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-rw-r--r--3432/CH5/EX5.8/Ex5_8_f1.pdfbin0 -> 25093 bytes
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+//Example 5.8
+//Root locus for noncollocated case.
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+
+//------------------------------------------------------------------
+//System transfer function with controller
+
+s=poly(0,'s');
+NumD=(s+1);
+DenD=(s+12);
+sysD=NumD/DenD;
+
+NumG=1
+DenG=s^2*((s+0.1)^2+(6.6)^2)
+
+sysG=NumG/DenG;
+
+NumL=NumD*NumG;
+DenL=DenD*DenG;
+
+sysL=NumL/DenL;
+
+zr=roots(NumL);
+pl=roots(DenL);
+
+//------------------------------------------------------------------
+//Angle of departure.
+//Find angle of departure from pole at phi1= - 0.1 + 6.6i
+//(real poles don't have angle of departure,
+//they move along real axis only)
+
+//psi1=angle[(Departing pole)- (zero at - 1]
+[Mpsi1, psi1] = polar(pl(2)-zr(1))
+psi1=real(psi1)*180/%pi; //angle in degree
+
+//phi2=angle[(Departing pole)- (pole at 0)]
+[Mphi2, phi2] = polar(pl(2)-pl(4))
+phi2=real(phi2)*180/%pi; //angle in degree
+
+//phi3 is same as phi2, as pole is repeated at 0.
+phi3=phi2;
+
+//phi4=angle[(Departing pole)-(pole at - 0.1 - 6.6i )]
+[Mphi4, phi4] = polar(pl(2)-pl(3))
+phi4=real(phi4)*180/%pi; //angle in degree
+
+//phi5=angle[(Departing pole)- (pole at - 12 )]
+[Mphi5, phi5] = polar(pl(2)-pl(1))
+phi5=real(phi5)*180/%pi; //angle in degree
+
+//Therefore angle of departure phi1 at - 0.1 + 6.6i is
+//phi1 = 180 + sum(angle to zeros) - sum(angle to poles)
+
+phi1 = 180 + sum(psi1) - sum(phi2+phi3+phi4+phi5)
+
+//angle contributions in figure
+figure(0)
+plzr(sysL)
+xset('font size',1.5)
+xarrows([real(pl(1));real(pl(2))],[imag(pl(1));imag(pl(2))],0,2)
+xarrows([real(pl(1)); -10],[0;0],0,2)
+xarc(-13,1,2,2,0,phi5*64)
+xstring(-11,0.05,"$\phi_5$")
+
+xarrows([real(zr(1));real(pl(2))],[imag(zr(1));imag(pl(2))],0,6)
+xarrows([real(zr(1)); -0.3],[0;0],0,6)
+xarc(-2,1,2,2,0,psi1*64)
+xstring(-0.7,1,"$\psi_1$")
+
+xarrows([real(pl(4));real(pl(2))],[imag(pl(4));imag(pl(2))],0,5)
+xarrows([real(pl(4)); 1],[0;0],0,5)
+xarc(-1,1,2,2,0,phi2*64)
+xstring(0.8,0.5,"$\phi_2,\,\phi_3$")
+
+xarrows([real(pl(3));real(pl(2))],[imag(pl(3));imag(pl(2))],0,17)
+xarrows([real(pl(3)); 2],[imag(pl(3));imag(pl(3))],0,17)
+xarc(-1.1,-5.6,2,2,0,phi4*64)
+xstring(0.8,-5.5,"$\phi_4$")
+
+xstring(0.3,6.5,"$\phi_1$")
+
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(['Figure to compute a departure angle for',...
+'$L(s)=\frac{s+1}{s+12}\frac{1}{s^2[(s+0.1)^2+6.6^2]}$'],...
+'fontsize',3)
+zoom_rect([-15 -8 5 8])
+h=legend('');
+h.visible = "off"
+
+//------------------------------------------------------------------
+//Root locus of system transfer function with controller
+figure(1)
+evans(sysL)
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; //custom script for setting figure properties
+title(['Root locus for','$L(s)=\frac{s+1}{s+12}\frac{1}...
+{s^2[(s+0.1)^2+6.6^2]}$'],'fontsize',3)
+zoom_rect([-15 -8 5 8])
+h=legend('');
+h.visible = "off"
+
+//------------------------------------------------------------------
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