Question

For the following feedback system G(s) = 1/((s + 1) + (s + 2)). For the following feedback system

Which one of the following compensators C(s) achieves this?

(A) 3(1/(s + 5))

(B) 5(0.03/s + 1)

(C) 2(s + 4)

(D) 4(s + 8/s + 3)

Answer 1

Correct option (C) 2(s + 4)  

Explanation:

By observing the options, if we place other options, characteristic equation will have 3rd order one, where we cannot describe the settling time.

If C(s) = 2(s + 4) is  considered

The characteristic equation, is

s² + 3s + 2 + 2s + 8 = 0

⇒ s² + 5s + 10 = 0

Standard character equation s² + 2ξω_ns + ω_n² = 0

ω₂ⁿ = 10; ξω_n = 2.5

Given, 2% settling time, 4/ξω_n  < 2 ⇒ ξω_n  > 2