Question

B-7-6. Consider the system shown in Figure 7-59. Plot the root loci for the system. Determine the value of K such that the damping ratio ζ of the dominant closed-loop poles is 05. Then determine all closed-loop poles. Plot the unit-step response curve with MATLAB. s(s2 +4s +5) Figure 7-59 Control system.

Can you Solve in matlab please. I need your help

Answer 1

Ans 8-7- 2 2. -123 130, (Qi+1) 2. Th

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1)matlab code and result

clear;clc;
%%
s=tf('s');
G=1/(s*(s^2+4*s+5));%open loop transfer function
zeta=0.5;
figure(1)
rlocus(G);
sgrid([0.5],[]);
[k,p]=rlocfind(G);%select a point where zeta=0.5 line cut rootlocus
disp(['value of k at zeta=0.5 K=',num2str(k)]);
disp('closed loop ploe at zeta=0.5');
disp(p);
T=feedback(k*G,1);%close loop transfer function
figure(2)
step(T);

2)matlab result

Select a point in the graphics window

selected_point =

-0.6262 + 1.0829i

value of k at zeta=0.5 K=4.2956
closed loop ploe at zeta=0.5
-2.7498 + 0.0000i
-0.6251 + 1.0823i
-0.6251 - 1.0823i

Root Locus 0.5 0 -2 0.5 -3 -5 -1 -3 -2 Real Axis (seconds)

1.2 Step Response 0.8 0.6 0.4 0.2 6 Time (seconds) 10