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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,"$\rho=10$")

+//------------------------------------------------------------------

diff --git a/3432/CH7/EX7.24/Ex7_24_f0.pdf b/3432/CH7/EX7.24/Ex7_24_f0.pdf
new file mode 100644
index 000000000..b91050fcc
--- /dev/null
+++ b/3432/CH7/EX7.24/Ex7_24_f0.pdf