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+//Example 5.9
+//Root locus for the system having complex multiple roots.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+//System transfer function
+
+s=poly(0,'s');
+
+NumL=1;
+DenL=s*(s+2)*[(s+1)^2+4];
+
+L=NumL/DenL;
+
+zr=roots(NumL);
+pl=roots(DenL);
+
+//------------------------------------------------------------------
+//Angle of departure.
+//Find angle of departure from pole at phi1= - 1 + 2i
+//(real poles don't have angle of departure,
+// they move along real axis only) 
+
+//phi2=angle[(Departing pole)- (pole at 0)]
+[Mphi1, phi1] = polar(pl(1)-pl(4)) 
+phi1=real(phi1)*180/%pi;           //angle in degree
+
+//phi2=angle[(Departing pole)- (pole at -2)]
+[Mphi2, phi2] = polar(pl(1)-pl(3)) 
+phi2=real(phi2)*180/%pi;           //angle in degree
+
+//phi2=angle[(Departing pole)- (pole at - 1 - 2i)]
+[Mphi4, phi4] = polar(pl(1)-pl(2))
+phi4=real(phi4)*180/%pi;           //angle in degree
+
+//Therefore angle of departure phi1 at - 1 + 2i is
+//phi3 = 180 + sum(angle to zeros) - sum(angle to poles)
+
+phi3 = 180 - sum(phi1+phi2+phi4)
+
+//angle contributions in figure 
+figure(0)
+plzr(L)
+xset('font size',1.5)
+xarrows([real(pl(4));real(pl(1))],[imag(pl(4));imag(pl(1))],0,2)
+xarrows([real(pl(4)); 1],[0;0],0,2)
+xarc(-0.5,0.5,1,1,0,phi1*64)
+xstring(0.5,0.25,"$\phi_1$")
+
+xarrows([real(pl(3));real(pl(1))],[imag(pl(3));imag(pl(1))],0,5)
+xarrows([real(pl(3)); -1.3],[0;0],0,5)
+xarc(-2.5,0.5,1,1,0,phi2*64)
+xstring(-1.5,0.25,"$\phi_2$")
+
+xarrows([real(pl(2));real(pl(1))],[imag(pl(2));imag(pl(1))],0,17)
+xarrows([real(pl(2)); -0.3],[-2;-2],0,17)
+xarc(-1.5,-1.5,1,1,0,phi4*64)
+xstring(-0.5,-1.7,"$\phi_4$")
+
+xstring(-0.8,2,"$\phi_1$")
+
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(['Figure to computing a departure angle for',...
+'$L(s)=\frac{1}{s(s+2)[(s+1)^2+4]}$'],'fontsize',3)
+zoom_rect([-4 -3 4 3])
+h=legend('');
+h.visible = "off"
+//------------------------------------------------------------------
+//Root locus of system transfer function with controller
+figure(1)
+evans(L)
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title(['Root locus for','$L(s)=\frac{1}{s(s+2)[(s+1)^2+4]}$']...
+,'fontsize',3)
+zoom_rect([-4 -3 4 3])
+h=legend('');
+h.visible = "off"
+//------------------------------------------------------------------