Question

Given the unity feedback system

G(s)= K(s+4)/s(s+1.2)(s+2)

Find:

a. The range of K that keeps the system stable
b. The value of K that makes the system oscillate
c. The frequency of oscillation when K is set to the value that makes the system oscillate

Answer 1

A.) 0 > K > 9.6

B.) K = 9.6

C.) w = +/- 2 sqrt (3)

Step-by-step explanation:

G(s)= K(s+4)/s(s+1.2)(s+2)

For a closed loop stability, we can analyse by using Routh - Horwitz analysis.

To make the pole completely imaginary, K must be equal to 9.6 Because for oscillations. Whereas, one pair of pole must lie at the imaginary axis.

Please find the attached files for the solution