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+//Example 7.24
+// LQR Design for a Tape Drive
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+// State space model for a Tape Drive
+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]';
+H3=[0.5 0 0.5 0 0];
+//------------------------------------------------------------------
+// State feedback gain matrix via LQR (riccati equation)
+// (a) Continuous LQR for rho=1
+rho=1;
+R1=1;
+Q1=rho*H3'*H3;
+// Riccati equation
+P1=riccati(F, G*inv(R1)*G', Q1, 'c')
+K1=inv(R1)*G'*P1
+disp(K1,'K1')
+//------------------------------------------------------------------
+// State feedback gain matrix via LQR (riccati equation)
+// (a) Comparision in step response with rho=0.1,1,10.
+rho=0.1;
+R2=1;
+Q2=rho*H3'*H3;
+// Riccati equation
+P2=riccati(F, G*inv(R2)*G', Q2, 'c')
+K2=inv(R2)*G'*P2
+
+rho=10;
+R3=1;
+Q3=rho*H3'*H3;
+// Riccati equation
+P3=riccati(F, G*inv(R3)*G', Q3, 'c')
+K3=inv(R3)*G'*P3
+//------------------------------------------------------------------
+//input gains for step reference with rho=0.1,1,10.
+Ntilde1=-inv(H3*inv(F-G*K1)*G);
+Ntilde2=-inv(H3*inv(F-G*K2)*G);
+Ntilde3=-inv(H3*inv(F-G*K3)*G);
+
+//Closed loop system with rho=0.1,1,10.
+syscl1=syslin('c',(F-G*K1),G*Ntilde1,H3,0);
+syscl2=syslin('c',(F-G*K2),G*Ntilde2,H3,0);
+syscl3=syslin('c',(F-G*K3),G*Ntilde3,H3,0);
+
+//step response with rho=0.1,1,10.
+t=0:0.1:12;
+[y1 x1]=csim('step',t,syscl1); //closed loop response
+[y2 x2]=csim('step',t,syscl2); //closed loop response
+[y3 x3]=csim('step',t,syscl3); //closed loop response
+
+figure,
+a1=newaxes();
+a1.axes_bounds=[0,0,1.0,0.5];
+plot(t,y1);
+plot(t,y2,'r-.');
+plot(t,y3,'m:');
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('(a)Step response of step servo motor for LQR Design','fontsize',3);
+xlabel('Time t (sec.)','fontsize',2);
+ylabel(["Tape Position","$x_3$"],'fontsize',2);
+
+xstring(4.1,0.85,"$\rho=1$")
+xstring(5.5,0.75,"$\rho=0.1$")
+xstring(2.1,1.05,"$\rho=10$")
+//------------------------------------------------------------------
+//Tensions for the Tape
+//For tape output is Ht=[-0.2 -0.2 0.2 0.2 0];
+Ht=[-0.2 -0.2 0.2 0.2 0];
+H3=Ht;
+//input gains can not be computed because of singularity. so set it 1;
+Ntilde1=1;
+Ntilde2=1;
+Ntilde3=1;
+
+//Closed loop system with rho=0.1,1,10.
+syscl1=syslin('c',(F-G*K1),G*Ntilde1,H3,0);
+syscl2=syslin('c',(F-G*K2),G*Ntilde2,H3,0);
+syscl3=syslin('c',(F-G*K3),G*Ntilde3,H3,0);
+
+//step response with rho=0.1,1,10.
+t=0:0.1:12;
+[y1 x1]=csim('step',t,syscl1); //closed loop response
+[y2 x2]=csim('step',t,syscl2); //closed loop response
+[y3 x3]=csim('step',t,syscl3); //closed loop response
+
+a2=newaxes();
+a2.axes_bounds=[0,0.5,1.0,0.5];
+plot(t,y1);
+plot(t,y2,'r-.');
+plot(t,y3,'m:');
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('(b)Corresponding tension for Tape servomotor step response','fontsize',3);
+xlabel('Time t (sec.)','fontsize',2);
+ylabel(["Tape Tension","T"],'fontsize',2);
+
+
+xstring(4.3,-0.05,"$\rho=1$")
+xstring(6,-0.1,"$\rho=0.1$")
+xstring(1.5,-0.03,"$\rho=10$")
+//------------------------------------------------------------------