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+//Example 7.20
+// Pole Placement as a Dominant Second-Order System
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+
+clc;
+clear all;
+
+// State space representation
+F=[0 2 0 0 0;-0.10 -0.35 0.1 0.1 0.75; 0 0 0 2 0;...
+ 0.4 0.4 -0.4 -1.4 0; 0 -0.03 0 0 -1];
+G=[0 0 0 0 1]';
+H=[0.5 0 0.5 0 0]; //Tape position at the head
+Ht=[-0.2 -0.2 0.2 0.2 0]; //Tension output
+J=0;
+n=sqrt(length(F))
+// Desired poles
+Pc=[-0.707+0.707*%i -0.707-0.707*%i -4 -4 -4]/1.5;
+//------------------------------------------------------------------
+// State feedback gain matrix via LQR (riccati equation)
+Q = eye(5,5);
+R =1
+// Riccati equation
+P=riccati(F, G*inv(R)*G', Q, 'c')
+K1=inv(R)*G'*P
+//------------------------------------------------------------------
+// State feedback gain matrix via pole-placement
+exec('./acker_dk.sci', -1);
+K2=acker_dk(F,G,Pc);
+disp(K2,'K2=',"Gain by ackermans formula" );
+//------------------------------------------------------------------
+Ntilde1=-inv(H*inv(F-G*K1)*G); //input gain for LQR feedback gain.
+Ntilde2=-inv(H*inv(F-G*K2)*G); //input gain for Ackerman's feedback gain.
+
+syscl1=syslin('c',(F-G*K1),G*Ntilde1,H,J); //closed loop system with K1
+syscl2=syslin('c',(F-G*K2),G*Ntilde2,H,J); //closed loop system with K2
+
+t=0:0.1:12;
+[y1 x1]=csim('step',t,syscl1); //response of position head with K1
+[y2 x2]=csim('step',t,syscl2); //response of position head with K2
+
+//plot of a position of read write head
+plot(t,y1,"m-."); //Design via LQR
+plot(t,y2,2); //Design via Ackerman's Formula
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Step response of tape servomotor designs','fontsize',3);
+xlabel('Time t (sec.)','fontsize',2);
+ylabel('Tape Posotion','fontsize',2);
+
+xstring(2.5,1.1,"LQR")
+xarrows([3;4],[1.1;0.95],-1,1)
+xstring(5,0.7,["Dominant";"second order"])
+xarrows([5;4.2],[0.8;0.9],-1.5,1)
+//------------------------------------------------------------------
+
+//response as a tape tension
+yt1=Ht*x1;
+yt2=Ht*x2;
+
+figure(1)
+plot(t,yt1,"m-."); //Design via LQR
+plot(t,yt2,2); //Design via Ackerman's Formula
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Tension plots for tape servomotor step responses','fontsize',3);
+xlabel('Time t (sec.)','fontsize',2);
+ylabel('Tape Tension','fontsize',2);
+
+xstring(3.5,0,"LQR")
+xarrows([3.7;4.7],[0;0],-1)
+xstring(6.1,-0.015,["Dominant";"second order"])
+xarrows([6;6],[-0.013;-0.002],-1)
+//------------------------------------------------------------------