Question

The transfer function Y(s)/U(s) of a system described by the state equations dx/dt=-2x+2u  and y(t) = 0.5x is:

(a) 0.5/(s-2)

(b) 1/(s-2)

(c) 0.5/(s+2)

(d) 1/(s+2)

The question was posed to me in an interview for job.

My question is taken from State Variable Analysis topic in section Time Response Analysis, Design Specifications and Performance Indices of Control Systems

Answer 1

Right choice is (d) 1/(s+2)

To explain I would say: Taking Laplace transform of the equation X(s) = 2U(s)/(s+2)

Then Y(s)/U(s) =1/(s+2).