Question

A system with unity feedback having open loop transfer function as G(s) = K(s+1)/s3+as2+2s+1. What values of ‘K’ and ’a’ should be chosen so that the system oscillates ?

(a) K =2, a =1

(b) K =2, a =0.75

(c) K =4, a =1

(d) K =4, a =0.75

I had been asked this question during an online exam.

My question is taken from Relative Stability Analysis in portion Stability and Algebraic Criteria of Control Systems

Answer 1

The correct option is (b) K =2, a =0.75

Easiest explanation: Solving Routh Hurwitz table whenever row of zero occurs, the roots are located symmetrically on the imaginary axis then the system response oscillates, a =1+K/2+K. If K =2 is consider then a =0.75.