Question

Linear Control Systems MCTE4250 Question 4 (5 points) Note: The solution to this question is not unique and should be optimized. A feedback control system is shown in Figure below where H(s) is representing the FL'17 controller transfer function. and H(s)=(s+a) H(s) It is desired that the system behaves approximately like a second order system with a maximum overshoot of-5% and a settling time of~4 sec. Determine the controller parameters that achieve the control objective.

Answer 1

Given G(s) = 1/s(s + 2): M(s) = k/s + a y(s)/R(s) = G(s)/1 + G(s). H(s) 1/s(s + 2)/1 + 1/s(s + 2). k/(s + a) = 1/s(s + 2)/s(s + 2) (s + a) + k/s(s + 2) (s + a) = s + a/a(s^2 + 2s + as + 2a) + k = s + a/s^3 + 2s^2 + as^2 + 2as + k therefore y(s)/R(s) = s + a/s^3 + (2 + a)s^2 + 2as + k But given system behaves approximately like a second - order system therefore we can assume y(s)/R(s) approximatelyequalto s + a/(2 + a)s^2 + 2as + k \r\n k = 4.5/0.476 = 9.45 therefore k = 9.45: a = 6