→Kp(1+SKD) X(s) E(s) Input in V Error C(s) Input in V 1 (1+4s)(1 +0.8s) Y(S) Output in °C

316 and controller C(s), as shown in the 3. Consider a unity-feedback control system with plant G(s) following figure. Reference Error Controller Plant r(t) e(t) u(t) y(1) C(s) G(s) (a) Determine the poles, zeros, order, type, relative degree, and de gain of the plant G(s) and show using the Routh-Hurwitz criterion that G(s) is not stable. = Kp stabilize the plant G(s)? If so, find the values of Kp that are (b) Can a P controller C(s) necessary and sufficient. (c) Show using the Final Value Theorem that the system with the P controller from (b) can track a unit-step reference r(t) = 1 with zero steady-state error limo e(t) = 0. (d) Show that it however cannot track a unit-ramp reference r(t) =t with zero steady-state error. Can the error be made arbitrarily small with Kp without losing stability? (e) Can a PI controller C(s) = Kp + AL stabilize the plant G(8) 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…

Explain the fundamental differences between open-loop and closed-loop control systems. Provide examples of each and discuss the advantages and limitations of both approaches.

determine Vo: