Question

6 and controller C(s), as shown in the Consider a unity-feedback control system with plant G(s)- following figure. Reference Error Controller Plant r(t) e(t) u(t) y(t) C(s) G(s) [5] (a) Determine the poles, zeros, order, type, relative degree, and de gain of the plant G(s) and show [5] (b) Can a P controller C(s)Kp stabilize the plant G(s)? If so, find the values of Kp that are [4] (c) Show using the Final Value Theorem that the system with the P controller from (b) can track a [6] (d) Show that it however cannot track a unit-ramp reference r(t)t with zero steady-state error using the Routh-Hurwitz criterion that G(s) is not stable necessary and sufficient unit-step reference r(t)1 with zero steady-state error lime(t) 0. Can the error be made arbitrarily small with Kp without losing stability? 12] (e) Can a PI controller C(s)Kpstabilize the plant G(s) and, at the same time, yield zero steady-state error to both unit-step and unit-ramp references? If so, find the values of Kp and K1 that are necessary and sufficient

Answer 1