diff options
Diffstat (limited to 'Working_Examples/3432/CH7/EX7.32')
| -rwxr-xr-x | Working_Examples/3432/CH7/EX7.32/DEPENDENCIES/acker_dk.sci | 73 | ||||
| -rwxr-xr-x | Working_Examples/3432/CH7/EX7.32/DEPENDENCIES/fig_settings.sci | 9 | ||||
| -rwxr-xr-x | Working_Examples/3432/CH7/EX7.32/DEPENDENCIES/zpk_dk.sci | 43 | ||||
| -rwxr-xr-x | Working_Examples/3432/CH7/EX7.32/Ex7_32.sce | 122 | ||||
| -rwxr-xr-x | Working_Examples/3432/CH7/EX7.32/Ex7_32_f0.pdf | bin | 0 -> 22578 bytes | |||
| -rwxr-xr-x | Working_Examples/3432/CH7/EX7.32/Ex7_32_f2.pdf | bin | 0 -> 23733 bytes | |||
| -rwxr-xr-x | Working_Examples/3432/CH7/EX7.32/Ex7_32_model.xcos | 1 |
7 files changed, 248 insertions, 0 deletions
diff --git a/Working_Examples/3432/CH7/EX7.32/DEPENDENCIES/acker_dk.sci b/Working_Examples/3432/CH7/EX7.32/DEPENDENCIES/acker_dk.sci new file mode 100755 index 0000000..3391d24 --- /dev/null +++ b/Working_Examples/3432/CH7/EX7.32/DEPENDENCIES/acker_dk.sci @@ -0,0 +1,73 @@ +//------------------------------------------------------------------ +//------------------------------------------------------------------ +//A function written by Deepti Khimani. +//Usage:- +//[K, lambda]=acker_dk(a, b, pl) +//K=acker_dk(a, b, pl) +//a:- System matrix. +//b:- input matrix. +//p:- Desired poles. +//K:-State feedback gain for the control law u=-Kx. +//lambda:- Eigen values of (a-b*k) +//------------------------------------------------------------------ +//------------------------------------------------------------------ + +function [K, lambda]=acker_dk(a, b, pl) + [lhs,rhs]=argn(0) + + if rhs == 0 then + disp(["K=acker_dk(a, b, pl)";"[K, lambda]=acker_dk(a, b, pl)"]); + disp(["a:- System matrix";"b:- input matrix";"p:- Desired poles"]); + disp(["K:-State feedback gain for the control law u=-Kx";... + "lambda:- Eigen values of (a-b*k)"]); + return; + end +[ra ca]=size(a); +[rb cb]=size(b); +l=length(pl); + +CO=cont_mat(a,b); + +if ra~=l then + error(["Dimension error:";"number of desired poles must equal... + to order of the system"]); +elseif ra~=ca then + error(["Dimension error:";"system matrix should be... + a sqaure matrix"]); +elseif rb~=ra then + error (["Dimension error:","Input matrix should have... + as many rows as a system matrix."]); +elseif rank(CO)<ra then + error("system is not controllable"); +end +//------------------------------------------------------------------ +//controllable canonical form +[Ac,Bc,T,ind]=canon(a,b); + +//CO=zeros(ra,cb); +for i=1:ra + CO(:,ra+1-i)=Ac^(i-1)*Bc; +end +//------------------------------------------------------------------ +chr_eq=poly(pl,'s'); +des_chr_coeff=coeff(chr_eq); + +des_chr_coeff=des_chr_coeff(1:ra); +alpha_c=Ac^ra; + +for k=1:ra + alpha_c=alpha_c + des_chr_coeff(k)*Ac^(k-1) +end +//------------------------------------------------------------------ +//State feedback gain +temp=zeros(1,ra); +temp(1)=1; +K=temp*inv(CO)*alpha_c; +K=K/T; +lambda=spec(a-b*K); +endfunction +//------------------------------------------------------------------ + + + + diff --git a/Working_Examples/3432/CH7/EX7.32/DEPENDENCIES/fig_settings.sci b/Working_Examples/3432/CH7/EX7.32/DEPENDENCIES/fig_settings.sci new file mode 100755 index 0000000..5d5e7d4 --- /dev/null +++ b/Working_Examples/3432/CH7/EX7.32/DEPENDENCIES/fig_settings.sci @@ -0,0 +1,9 @@ +//------------------------------------------------------------------
+//figure handel settings
+f=get("current_figure"); //Current figure handle
+f.background=8; //make the figure window background white
+l=f.children(1);
+l.background=8 ;//make the text background white
+id=color('grey');
+xgrid(id);
+//------------------------------------------------------------------
diff --git a/Working_Examples/3432/CH7/EX7.32/DEPENDENCIES/zpk_dk.sci b/Working_Examples/3432/CH7/EX7.32/DEPENDENCIES/zpk_dk.sci new file mode 100755 index 0000000..95b4e6c --- /dev/null +++ b/Working_Examples/3432/CH7/EX7.32/DEPENDENCIES/zpk_dk.sci @@ -0,0 +1,43 @@ +//------------------------------------------------------------------ +//------------------------------------------------------------------ +//A function written by Deepti Khimani. +//Usage:- +//p=zpk_dk(sl) +//[p, z]=zpk_dk(sl) +//[p, z, k]=zpk_dk(sl) +//p:- Poles of the system +//z:- zeros of the system +//k:- DC gain of the system +//------------------------------------------------------------------ +//------------------------------------------------------------------ + +function[pl,zr,k]=zpk_dk(sysmodel) + [lhs,rhs]=argn(0) + + if rhs == 0 then + disp(["p=zpk_dk(sl)";"[p, z]=zpk_dk(sl)";"[p, z, k]=zpk_dk(sl)"]); + disp(["p:- Poles of the system";"z:- zeros of the system"]); + disp("k:- DC gain of the system"); + return; + end + + if typeof(sysmodel)=="rational" then + sys=tf2ss(sysmodel); + pl=spec(sys.A); + zr=trzeros(sys); + temp1=poly(zr,'s','roots')/poly(pl,'s','roots'); + temp2=sysmodel/temp1; + temp3=tf2ss(temp2); + k=temp3.D; + elseif typeof(sysmodel)=="state-space" then + pl=spec(sysmodel.A); + zr=trzeros(sysmodel); + g=ss2tf(sysmodel); + temp1=poly(zr,'s','roots')/poly(pl,'s','roots'); + temp2=g/temp1; + temp3=tf2ss(temp2); + k=temp3.D + else + error("Wrong type of input argument.") + end +endfunction diff --git a/Working_Examples/3432/CH7/EX7.32/Ex7_32.sce b/Working_Examples/3432/CH7/EX7.32/Ex7_32.sce new file mode 100755 index 0000000..ca11844 --- /dev/null +++ b/Working_Examples/3432/CH7/EX7.32/Ex7_32.sce @@ -0,0 +1,122 @@ +//Example 7.32
+// Redesign of the Dc servo compensator using SRL
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+
+// State space representation
+//Transfer function model for DC Servo
+s=poly(0,'s');
+num=10;
+den=s*(s+2)*(s+8);
+Gs=syslin('c',num/den);
+
+// State space representation
+F=[-10 1 0;-16 0 1;0 0 0]
+G=[0 0 10]';
+H=[1 0 0];
+J=0;
+n=sqrt(length(F));
+//Desired poles for the DC Servo system.
+Pc=[-2+1.56*%i -2-1.56*%i -8.04]
+
+
+// State feedback gain
+K=ppol(F,G,Pc)
+disp(K,'K=',"State feedback gain")
+
+//Estimator - error roots are at
+Pe=[-4+4.49*%i -4-4.49*%i -9.169]
+exec .\acker_dk.sci;
+Lt=ppol(F',H',Pe);
+L=clean(Lt');
+disp(L,'L=',"Observer gain")
+//Error in book, Gain values are different in book.
+//------------------------------------------------------------------
+//Compensator Design
+DK=-K*inv(s*eye(n,n)-F+G*K+L*H)*L;
+DK=syslin('c',DK)
+exec('./zpk_dk.sci', -1);
+[pl,zr,Kp]=zpk_dk(DK);
+Dc=poly(zr,'s','roots')/poly(pl,'s','roots')
+//------------------------------------------------------------------
+//symmetric root locus
+G_s=horner(Gs,-s);
+evans(Gs*G_s)
+zoom_rect([-10 -5 10 5])
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+xset("color",2);
+h=legend('');
+h.visible = "off"
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script for setting figure properties
+title('Symmetric root locus','fontsize',3);
+//------------------------------------------------------------------
+//root locus
+figure,
+evans(Gs*Dc) //Correct root locus
+zoom_rect([-11 -6 1 6])
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+xset("color",2);
+h=legend('');
+h.visible = "off"
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Root locus for pole assignment from the SRL','fontsize',3);
+//------------------------------------------------------------------
+//Discrete-time controller
+nc=94.5*conv([7.98 1],[2.52 1])
+dc=conv([59.5348 8.56 1],[10.6 1])
+sysDc=poly(nc,'s','coeff')/poly(dc,'s','coeff');
+sysDc_ss=syslin('c',tf2ss(sysDc));
+ts=0.1;
+sysDd=dscr(sysDc_ss,ts)
+Gdz=ss2tf(sysDd);
+
+disp(sysDc,"Continuous-time compensator")
+disp(Gdz,"Discrete-time compensator")
+//------------------------------------------------------------------
+//step responses
+importXcosDiagram(".\Ex7_32_model.xcos")
+
+xcos_simulate(scs_m,4);
+scs_m.props.context
+figure,
+plot(yt.time,yt.values(:,1),2)
+plot(yt.time,yt.values(:,2),'r--')
+xlabel('Time (sec)');
+ylabel('y');
+title("Comaprison of step responses for continuous and discrete...
+ controllers",'fontsize',3)
+exec .\fig_settings.sci; //custom script for setting figure properties
+legend("continuous controller","digital controller",4)
+
+//Control inputs
+figure,
+plot(ut.time,ut.values(:,1),2)
+plot(ut.time,ut.values(:,2),'r--')
+xlabel('Time (sec)');
+ylabel('u');
+title("Comaprison of control signals for continuous and discrete...
+ controllers",'fontsize',3)
+exec .\fig_settings.sci; //custom script for setting figure properties
+legend("continuous controller","digital controller")
+//------------------------------------------------------------------
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/Working_Examples/3432/CH7/EX7.32/Ex7_32_f0.pdf b/Working_Examples/3432/CH7/EX7.32/Ex7_32_f0.pdf Binary files differnew file mode 100755 index 0000000..10af892 --- /dev/null +++ b/Working_Examples/3432/CH7/EX7.32/Ex7_32_f0.pdf diff --git a/Working_Examples/3432/CH7/EX7.32/Ex7_32_f2.pdf b/Working_Examples/3432/CH7/EX7.32/Ex7_32_f2.pdf Binary files differnew file mode 100755 index 0000000..0c39c39 --- /dev/null +++ b/Working_Examples/3432/CH7/EX7.32/Ex7_32_f2.pdf diff --git a/Working_Examples/3432/CH7/EX7.32/Ex7_32_model.xcos b/Working_Examples/3432/CH7/EX7.32/Ex7_32_model.xcos new file mode 100755 index 0000000..7f778e4 --- /dev/null +++ b/Working_Examples/3432/CH7/EX7.32/Ex7_32_model.xcos @@ -0,0 +1 @@ +<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1" finalIntegrationTime="5.0" title="Ex7_32_model"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406 2040--><mxGraphModel as="model"><root><mxCell id="-2dd55334:14dcbdd0183:-7fd2"/><mxCell 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