Slow dominant pole num=5;den=conv([1 1],[1 5]);step(num,den,6) Amplitude Time (sec.) Step Response 0 1 2 3 4 5 6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fast dominant pole num=5.5*[1 0.91];den=conv([1 1],[1 5]);step(num,den,6) Amplitude Time (sec.) Step Response 0 1 2 3 4 5 6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Similar example, but with second order dynamics combined with a simple real pole. z=.15;wn=1;plist=[wn/2:1:10*wn]; nd=wn^2;dd=[1 2*z*wn wn^2];t=[0:.25:20]'; sys=tf(nd,dd);[y]=step(sys,t); for p=plist; num=nd;den=conv([1/p 1],dd); sys=tf(num,den);[ytemp]=step(sys,t); y=[y ytemp]; end plot(t,y(:,1),'d',t,y(:,2),'+',t,y(:,4),'+',t,y(:,8),'v'); ylabel('step response');xlabel('time (sec)') legend('2 nd ',num2str(plist(1)),num2str(plist(3)),num2str(plist(7))) 0 5 10 15 20 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 step response time (sec) 2nd 0.5 2.5 6.5 For values of p=2.5 and 6.5, the response is very similar to the second order system. The response with p=0.5 is clearly no longer dominated by the second-order dynamics Example: G(s)=1/2^2 Design Gc(s) to put the clp poles at –1 + 2j z=roots([-20 49 -10]);z=max(z),k=25/(5-2*z),alpha=5*z/(5-2*z), num=1;den=[1 0 0]; knum=k*[1 z];kden=[1 10*z]; rlocus(conv(num,knum),conv(den,kden)); hold;plot(-alpha+eps*j,'d');plot([-1+2*j,-1-2*j],'d');hold off r=rlocus(conv(num,knum),conv(den,kden),1)' z = 2.2253 k = 45.5062 alpha = 20.2531 These are the actual roots that I found from the locus using a gain of 1 (recall that the K gain is already in the compensator) r = -20.2531 -1.0000 - 2.0000i -1.0000 + 2.0000i -20 -15 -10 -5 0 5 -20 -15 -10 -5 0 5 10 15 20 Real Axis Imag Axis