5.8.1.40 For the system of Figure 1 let For the system of Figure 1 G H C R + - Figure 1: Standard Closed Loop Con guration G(s)H(s)= K(s+2) s(s+ 1)(s+20)(s+30) ;; The MATLAB program %sm5.5.1.40 z1=2 p1 = 0 p2 = 1 p3 = 20 p4 = 30 s=linspace(-19,-4,500) K=(abs(s+p1).*abs(s +p2).*abs(s+p3).*abs(s+p4))./abs(s + z1);; figure(1) plot(s,K) grid on axis([-10,-4,2400,2600]) print -deps 58140bo.eps K=linspace(0,1000,1000);; gh = zpk([-2],[0 -1 -20 -30],10) [R,K] = rlocus(gh,K);; figure(2) plot(R,'k.') print -deps 58140rl.eps Draws the plot of gain versus position along the negativerealaxis, shown in Figure 2 and the root locus shown in Figure 3 1 -10 -9 -8 -7 -6 -5 -4 2400 2420 2440 2460 2480 2500 2520 2540 2560 2580 2600 Figure 2: Searchfor breakin and break out points -45 -40 -35 -30 -25 -20 -15 -10 -5 0 -15 -10 -5 0 5 10 15 Figure 3: accurate root locus 2