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+//Example 7.29
+// A reduced order compensator design for a satellite attitude control
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+// State space representation
+F=[0 1;0 0];
+G=[0 1]';
+H=[1 0];
+J=0;
+n=sqrt(length(F));//order of the system
+
+//partioned system
+Faa=F(1,1); Fab=F(1,2);
+Fba=F(2,1); Fbb=F(2,2);
+Ga=G(1);Gb=G(2);
+
+// Desired estimator poles
+Pe=[-5];
+// Observer gain matrix for system 
+L=ppol(Fbb',Fab',Pe);
+L=L';
+disp(L,"L=" );
+//------------------------------------------------------------------
+//State feedback control law u=-Kx=-(K+[L*k2 0])[y xc]'; 
+k1=1; k2=sqrt(2);
+K=[k1 k2];
+Kc=K+[L*k2 0];
+//------------------------------------------------------------------
+//compensator differential equation
+//xc_dot=(Fbb-L*Fab)*xb_hat + (Fba - L*Faa)*y + (Gb - L*Ga)*u
+//xc_dot=((Fbb-L*Fab)-k2)*xc + [(Fba - L*Faa)-(Gb - L*Ga)*(k1+L*k2)+L*(Fbb-L*Fab)]*y 
+Fc=(Fbb-L*Fab)-Gb*k2
+Fy=(Fba - L*Faa)-(Gb - L*Ga)*(k1+k2*L)+(Fbb-L*Fab)*L
+//compensator transfer function
+s=poly(0,'s');
+Gest=syslin('c',Fy/(s-Fc))//estimator transfer function
+Dcr=-[k1+L*k2+k2*Gest]
+disp(Dcr,'Dcr','compensator transfer function')
+//------------------------------------------------------------------
+//Root locus with reduced order compensator
+G=1/s^2;
+G=syslin('c',G);
+exec('./zpk_dk.sci', -1);
+[pl,zr Kp]=zpk_dk(Dcr);
+
+Dcr=poly(zr,'s','roots')/poly(pl,'s','roots')
+Dcr=syslin('c',Dcr);
+evans(G*Dcr)
+zoom_rect([-8 -4  2 4])
+
+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 a reduced order controller and',"$1/s^2$",...
+ "process"],'fontsize',3);
+//------------------------------------------------------------------
+//Frequnecy response for 1/s^2 and compensated
+
+figure,
+bode([-Kp*G*Dcr;G],0.01/2/%pi,100/2/%pi,"rad");
+title(["Frequency response","$G(s)=1/s^2$", "with a reduced...
+ order estimator"],'fontsize',3)
+exec .\fig_settings.sci; //custom script for setting figure properties
+legend('Compensated','Uncompensated')
+//------------------------------------------------------------------