Question

Question 2: Given the below s-plane, and that H(2)=10. Answer the following questions: jo j 0 -4 -3 -2 -1 j a. Find the zeros and poles of the system? b. What is the transfer function H(S)? C. What is the impulse response (in S-domain only)? d. What is the step response (in S-domain only)?

Answer 1

2) Oriven H (2) =10 so j . a) t sign shows Location of pole and a sign shows location Zeros so, Zeros is at two zeros 7,1 and 2 - 3 Now Poles at P20 P and P₂ = -6 three poles. b) we as know transfer function is H(S) = K[S-Zi)(5-72) (S-P) (5-P2) (5-P₂) where k is the overall gain .: HCS) = K (5+1)(5+3) S (5+2)(5+4) HON, 1 given H(2) = 10 so at s-2 H12) = K (a+1)(2+3) lo 2 (2+2)(2+4) K = 10 X 48 15 k=80x2 0X2 = 32 k = 32 His) = 32(5+1)(5+3) $(5+2)(5+4) transfer function This is the

c) as transfer Imp ulse response is same of system Hes) function Impulse response response = 32 (5+1)(+3. S (5+2)(5+4) d). Step response yes) = HIS). XC5) Where X (s) is unit step '' X (S) = 1 ::y(s) = 32(5+1)(8+3) x [ s(s+2)(5+4) s yes) 32 (5+1)(5+3) S2(5+2) (S+4) this is the step response in s-domain
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