Question

The steady state error for a unity feedback system for the input r(t) to the system G(s) =       K(s+2)/s(s^3+7s^2+12s) is 6R/K. The input r (t) is _______

(a) Rt2/2

(b) Rt3/2

(c) Rt5/2

(d) Rt7/2

The question was asked in an international level competition.

The origin of the question is Steady State Error in division Error Analysis of Control Systems

Answer 1

Correct choice is (a) Rt2/2

The best explanation: Ka = 2K/12 = K/6. Ess = 6R/K. So, as we take Rt^2/2 we get 6R/K as the error. The other options can’t be true because the input is exceeding the desired input. It is inversely proportional to the gain.