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author | Siddharth Agarwal | 2019-09-03 18:27:40 +0530 |
---|---|---|
committer | Siddharth Agarwal | 2019-09-03 18:27:40 +0530 |
commit | 8ac15bc5efafa2afc053c293152605b0e6ae60ff (patch) | |
tree | e1bc17aae137922b1ee990f17aae4a6cb15b7d87 /Working_Examples/3432/CH7/EX7.34 | |
parent | 52a477ec613900885e29c4a0b02806a415b4f83a (diff) | |
download | Xcos_block_examples-master.tar.gz Xcos_block_examples-master.tar.bz2 Xcos_block_examples-master.zip |
Diffstat (limited to 'Working_Examples/3432/CH7/EX7.34')
-rwxr-xr-x | Working_Examples/3432/CH7/EX7.34/DEPENDENCIES/acker_dk.sci | 73 | ||||
-rwxr-xr-x | Working_Examples/3432/CH7/EX7.34/DEPENDENCIES/fig_settings.sci | 9 | ||||
-rwxr-xr-x | Working_Examples/3432/CH7/EX7.34/Ex7_34.sce | 110 | ||||
-rwxr-xr-x | Working_Examples/3432/CH7/EX7.34/Ex7_34_f0.pdf | bin | 0 -> 20224 bytes | |||
-rwxr-xr-x | Working_Examples/3432/CH7/EX7.34/Ex7_34_f4.pdf | bin | 0 -> 23830 bytes | |||
-rwxr-xr-x | Working_Examples/3432/CH7/EX7.34/Ex7_34_model.xcos | 1 |
6 files changed, 193 insertions, 0 deletions
diff --git a/Working_Examples/3432/CH7/EX7.34/DEPENDENCIES/acker_dk.sci b/Working_Examples/3432/CH7/EX7.34/DEPENDENCIES/acker_dk.sci new file mode 100755 index 0000000..3391d24 --- /dev/null +++ b/Working_Examples/3432/CH7/EX7.34/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/EX7.34/DEPENDENCIES/fig_settings.sci b/Working_Examples/3432/CH7/EX7.34/DEPENDENCIES/fig_settings.sci new file mode 100755 index 0000000..5d5e7d4 --- /dev/null +++ b/Working_Examples/3432/CH7/EX7.34/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/EX7.34/Ex7_34.sce b/Working_Examples/3432/CH7/EX7.34/Ex7_34.sce new file mode 100755 index 0000000..2e77ebe --- /dev/null +++ b/Working_Examples/3432/CH7/EX7.34/Ex7_34.sce @@ -0,0 +1,110 @@ +//Example 7.34
+// Servomechanism, increasing the velocity constant through
+// zero assignment.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+
+// State space representation
+//Transfer function model for DC Servo
+s=poly(0,'s');
+num=1;
+den=s*(s+1);
+Gs=syslin('c',num/den);
+
+// State space representation
+F=[0 1;0 -1]
+G=[0 1]';
+H=[1 0];
+J=0;
+n=sqrt(length(F));
+//Desired poles for the DC Servo system.
+Pc=[-2 -2]
+
+// State feedback gain
+exec .\acker_dk.sci;
+K=acker_dk(F,G,Pc)//Gain computed in book is incorrect.
+disp(K,'K=',"State feedback gain")
+//------------------------------------------------------------------
+//Overall transfer function with reduced order estimator.
+Gred=8.32*(0.096+s)/(0.1 +s)/(8 + 4*s+s^2)
+Gred=syslin('c',Gred)
+disp(Gred,'Ys/Rs',"Overall transfer function with reduced...
+ order estimator")
+
+//Compensator
+D=(0.096+s)*(s+1)/(4.08 +s)/(0.0196+s)
+Ds=syslin('c',D*8.32)
+disp(Ds,'Ds=',"Compensator transfer function")
+//------------------------------------------------------------------
+//root locus
+figure(0)
+evans(D*Gs,100) //Correct root locus
+zoom_rect([-0.2 -0.1 0.1 0.1])
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+xset("color",2);
+h=legend('');
+h.visible = "off"
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Root locus of lag-lead compensation','fontsize',3);
+//------------------------------------------------------------------
+//Bode plot
+figure(1)
+bode(Ds*Gs,0.01/2/%pi,100/2/%pi,"rad") //Correct root locus
+
+f=gca();
+h=legend('');
+h.visible = "off"
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script for setting figure properties
+title('Frequency response of lag-lead compensation','fontsize',3);
+//------------------------------------------------------------------
+//step response of the system with lag compensation
+t=0:0.1:5;
+ylag=csim('step',t,8.32*Gs*D/(1+8.32*Gs*D));
+figure
+plot(t,ylag,2);
+xlabel('Time (sec)');
+ylabel('y');
+title("Step response of the system with lag compensation",'fontsize',3)
+exec .\fig_settings.sci; //custom script for setting figure properties
+//------------------------------------------------------------------
+//Discrete-time controller
+sysDc_ss=syslin('c',tf2ss(Ds));
+ts=0.1;
+sysDd=dscr(sysDc_ss,ts)
+Gdz=ss2tf(sysDd)
+
+disp(Gdz,"Discrete-time compensator")
+//------------------------------------------------------------------
+//step responses comparision
+importXcosDiagram(".\Ex7_34_model.xcos")
+
+xcos_simulate(scs_m,4);
+scs_m.props.context
+figure,
+plot(yt.time,yt.values(:,1),2)
+plot(yt.time,yt.values(:,2),'r--')
+xlabel('Time (sec)');
+ylabel('y');
+title("Comaprison of step responses for continuous and discrete...
+ controllers",'fontsize',3)
+exec .\fig_settings.sci; //custom script for setting figure properties
+legend("continuous controller","digital controller",4)
+
+//Control inputs
+figure,
+plot(ut.time,ut.values(:,1),2)
+plot(ut.time,ut.values(:,2),'r--')
+xlabel('Time (sec)');
+ylabel('u');
+title("Comaprison of control signals for continuous and discrete...
+ controllers",'fontsize',3)
+exec .\fig_settings.sci; //custom script for setting figure properties
+legend("continuous controller","digital controller")
+//------------------------------------------------------------------
diff --git a/Working_Examples/3432/CH7/EX7.34/Ex7_34_f0.pdf b/Working_Examples/3432/CH7/EX7.34/Ex7_34_f0.pdf Binary files differnew file mode 100755 index 0000000..d7b791b --- /dev/null +++ b/Working_Examples/3432/CH7/EX7.34/Ex7_34_f0.pdf diff --git a/Working_Examples/3432/CH7/EX7.34/Ex7_34_f4.pdf b/Working_Examples/3432/CH7/EX7.34/Ex7_34_f4.pdf Binary files differnew file mode 100755 index 0000000..c76fc78 --- /dev/null +++ b/Working_Examples/3432/CH7/EX7.34/Ex7_34_f4.pdf diff --git a/Working_Examples/3432/CH7/EX7.34/Ex7_34_model.xcos b/Working_Examples/3432/CH7/EX7.34/Ex7_34_model.xcos new file mode 100755 index 0000000..0f9e52f --- /dev/null +++ b/Working_Examples/3432/CH7/EX7.34/Ex7_34_model.xcos @@ -0,0 +1 @@ +<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1" finalIntegrationTime="5.0" title="Ex7_34_model"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406 2040--><mxGraphModel as="model"><root><mxCell id="-2dd55334:14dcbdd0183:-7fd2"/><mxCell 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