+16
+routh=routh_t(P)
+disp(routh)
+r=coeff(P)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("there are %d roots on RHS",c)
+ else printf("there are no roots in RHS")
+ end
+ disp("s is")
+R=(sqrt(roots(routh(3,:))))
+ disp(R)
+k=0
+for(i=1:3)
+ if(real (R(i,1))==0)
+ k=k+1
+ end
+ end
+
+printf("thus %d roots on imaginary axis and there are %d roots in LHS",2*(k-1),6-c-2*(k-1))
\ No newline at end of file diff --git a/257/CH8/EX8.24/example_8_24.sce b/257/CH8/EX8.24/example_8_24.sce new file mode 100644 index 000000000..335718daa --- /dev/null +++ b/257/CH8/EX8.24/example_8_24.sce @@ -0,0 +1,21 @@ +s=%s
+syms K
+m=0.125*s^3+0.875*s^2+(1.75)*s+1+K
+cof_a_0 = coeffs(m,'s',0);
+cof_a_1 = coeffs(m,'s',1);
+cof_a_2 = coeffs(m,'s',2);
+cof_a_3 = coeffs(m,'s',3);
+
+r=[cof_a_0 cof_a_1 cof_a_2 cof_a_3]
+
+n=length(r);
+routh=[r([4,2]);r([3,1])];
+routh=[routh;-det(routh)/routh(2,1),0];
+t=routh(2:3,1:2); //extracting the square sub block of routh matrix
+routh=[routh;-det(t)/t(2,1),0]
+disp(routh,"rouths tabulation=")
+routh(3,1)=0 //For marginaly stable system
+
+sys=syslin('c',1/(0.125*s^3+0.875*s^2+(1.75)*s+1))
+k=kpure(sys)
+disp(k,"K(marginal)=")
diff --git a/257/CH8/EX8.25/example_8_25.sce b/257/CH8/EX8.25/example_8_25.sce new file mode 100644 index 000000000..0d03de8b8 --- /dev/null +++ b/257/CH8/EX8.25/example_8_25.sce @@ -0,0 +1,23 @@ +s=%s
+P=s^5-s^4-2*s^3+2*s^2-8*s+8
+routh=routh_t(P)
+disp(routh)
+r=coeff(P)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("there are %d roots on RHS",c)
+ else printf("there are no roots on RHS")
+ end
+
+ disp("s^2 is")
+ disp(roots(routh(2,:)))
+
+
+
+
\ No newline at end of file diff --git a/257/CH8/EX8.26/example_8_26.sce b/257/CH8/EX8.26/example_8_26.sce new file mode 100644 index 000000000..54d87cc0c --- /dev/null +++ b/257/CH8/EX8.26/example_8_26.sce @@ -0,0 +1,21 @@ +//determining critical value of K
+s=%s
+syms K
+m=0*s^3+s^2+(K+1)*s+2*K
+cof_a_0 = coeffs(m,'s',0);
+cof_a_1 = coeffs(m,'s',1);
+cof_a_2 = coeffs(m,'s',2);
+cof_a_3 = coeffs(m,'s',3);
+
+r=[cof_a_0 cof_a_1 cof_a_2 cof_a_3]
+
+n=length(r);
+routh=[r([4,2]);r([3,1])];
+routh=[routh;-det(routh)/routh(2,1),0];
+t=routh(2:3,1:2); //extracting the square sub block of routh matrix
+routh=[routh;-det(t)/t(2,1),0]
+disp(routh,"rouths tabulation=")
+routh(3,1)=0 //For marginaly stable system
+sys=syslin('c',s*(3*s+1)/(s^3+2*s+4))
+k=kpure(sys)
+disp(k,"K(marginal)=")
\ No newline at end of file diff --git a/257/CH8/EX8.27/example_8_27.sce b/257/CH8/EX8.27/example_8_27.sce new file mode 100644 index 000000000..d1a4ff496 --- /dev/null +++ b/257/CH8/EX8.27/example_8_27.sce @@ -0,0 +1,27 @@ +s=%s
+//P=s^4+2*s^3+3*s^2+s+1
+s'=%s
+P=(s'-1)^4+2*(s'-1)^3+3*(s'-1)^2+(s'-1)+1 //putting s=s'-1
+routh=routh_t(P)
+disp(routh)
+r=coeff(P)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("there are 2*%d roots to the right of s=-1",c) //2 terms with negetive signs implies 4 sign changes//
+ else printf("system is stable")
+ end
+
+F=(s'-0.5)^4+2*(s'-0.5)^3+3*(s'-0.5)^2+(s'-0.5)+1
+disp(routh_t(F))
+r=coeff(F)
+rouths=routh_t(F)
+n=length(r)
+
+ printf("there are 2 sign changes.so there are 2 roots to the right of s=-0.5")
+
\ No newline at end of file diff --git a/257/CH8/EX8.28/example_8_28.sce b/257/CH8/EX8.28/example_8_28.sce new file mode 100644 index 000000000..7e26f1770 --- /dev/null +++ b/257/CH8/EX8.28/example_8_28.sce @@ -0,0 +1,23 @@ +//determining critical value of K
+s=%s
+syms K
+m=s^4+18*s^3+121*s^2+360*s+400-2*K^2
+cof_a_0 = coeffs(m,'s',0);
+cof_a_1 = coeffs(m,'s',1);
+cof_a_2 = coeffs(m,'s',2);
+cof_a_3 = coeffs(m,'s',3);
+
+r=[cof_a_0 cof_a_1 cof_a_2 cof_a_3]
+
+n=length(r);
+routh=[r([4,2]);r([3,1])];
+routh=[routh;-det(routh)/routh(2,1),0];
+t=routh(2:3,1:2); //extracting the square sub block of routh matrix
+routh=[routh;-det(t)/t(2,1),0]
+disp(routh,"rouths tabulation=")
+routh(3,1)=0 //For marginaly stable system
+
+disp("k marginal is")
+k=sqrt(200)
+disp(k)
+
diff --git a/257/CH8/EX8.29/example_8_29.sce b/257/CH8/EX8.29/example_8_29.sce new file mode 100644 index 000000000..6d5e0b848 --- /dev/null +++ b/257/CH8/EX8.29/example_8_29.sce @@ -0,0 +1,27 @@ +syms s K
+G=K*(s+2)/(s*(s+3)*(s^2+5*s+10))
+H=1
+Kv=limit(s*G*H,s,0)
+disp(Kv, " Kv = ")
+
+Ess=0.01 //given
+K=15/Ess
+disp(K,"K=")
+
+s=%s
+F=s^3+8*s^2+1525*s+3030
+
+disp(routh_t(F))
+r=coeff(F)
+routh=routh_t(F)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("system is unstable")
+ else printf("there are no roots on RHS")
+ end
\ No newline at end of file diff --git a/257/CH8/EX8.3/example_8_3.sce b/257/CH8/EX8.3/example_8_3.sce new file mode 100644 index 000000000..ac3949380 --- /dev/null +++ b/257/CH8/EX8.3/example_8_3.sce @@ -0,0 +1,16 @@ +s=%s;
+P=s^3+4*s^2+s+16;
+routh=routh_t(P)
+disp(routh)
+r=coeff(P)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("system is unstable")
+ else printf("system is stable")
+ end
diff --git a/257/CH8/EX8.30/example_8_30.sce b/257/CH8/EX8.30/example_8_30.sce new file mode 100644 index 000000000..37241f42f --- /dev/null +++ b/257/CH8/EX8.30/example_8_30.sce @@ -0,0 +1,34 @@ +s=%s
+
+F=s^8+s^7+4*s^6+3*s^5+14*s^4+11*s^3+20*s^2+9*s+9
+disp(routh_t(F))
+r=coeff(F)
+routh=routh_t(F)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("there are %d roots with positive real part as there are %d sign cganges",c+1,c+1) //two number of sign changes
+ else printf("no roots with positive real part")
+ end
+
+
+P=1+s^1+3*s^2+2*s^3+5*s^4+3*s^5+1*s^6
+routh=routh_t(P)
+disp(routh)
+r=coeff(P)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<=0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("there are %d roots with positive real part",c+1)
+ else printf("no roots with positive real part")
+ end
diff --git a/257/CH8/EX8.31/example_8_31.sce b/257/CH8/EX8.31/example_8_31.sce new file mode 100644 index 000000000..c1aaabd74 --- /dev/null +++ b/257/CH8/EX8.31/example_8_31.sce @@ -0,0 +1,27 @@ +syms s K
+G=(10+s)*K/(s^2*(s^2+2*s+10))
+H=1
+
+Ka=limit(s^2*G*H,s,0)
+disp(Ka, " Ka = ")
+Ess=0.1 //given
+K=1/Ess //A=1
+disp(K,"K=")
+
+s=%s
+F=s^4+2*s^3+10*s^2+10*s+100
+
+disp(routh_t(F))
+r=coeff(F)
+routh=routh_t(F)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("system is unstable")
+ else printf("there are no roots on RHS")
+ end
diff --git a/257/CH8/EX8.32/example_8_32.sce b/257/CH8/EX8.32/example_8_32.sce new file mode 100644 index 000000000..05525be20 --- /dev/null +++ b/257/CH8/EX8.32/example_8_32.sce @@ -0,0 +1,21 @@ +//determining critical value of K
+s=%s
+syms K
+m=s^4+5*s^3+5*s^2+4*s+K
+cof_a_0 = coeffs(m,'s',0);
+cof_a_1 = coeffs(m,'s',1);
+cof_a_2 = coeffs(m,'s',2);
+cof_a_3 = coeffs(m,'s',3);
+
+r=[cof_a_0 cof_a_1 cof_a_2 cof_a_3]
+
+n=length(r);
+routh=[r([4,2]);r([3,1])];
+routh=[routh;-det(routh)/routh(2,1),0];
+t=routh(2:3,1:2); //extracting the square sub block of routh matrix
+routh=[routh;-det(t)/t(2,1),0]
+disp(routh,"rouths tabulation=")
+routh(3,1)=0 //For marginaly stable system
+sys=syslin('c',1/(s^4+5*s^3+5*s^2+4*s))
+k=kpure(sys)
+disp(k,"K(marginal)=")
\ No newline at end of file diff --git a/257/CH8/EX8.33/example_8_33.sce b/257/CH8/EX8.33/example_8_33.sce new file mode 100644 index 000000000..79d877e7c --- /dev/null +++ b/257/CH8/EX8.33/example_8_33.sce @@ -0,0 +1,27 @@ +//determining critical value of K
+s=%s
+syms K
+m=s^4+12*s^3+44*s^2+48*s+K
+cof_a_0 = coeffs(m,'s',0);
+cof_a_1 = coeffs(m,'s',1);
+cof_a_2 = coeffs(m,'s',2);
+cof_a_3 = coeffs(m,'s',3);
+
+r=[cof_a_0 cof_a_1 cof_a_2 cof_a_3]
+
+n=length(r);
+routh=[r([4,2]);r([3,1])];
+routh=[routh;-det(routh)/routh(2,1),0];
+t=routh(2:3,1:2); //extracting the square sub block of routh matrix
+routh=[routh;-det(t)/t(2,1),0]
+disp(routh,"rouths tabulation=")
+routh(3,1)=0 //For marginaly stable system
+sys=syslin('c',1/(s^4+12*s^3+44*s^2+48*s))
+k=kpure(sys)
+disp(k,"K(marginal)=")
+
+omega=sqrt(k/routh(3,1))
+
+
+
+
diff --git a/257/CH8/EX8.4/example_8_4.sce b/257/CH8/EX8.4/example_8_4.sce new file mode 100644 index 000000000..2eb74881b --- /dev/null +++ b/257/CH8/EX8.4/example_8_4.sce @@ -0,0 +1,19 @@ +s=%s;
+//F=s^5+s^4+2*s^3+2*s^2+3*s+15//
+//replacing 's' by '1/z' we get F//
+z=%z;
+F=15*z^5+3*z^4+2*z^3+2*z^2+z+1;
+disp(routh_t(F))
+r=coeff(F)
+routh=routh_t(F)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("system is unstable")
+ else printf("system is stable")
+ end
diff --git a/257/CH8/EX8.5/example_8_5.sce b/257/CH8/EX8.5/example_8_5.sce new file mode 100644 index 000000000..f3503b097 --- /dev/null +++ b/257/CH8/EX8.5/example_8_5.sce @@ -0,0 +1,11 @@ +s=%s;
+F=s^6+4*s^5+3*s^4-16*s^2-64*s-48;
+//replace 's' by '1/z'//
+//F=48*z^6+64*z^5+16*z^4-3*z^2-4*z-1;
+disp(routh_t(F))
+routh=routh_t(F)
+r=coeff(F)
+n=length(r)
+c=0;
+
+disp("positive real=1, zero real part=2, negative real part=3")
diff --git a/257/CH8/EX8.6/example_8_6.sce b/257/CH8/EX8.6/example_8_6.sce new file mode 100644 index 000000000..14192064f --- /dev/null +++ b/257/CH8/EX8.6/example_8_6.sce @@ -0,0 +1,27 @@ +//determining critical value of K
+s=%s
+syms K
+m=0.1*s^3+0.65*s^2+s+K
+cof_a_0 = coeffs(m,'s',0);
+cof_a_1 = coeffs(m,'s',1);
+cof_a_2 = coeffs(m,'s',2);
+cof_a_3 = coeffs(m,'s',3);
+
+r=[cof_a_0 cof_a_1 cof_a_2 cof_a_3]
+
+n=length(r);
+routh=[r([4,2]);r([3,1])];
+routh=[routh;-det(routh)/routh(2,1),0];
+t=routh(2:3,1:2); //extracting the square sub block of routh matrix
+routh=[routh;-det(t)/t(2,1),0]
+disp(routh,"rouths tabulation=")
+routh(3,1)=0 //For marginaly stable system
+sys=syslin('c',1/(0.1*s^3+0.65*s^2+s))
+k=kpure(sys)
+disp(k,"K(marginal)=")
+
+w=sqrt(-k/0.65)
+disp(w,"w = ")
+
+
+
diff --git a/257/CH8/EX8.7/example_8_7.sce b/257/CH8/EX8.7/example_8_7.sce new file mode 100644 index 000000000..9560835c3 --- /dev/null +++ b/257/CH8/EX8.7/example_8_7.sce @@ -0,0 +1,27 @@ +//determining critical value of K
+s=%s
+syms K
+m=s^4+22*s^3+10*s^2+s+K
+cof_a_0 = coeffs(m,'s',0);
+cof_a_1 = coeffs(m,'s',1);
+cof_a_2 = coeffs(m,'s',2);
+cof_a_3 = coeffs(m,'s',3);
+
+r=[cof_a_0 cof_a_1 cof_a_2 cof_a_3]
+
+n=length(r);
+routh=[r([4,2]);r([3,1])];
+routh=[routh;-det(routh)/routh(2,1),0];
+t=routh(2:3,1:2); //extracting the square sub block of routh matrix
+routh=[routh;-det(t)/t(2,1),0]
+disp(routh,"rouths tabulation=")
+routh(3,1)=0 //For marginaly stable system
+sys=syslin('c',1/(s^4+22*s^3+10*s^2+s))
+k=kpure(sys)
+disp(k,"K(marginal)=")
+
+w=sqrt(-k/9.95)
+disp(w,"w = ")
+
+
+
diff --git a/257/CH8/EX8.8/example_8_8.sce b/257/CH8/EX8.8/example_8_8.sce new file mode 100644 index 000000000..dccb26a9b --- /dev/null +++ b/257/CH8/EX8.8/example_8_8.sce @@ -0,0 +1,24 @@ +s=%s
+F=s^6+3*s^5+4*s^4+6*s^3+5*s^2+3*s+2
+
+disp(routh_t(F))
+r=coeff(F)
+routh=routh_t(F)
+n=length(r)
+c=0;
+for i=1:n
+if (routh(i,1)<0)
+c=c+1;
+ end
+ end
+ if(c>=1)
+ printf("system is unstable")
+ else printf("there are no roots on RHS")
+ end
+
+disp("s^2 is")
+R=roots(routh(3,:))
+disp(R)
+
+disp("as there are 2 pairs of repeated roots on the imaginary axis, the system is unstable")
+
diff --git a/257/CH8/EX8.9/example_8_9.sce b/257/CH8/EX8.9/example_8_9.sce new file mode 100644 index 000000000..7f1ffa052 --- /dev/null +++ b/257/CH8/EX8.9/example_8_9.sce @@ -0,0 +1,22 @@ +//determining critical value of K
+s=%s
+syms K p
+m=s^3+p*s^2+(2+K)*s+K+1
+cof_a_0 = coeffs(m,'s',0);
+cof_a_1 = coeffs(m,'s',1);
+cof_a_2 = coeffs(m,'s',2);
+cof_a_3 = coeffs(m,'s',3);
+
+r=[cof_a_0 cof_a_1 cof_a_2 cof_a_3]
+
+n=length(r);
+routh=[r([4,2]);r([3,1])];
+routh=[routh;-det(routh)/routh(2,1),0];
+t=routh(2:3,1:2); //extracting the square sub block of routh matrix
+routh=[routh;-det(t)/t(2,1),0]
+disp(routh,"rouths tabulation=")
+routh(3,1)=0 //For marginaly stable system
+
+
+
+
diff --git a/257/CH9/EX9.1/example_9_1.sce b/257/CH9/EX9.1/example_9_1.sce new file mode 100644 index 000000000..83b111455 --- /dev/null +++ b/257/CH9/EX9.1/example_9_1.sce @@ -0,0 +1,4 @@ +//root locus
+s=%s
+sys=syslin('c',(k)/(s))
+evans(sys)
diff --git a/257/CH9/EX9.10/example_9_10.sce b/257/CH9/EX9.10/example_9_10.sce new file mode 100644 index 000000000..eb5db031e --- /dev/null +++ b/257/CH9/EX9.10/example_9_10.sce @@ -0,0 +1,3 @@ +s=%s
+sys=syslin('c',(k)*(s+2)*(s+4)/(s^2*(s+6)))
+evans(sys)
diff --git a/257/CH9/EX9.11/example_9_11.sce b/257/CH9/EX9.11/example_9_11.sce new file mode 100644 index 000000000..13e358b6e --- /dev/null +++ b/257/CH9/EX9.11/example_9_11.sce @@ -0,0 +1,3 @@ +s=%s
+sys=syslin('c',(k)*(s+4)/((s+2)*(s^2+2*s+2)))
+evans(sys)
diff --git a/257/CH9/EX9.12/example_9_12.sce b/257/CH9/EX9.12/example_9_12.sce new file mode 100644 index 000000000..66d216f0c --- /dev/null +++ b/257/CH9/EX9.12/example_9_12.sce @@ -0,0 +1,8 @@ +s=%s
+sys=syslin('c',(k)/(s*(s+1)*(s+4)))
+evans(sys)
+
+//breakaway points
+
+disp("break away points are")
+disp(roots(numer(derivat(sys))))
\ No newline at end of file diff --git a/257/CH9/EX9.13/example_9_13.sce b/257/CH9/EX9.13/example_9_13.sce new file mode 100644 index 000000000..7bc97da9d --- /dev/null +++ b/257/CH9/EX9.13/example_9_13.sce @@ -0,0 +1,6 @@ +//angles of departure
+sys=syslin('c',k*(s+2)/(s*(s+4)*(s^2+2*s+2)))
+evans(sys)
+
+theta=180-(135+90+18.43-45)
+disp(theta)
\ No newline at end of file diff --git a/257/CH9/EX9.14/example_9_14.sce b/257/CH9/EX9.14/example_9_14.sce new file mode 100644 index 000000000..7ee66f365 --- /dev/null +++ b/257/CH9/EX9.14/example_9_14.sce @@ -0,0 +1,9 @@ +s=%s
+sys=syslin('c',(k)/(s*(s+5)*(s+10)))
+clf
+evans(sys)
+
+//stability
+
+[Ki,s]=kpure(sys)
+disp(Ki)
\ No newline at end of file diff --git a/257/CH9/EX9.15/example_9_15.sce b/257/CH9/EX9.15/example_9_15.sce new file mode 100644 index 000000000..8bf3da37f --- /dev/null +++ b/257/CH9/EX9.15/example_9_15.sce @@ -0,0 +1,3 @@ +s=%s
+sys=syslin('c',(k)/(s*(s+1)*(s+2)*(s+3)))
+evans(sys)
\ No newline at end of file diff --git a/257/CH9/EX9.16/example_9_16.sce b/257/CH9/EX9.16/example_9_16.sce new file mode 100644 index 000000000..8d7e381c8 --- /dev/null +++ b/257/CH9/EX9.16/example_9_16.sce @@ -0,0 +1,3 @@ +s=%s
+sys=syslin('c',(k)/(s*(s+3)*(s^2+3*s+4.5)))
+evans(sys)
\ No newline at end of file diff --git a/257/CH9/EX9.17/example_9_17.sce b/257/CH9/EX9.17/example_9_17.sce new file mode 100644 index 000000000..c60c035d0 --- /dev/null +++ b/257/CH9/EX9.17/example_9_17.sce @@ -0,0 +1,3 @@ +s=%s
+sys=syslin('c',(k)/(s*(s+3)*(s^2+3*s+11.25)))
+evans(sys)
\ No newline at end of file diff --git a/257/CH9/EX9.18/example_9_18.sce b/257/CH9/EX9.18/example_9_18.sce new file mode 100644 index 000000000..cf32c764d --- /dev/null +++ b/257/CH9/EX9.18/example_9_18.sce @@ -0,0 +1,3 @@ +s=%s
+sys=syslin('c',(k)/(s*(s+3)*(s^2+3*s+3)))
+evans(sys)
\ No newline at end of file diff --git a/257/CH9/EX9.2/eg_9_2.sce b/257/CH9/EX9.2/eg_9_2.sce new file mode 100644 index 000000000..b921c35b4 --- /dev/null +++ b/257/CH9/EX9.2/eg_9_2.sce @@ -0,0 +1,14 @@ +//angle condition
+s=%s
+sys=syslin('c',(k)/(s*(s+2)*(s+4)))
+
+f=-0.75;
+//disp(-atan(s,0))
+disp(-atan(f,0)-atan(f,2)-atan(f,4))
+if(-atan(f,0)-atan(f,2)-atan(f,4)==(-3.14))
+ printf("yes")
+
+else
+ printf("no")
+end
+
diff --git a/257/CH9/EX9.20/example_9_20.sce b/257/CH9/EX9.20/example_9_20.sce new file mode 100644 index 000000000..6d7cff76e --- /dev/null +++ b/257/CH9/EX9.20/example_9_20.sce @@ -0,0 +1,8 @@ +s=%s
+sys=syslin('c',(s+1)*k/(s*(s-1)*(s^2+5*s+20)))
+evans(sys)
+
+//stability
+
+[Ki,s]=kpure(sys)
+disp(Ki)
\ No newline at end of file diff --git a/257/CH9/EX9.21/example_9_21.sce b/257/CH9/EX9.21/example_9_21.sce new file mode 100644 index 000000000..49be78017 --- /dev/null +++ b/257/CH9/EX9.21/example_9_21.sce @@ -0,0 +1,4 @@ +//given characteristic equation s^3 + 9*s^2 +k*s + k
+s=%s
+sys=syslin('c',(s+1)*k/((s+9)*(s^2)))
+evans(sys)
diff --git a/257/CH9/EX9.23/example_9_23.sce b/257/CH9/EX9.23/example_9_23.sce new file mode 100644 index 000000000..7f1cc10c5 --- /dev/null +++ b/257/CH9/EX9.23/example_9_23.sce @@ -0,0 +1,3 @@ +s=%s
+sys=syslin('c',k/(s*(s+4)*(s^2+4*s+20)))
+evans(sys)
diff --git a/257/CH9/EX9.24/example_9_24.sce b/257/CH9/EX9.24/example_9_24.sce new file mode 100644 index 000000000..94d7a1535 --- /dev/null +++ b/257/CH9/EX9.24/example_9_24.sce @@ -0,0 +1,3 @@ +s=%s
+sys=syslin('c',k/(s*(s+2)*(s^2+6*s+25)))
+evans(sys)
diff --git a/257/CH9/EX9.25/example_9_25.sce b/257/CH9/EX9.25/example_9_25.sce new file mode 100644 index 000000000..17b53b06b --- /dev/null +++ b/257/CH9/EX9.25/example_9_25.sce @@ -0,0 +1,25 @@ +s=%s
+sys=syslin('c',k/(s*(s+4)*(s+2)))
+evans(sys)
+
+
+//values of k
+
+[Ki,s]=kpure(sys)
+disp("k should be less than")
+disp(Ki)
+
+//frequency of oscillations
+s=%s
+P=s^3+6*s^2+8*s+Ki
+routh=routh_t(P)
+disp(routh)
+disp("frequency of oscillations is")
+ disp(sqrt((roots(routh(2,:)))))
+
+ //damping ratio is 0.5 given
+// cos inverse of 0.5 is 60 degrees. from the root locus, the 60 degree line crosses the locus at (-0.75+j*1.25)
+
+f=(-0.75+%i*1.25)
+disp("k for damping ratio 0.5 is")
+disp(abs(f*(f+4)*(f+2)))
\ No newline at end of file diff --git a/257/CH9/EX9.26/example_9_26.sce b/257/CH9/EX9.26/example_9_26.sce new file mode 100644 index 000000000..82154dd9d --- /dev/null +++ b/257/CH9/EX9.26/example_9_26.sce @@ -0,0 +1,16 @@ +s=%s
+sys=syslin('c',((k)*(s^2-2*s+5))/((s+2)*(s-0.5)))
+clf
+evans(sys)
+
+//stability
+
+[Ki,s]=kpure(sys)
+disp(Ki)
+
+//damping ratio 0.5
+
+f=(-0.3+%i*0.55)
+disp("k for damping ratio 0.5 is")
+disp(abs(((f+2)*(f-0.5)))/(f^2-2*f+5))
+
diff --git a/257/CH9/EX9.27/example_9_27.sce b/257/CH9/EX9.27/example_9_27.sce new file mode 100644 index 000000000..7eebb552f --- /dev/null +++ b/257/CH9/EX9.27/example_9_27.sce @@ -0,0 +1,4 @@ +//when |a|<|b| then system is stable. hence let a=2 and b=3
+s=%s
+sys=syslin('c',k/((s-2)*(s+3)))
+evans(sys)
\ No newline at end of file diff --git a/257/CH9/EX9.28/example_9_28.sce b/257/CH9/EX9.28/example_9_28.sce new file mode 100644 index 000000000..5403989b2 --- /dev/null +++ b/257/CH9/EX9.28/example_9_28.sce @@ -0,0 +1,9 @@ +s=%s
+sys=syslin('c',k/((s+16)*(s^2+2*s+2)))
+evans(sys)
+
+//stability
+
+[Ki,s]=kpure(sys)
+disp("k marginal is")
+disp(Ki)
diff --git a/257/CH9/EX9.3/example_9_3.sce b/257/CH9/EX9.3/example_9_3.sce new file mode 100644 index 000000000..e0e179131 --- /dev/null +++ b/257/CH9/EX9.3/example_9_3.sce @@ -0,0 +1,4 @@ +//magnitude condition for GH=K/s*(s=2)*(s+4)
+s=-0.75
+k=-s*(4+s)*(2+s)
+disp(k)
\ No newline at end of file diff --git a/257/CH9/EX9.30/example_9_30.sce b/257/CH9/EX9.30/example_9_30.sce new file mode 100644 index 000000000..2d991d48a --- /dev/null +++ b/257/CH9/EX9.30/example_9_30.sce @@ -0,0 +1,11 @@ +s=%s
+sys=syslin('c',(k)/((s)*(s^2+8*s+17)))
+clf
+evans(sys)
+
+//damping ratio 0.5
+
+f=(-1.15+%i*2)
+disp("k for damping ratio 0.5 is")
+disp(abs(((f)*(f^2+8*f+17))))
+
diff --git a/257/CH9/EX9.31/example_9_31.sce b/257/CH9/EX9.31/example_9_31.sce new file mode 100644 index 000000000..5deb38b5e --- /dev/null +++ b/257/CH9/EX9.31/example_9_31.sce @@ -0,0 +1,4 @@ +s=%s
+sys=syslin('c',((k)*(s+2)*(s+3))/((s+1)*(s)))
+clf
+evans(sys)
\ No newline at end of file diff --git a/257/CH9/EX9.32/example_9_32.sce b/257/CH9/EX9.32/example_9_32.sce new file mode 100644 index 000000000..979ba13bd --- /dev/null +++ b/257/CH9/EX9.32/example_9_32.sce @@ -0,0 +1,22 @@ +//given characteristic equation we get GH
+s=%s
+sys=syslin('c',k/(s*(s^2+8*s+20)))
+clf
+evans(sys)
+
+//stability
+
+[Ki,s]=kpure(sys)
+disp(Ki)
+
+
+//damping ratio is 0.95
+
+f=(-1.8+%i*0.55)
+disp("k for damping ratio 0.95 is")
+disp(abs((f*(f^2+8*f+20))))
+
+
+f=(-03.6+%i*1.1)
+disp("k for damping ratio 0.95 is")
+disp(abs((f*(f^2+8*f+20))))
diff --git a/257/CH9/EX9.4/example_9_4.sce b/257/CH9/EX9.4/example_9_4.sce new file mode 100644 index 000000000..4092e3bf6 --- /dev/null +++ b/257/CH9/EX9.4/example_9_4.sce @@ -0,0 +1,4 @@ +s=%s
+sys=syslin('c',(k)/(s*(s+2)))
+evans(sys)
+printf("there are 2 branches approaching infinity")
\ No newline at end of file diff --git a/257/CH9/EX9.5/example_9_5.sce b/257/CH9/EX9.5/example_9_5.sce new file mode 100644 index 000000000..96b345c1c --- /dev/null +++ b/257/CH9/EX9.5/example_9_5.sce @@ -0,0 +1,3 @@ +s=%s
+sys=syslin('c',k*(s+1)/(s*(s+5)))
+evans(sys)
diff --git a/257/CH9/EX9.6/example_9_6.sce b/257/CH9/EX9.6/example_9_6.sce new file mode 100644 index 000000000..0de0dbe92 --- /dev/null +++ b/257/CH9/EX9.6/example_9_6.sce @@ -0,0 +1,3 @@ +s=%s
+sys=syslin('c',(k)*(s+1)*(s+4)/(s*(s+3)*(s+5)))
+evans(sys)
diff --git a/257/CH9/EX9.7/example_9_7.sce b/257/CH9/EX9.7/example_9_7.sce new file mode 100644 index 000000000..0de0dbe92 --- /dev/null +++ b/257/CH9/EX9.7/example_9_7.sce @@ -0,0 +1,3 @@ +s=%s
+sys=syslin('c',(k)*(s+1)*(s+4)/(s*(s+3)*(s+5)))
+evans(sys)
diff --git a/257/CH9/EX9.8/example_9_8.sce b/257/CH9/EX9.8/example_9_8.sce new file mode 100644 index 000000000..d214f1c9b --- /dev/null +++ b/257/CH9/EX9.8/example_9_8.sce @@ -0,0 +1,8 @@ +//Gh=k/((s+1)*(s+2+2j)*(s+2-2j))
+
+for n=0:2
+ theta=(2*n+1)*180/3 //poles=3 , zeroes=0
+ disp(theta)
+end
+
+disp(cntrd=(-1-2-2-0)/3) // real(poles-zeroes)/ number of poles-zeroes
\ No newline at end of file diff --git a/257/CH9/EX9.9/example_9_9.sce b/257/CH9/EX9.9/example_9_9.sce new file mode 100644 index 000000000..46438edf3 --- /dev/null +++ b/257/CH9/EX9.9/example_9_9.sce @@ -0,0 +1,3 @@ +s=%s
+sys=syslin('c',(k)*(s+6)/(s*(s+2)*(s+4)))
+evans(sys)
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