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+//Example 9.12
+//Conditionally stable system.
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function and its root locus 
+
+s=poly(0,'s');
+num=0.1;
+den=(s^2+0.2*s+1)*(s);
+Gs=syslin('c',num/den)
+
+//Nyquist plot of the system
+nyquist(Gs,0.035,10)
+title("Nyquist plot and describing function to determine limit...
+ cycle",'fontsize',3);
+
+f=gca();
+f.x_location = "origin"
+f.y_location = "origin"
+h=legend('');
+h.visible = "off"
+xset("color",2);
+
+// Nyquist Plot of Describing Function for saturation nonlinearity. 
+omegat=0.05:0.05:%pi;
+a=sin(omegat);
+N=0.1;
+k=1; 
+
+Keq=2/%pi*(k*asin(N ./a /k)+N ./a .* sqrt(1-(N/k ./a) .^2));
+DF_nyq=-1 ./Keq; 
+
+plot(DF_nyq,zeros(1,length(DF_nyq)),'m-.')
+exec .\fig_settings.sci; //custom script for setting figure properties
+zoom_rect([-0.8 -0.5 0.2 0.5])
+
+//limit cycle points
+plot(-0.5,0,'bo');
+
+xset('font size',3)
+xstring(-0.78,0.08,"limit cycle point");
+xarrows([-0.6;-0.52],[0.1;0.02],-1)
+xstring(-0.62,-0.22,"$-\frac{1}{K_{eq}$");
+xarrows([-0.55;-0.55],[-0.1;0],-1)
+//------------------------------------------------------------------
+//Describing Functin for saturation nonlinearity.
+Keq=[]
+i=1;
+
+for a=0:0.2:10
+    if k*a/N > 1 then
+    Keq(i,1)=2/%pi*(k*asin(N/a/k)+N/a*sqrt(1-(N/k/a)^2))
+    else
+    Keq(i,1)=k
+    end
+    i=i+1;
+end
+
+a=0:0.2:10;
+a=a';
+
+figure,
+plot(a,Keq)
+xlabel('$a$');
+ylabel('$K_{eq}$');
+
+xset('font size',3);
+title("Describing Function for a saturation nonlinearity...
+ with N=0.1 and k=1",'fontsize',3);
+exec .\fig_settings.sci; //custom script for setting figure properties
+zoom_rect([0 0 10 1.1])
+//------------------------------------------------------------------
+