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authorSiddharth Agarwal2019-09-03 18:27:40 +0530
committerSiddharth Agarwal2019-09-03 18:27:40 +0530
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treee1bc17aae137922b1ee990f17aae4a6cb15b7d87 /Working_Examples/3432/CH4
parent52a477ec613900885e29c4a0b02806a415b4f83a (diff)
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Xcos examples from textbooks and for blocksHEADmaster
Diffstat (limited to 'Working_Examples/3432/CH4')
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diff --git a/Working_Examples/3432/CH4/EX4.6/Ex4_6.sce b/Working_Examples/3432/CH4/EX4.6/Ex4_6.sce
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+//Example 4.6
+//PID Control of DC Motor Speed.
+
+//------------------------------------------------------------------
+//NOTE THAT--
+
+//The model as given in matlab program for this example in the book is
+
+//num=Ra*s + La*s^2 ;
+//den=Ke*ki + (Ra*Ke*Ke+Ke*kp)*s + (Ra*b+Ke*Ke+Ke*kd)*s^2 + Jm*La*s^3;
+
+//this does not match to the model of DC motor given on page 43.
+//Also, if we assume this model, disturbance response given
+//in figure 4.13 (a)
+//is different from expected.
+//For instance, with P control, output should asymptotically go to 0
+//for disturbance step input, because numerator is s(Ra + La*s)
+//and system is type 0 (no pole at origin).
+//i.e. y(inf)=lim s->0 s*Y(s)= s*[s(Ra + La*s)/den]*1/s=0;
+
+//In following code, we have considered correct model of DC motor as
+//given on page 43. Note that, this model must have been used
+//by authors of the book for
+//step reference tracking as it is correctly shown in figure 4.13 (b)
+
+//------------------------------------------------------------------
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+
+//------------------------------------------------------------------
+// System parameters
+Jm=0.0113; // N-m-s^2/rad
+b=0.028; // N-m-s/rad
+La=0.1; // henry
+Ra=0.45; // ohms
+Kt=0.067 // n-m/amp
+Ke=0.067; // V-sec/amp
+
+// Controller parameters
+kp=3;
+ki=15; // sec^-1
+kd=0.3; // sec
+
+// DC Motor Transfer function as given on page 43 of book (edition 5)
+//G=Kt/[Jm*La s^2 + (Jm*Ra + La*b)s +(Ra*b +Kt*Ke)]
+s=%s;
+num=[Kt];
+den=[(Ra*b +Kt*Ke) (Jm*Ra + La*b) Jm*La];
+Ns=poly(num,'s','coeff');
+Ds=poly(den,'s','coeff');
+G=syslin('c',Ns/Ds)
+
+//PID controller, Gc=(kd s^2 + kp s + ki)/s
+num=[ki kp kd;ki kp 0;0 kp 0]; //numerator parameters of controller)
+ //(row wise for PID, PI and P)
+den=[0 1]; //denominator parameters of controller
+Ds=poly(den,'s','coeff'); //denominator polynomial of controller
+t=0:0.005:10; // Simulation time
+//------------------------------------------------------------------
+//Step disturbance response with P, PI and PID controller.
+
+for i=1:3
+Ns=poly(num(i,:),'s','coeff');//numerator polynomial of controller
+sysG=syslin('c',Ns/Ds);
+sysD=G/. sysG;
+v(i,:)=csim('step',t,sysD);
+end
+plot(t',v');
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script to set the figure properties
+title('Responses of P,PI and PID control to step disturbance...
+ input','fontsize',3)
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('Amplitude','fontsize',2)
+hl=legend(['PID','PI','P']);
+
+//------------------------------------------------------------------
+//Reference step response
+
+figure
+for i=1:3
+Ns=poly(num(i,:),'s','coeff');
+Gc=syslin('c',Ns/Ds);
+// Step reference response with P, PI and PID controller.
+sysR=G*Gc/(1+G*Gc);
+v(i,:)=csim('step',t,sysR);
+end
+plot(t',v')
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script to set the figure properties
+title('Responses of PID control to step reference input','fontsize',3)
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('Amplitude','fontsize',2)
+hl=legend(['PID','PI','P']);
+
+//------------------------------------------------------------------
diff --git a/Working_Examples/3432/CH4/EX4.6/Ex4_6_f0.pdf b/Working_Examples/3432/CH4/EX4.6/Ex4_6_f0.pdf
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diff --git a/Working_Examples/3432/CH4/EX4.7/DEPENDENCIES/fig_settings.sci b/Working_Examples/3432/CH4/EX4.7/DEPENDENCIES/fig_settings.sci
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+//------------------------------------------------------------------
+//figure handel settings
+f=get("current_figure"); //Current figure handle
+f.background=8; //make the figure window background white
+l=f.children(1);
+l.background=8 ;//make the text background white
+id=color('grey');
+xgrid(id);
+//------------------------------------------------------------------
diff --git a/Working_Examples/3432/CH4/EX4.7/Ex4_7.sce b/Working_Examples/3432/CH4/EX4.7/Ex4_7.sce
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+//Example 4.7
+//Discrete Equivalent.
+//------------------------------------------------------------------
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+
+// Transfer function
+s=%s;
+num=[1 11];
+den=[1 3]
+Us=poly(num,'s','coeff');
+Es=poly(den,'s','coeff');
+Ds=syslin('c',Us/Es);
+sysc=tf2ss(Ds)
+
+//Discretize the system using sampling time Ts=1 and Bilinear Transform
+Ts=1;
+sysd=cls2dls(sysc,Ts);
+
+//Pulse transfer function
+Dd=ss2tf(sysd)
+disp(Dd,"Dd=")
+disp("Note that, multiply numerator and denomintor each by 7...
+ will give the result as in book.")
+//------------------------------------------------------------------
diff --git a/Working_Examples/3432/CH4/EX4.8/DEPENDENCIES/fig_settings.sci b/Working_Examples/3432/CH4/EX4.8/DEPENDENCIES/fig_settings.sci
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+//------------------------------------------------------------------
+//figure handel settings
+f=get("current_figure"); //Current figure handle
+f.background=8; //make the figure window background white
+l=f.children(1);
+l.background=8 ;//make the text background white
+id=color('grey');
+xgrid(id);
+//------------------------------------------------------------------
diff --git a/Working_Examples/3432/CH4/EX4.8/Ex4_8.sce b/Working_Examples/3432/CH4/EX4.8/Ex4_8.sce
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+//Example 4.8
+//Equivalent discrete controller for DC motor speed control.
+//------------------------------------------------------------------
+//NOTE THAT-- The system response (continuous) to sampled control
+//input depends on
+//the sampling time set for continuous signal in SIMULATION.
+//In this example we consider sampling period of 0.009 sec
+//to represent continuous time signal.
+//------------------------------------------------------------------
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+// Continuous time system and controller
+// System transfer function
+s=%s;
+num=[45 0];
+den=[45 14 1]
+Nms=poly(num,'s','coeff');
+Dns=poly(den,'s','coeff');
+Gp=syslin('c',Nms/Dns); //system transfer function
+
+// Controller
+
+numDa=[6 1];
+denDa=[0 1]
+Nms=poly(numDa,'s','coeff');
+Dns=poly(denDa,'s','coeff');
+sysD=syslin('c',1.4*Nms/Dns); //controller transfer function
+
+//Closed loop responses
+
+num=[1 0];
+den=[1 0];
+Nms=poly(num,'s','coeff');
+Dns=poly(den,'s','coeff');
+H=syslin('c',Nms/Dns)
+
+sysDa=Gp*sysD/.H;
+
+//step response and control input
+t=0:0.009:5;
+yt=csim('step',t,sysDa); //step response
+figure(0)
+plot2d(t,yt,1)
+Gu=sysD/(1+Gp*sysD);
+ut=csim('step',t,Gu); //control input
+figure(1)
+plot2d(t,ut,1)
+//------------------------------------------------------------------
+
+sys=tf2ss(Gp); //state space model of the system
+con=tf2ss(sysD); //controller state space model
+
+// discrete-time time system and controller
+
+//Discretize the system and control with sampling time Ts=0.07
+// using Bilinear Transform
+Ts=0.07;
+sysDd=cls2dls(sys,Ts); // discrete-time system state space model
+conDd=cls2dls(con,Ts); // discrete-time controller state space model
+
+//Pulse transfer function of system
+Gpz=ss2tf(sysDd);
+//Pulse transfer function of controller
+Gcz=ss2tf(conDd);
+//Closed loop response
+Gz=Gpz*Gcz/(1+Gpz*Gcz)
+//Control input pulse transfer function
+Guz=Gcz/(1+Gpz*Gcz)
+T=0:Ts:5;
+r=ones(1,length(T));
+yd=flts(r,Gz);............//Discrete respnse to discrete input
+ud=flts(r,Guz); //Discrete Control input
+//continuous response for digital input
+t=0:0.009:5;
+k=0;
+
+for i=1:length(yd)
+ for j=1:8
+ if (k+j)>length(t) then
+ break
+ else
+ YD(1,k+j)=yd(i);
+ end
+ end
+ k=k+j;
+end
+
+yt=csim(1-YD,t,Gp*sysD);
+scf(0)
+plot2d(t,yt,5);
+scf(1)
+plot2d2(T,ud,5);
+//------------------------------------------------------------------
+//Discretize the system and control with sampling time Ts=0.035
+// using Bilinear Transform
+Ts=0.035;
+sysDd=cls2dls(sys,Ts); // discrete-time system state space model
+conDd=cls2dls(con,Ts); // discrete-time controller state space model
+
+Gpz=ss2tf(sysDd); //Pulse transfer function of system
+Gcz=ss2tf(conDd); //Pulse transfer function of controller
+
+//Closed loop response
+Gz=Gpz*Gcz/(1+Gpz*Gcz)
+//Control input pulse transfer function
+Guz=Gcz/(1+Gpz*Gcz)
+T=0:Ts:5;
+r=ones(1,length(T));
+yd=flts(r,Gz);............//Discrete respnse to discrete input
+ud=flts(r,Guz); //Discrete Control input
+t=0:0.009:5;
+k=0;
+
+for i=1:length(yd)
+ for j=1:4
+ if (k+j)>length(t) then
+ break
+ else
+ YD(1,k+j)=yd(i);
+ end
+ end
+ k=k+j;
+end
+
+yt=csim(1-YD,t,Gp*sysD);
+scf(0)
+plot2d(t,yt,2);
+scf(1)
+plot2d2(T,ud,2);
+
+scf(0)
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script to set the figure properties
+title('Comparision plots of Speed-control system with continuous...
+ and discrete controllers','fontsize',3)
+xlabel('Time t (sec.)','fontsize',2)
+hl=legend(['Continuous time','Discrete-time, Ts=0.07 s'...
+,'Discrete-time, Ts=0.035 s'],4);
+scf(1)
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script to set the figure properties
+title('Comparision plots of Speed-control system with continuous...
+ and discrete controllers','fontsize',3)
+xlabel('Time t (sec.)','fontsize',2)
+hl=legend(['Continuous time','Discrete-time, Ts=0.07 s',...
+'Discrete-time, Ts=0.035 s']);
+//------------------------------------------------------------------
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