1.

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 =0.75I 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»

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.



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