Please only answer Part d) of this question! Q-1 (22 marks) Consider the system
ID: 2291837 • Letter: P
Question
Please only answer Part d) of this question!
Q-1 (22 marks) Consider the system G(s)as + bs s+c a) Let a - 1, b- -2 and c-1. Is G(s) stable or unstable? Why? b) Find the ranges of a, b and c such that the closed-loop system Ge(s)- c) Let a 1, b2 and c-2. Find the poles of the system G(s) G(s) 1+G(s) is stable. d) Let a = 0, b = 1 and c = 1, Design a PID controller of the form leading to a closed-loop system having the following performance * Zero steady state error for a unit-step input, * Settling time T,-2s, * Percent-Overshoot P.O. 5%.Explanation / Answer
1 for a=1 b=-2 and c=1 g(s) is not stable as one of the coefficient us negative which shows that one of the pole lies in the right half which makes the system unstable
2 To find the range if a, b, c in g(s)/(1+g(s))
We can use routh hurwitz criterion
We will get
Ac>b and c>0
The poles of g(s) when a=1,b=-2,c=-2
Poles will be
S=2,+j, -j