Question

a) root locus of uncompensated system:

clc;

clear all;

s=tf('s');

g=12/(s*(s+10)*(s+70));% plant transfer function

rlocus(g);grid % locus of uncompensated system

for 5% overshoot the system is not meeting the design requirements.

The compensator gain found by magnitude criteria at the dominant pole is K=459.7012

c) compensated system root locus:

clc;

clear all;

s=tf('s');

g=12/(s*(s+10)*(s+70));% plant transfer function

gc=(s+7.9364)/(s+11.4403)% compensator transfer function

rlocus(g*gc);grid % locus of compensated system

d) step response

clc;

clear all;

s=tf('s');

g=12/(s*(s+10)*(s+70));% plant transfer function

gc=(s+7.9364)/(s+11.4403)% compensator transfer function

k=459.7012;

step(feedback(k*g*gc,1));grid

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