Answer to Question #233487 in Chemical Engineering for Lok

Question

Consider the following transfer function Gp=S/(2S+1)^4 the time constant is in seconds. The crossover frequency of the process in rad's is

a. 20 b. 0.1

c. 0.5

d. 0.05

Answer 1

$G_p=\dfrac{S}{(2S+1)^4}$

Partial fraction expansion;

$\dfrac1{(2 (2 S + 1)^3)} - \dfrac1{(2 (2 S + 1)^4)}$

let s = 0 in the transfer function, the resulting response c(t) is

$c(t) = 1-\exp^{-2t}$

The time constant is thus,

$\tau =1/2$ second