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+//Example 7.23
+// SRL Design for an Inverted Pendulum 
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+
+//Transfer function model of Inverted Pendulum.
+s=poly(0,'s');
+
+nums=-(s+2);
+dens=(s^2-1)
+num_s=-(-s+2);
+den_s=((-s)^2-1)
+G0s=syslin('c',nums/dens); //G0(s)
+G0_s=syslin('c',num_s/den_s); //G0(-s)
+sysGG=G0s*G0_s;
+evans(sysGG)
+title('Symmetric root locus for Inverted Pendulum')
+zoom_rect([-3 -2 3 2])
+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('Symmetric root locus for the inverted pendulum','fontsize',3);
+//------------------------------------------------------------------
+//Root locus design
+//choose rho=1 that places pole at -1.36+-j0.606
+rho=1;
+p=[-1.36+0.606*%i, -1.36-0.606*%i];
+sig=real(p);
+omega=imag(p);
+plot(sig,omega,'ro')
+xstring(-1.25,0.5,["pole locations at";"$\rho=1$"])
+//------------------------------------------------------------------
+//pole-placement design;
+Ac=[0 1;1 0];Bc=[0 -1]'; Cc=[2 1];Dc=0;
+exec('./acker_dk.sci', -1);
+K=acker_dk(Ac,Bc,p);
+disp(K,"K=",spec(Ac-Bc*K),"Closed loop eigen values");
+
+//input gain calculation
+n=sqrt(length(Ac));
+A=[Ac Bc;Cc Dc];
+N=A\[zeros(1,n) 1]';
+Nx=N(1:n);
+Nu=N(n+1);
+
+//feedforward gain (input gain)
+Ntilde=Nu+K*Nx;
+
+//Step respose
+t=0:0.1:4.5;
+syscl=syslin('c',(Ac-Bc*K),Bc*Ntilde, Cc, Dc)
+[y x]=csim('step',t,syscl); //closed loop response
+figure,
+plot(t,y);
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title('Step response for inverted pendulum','fontsize',3);
+xlabel('Time t (sec.)','fontsize',2);
+ylabel(["Position","$x_1$"],'fontsize',2);
+//------------------------------------------------------------------