Ge(s) R(S) S C(s) (s + 2)(s? - 25) Figure Q2a The transfer function of an inverted pendulum plant is shown in Figure Q2a

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Ge S R S S C S S 2 S 25 Figure Q2a The Transfer Function Of An Inverted Pendulum Plant Is Shown In Figure Q2a 1 (109.26 KiB) Viewed 37 times

Ge(s) R(S) S C(s) (s + 2)(s? - 25) Figure Q2a The transfer function of an inverted pendulum plant is shown in Figure Q2a: (b) Using an s-plane graphical sketch and suitable control systems theory, show that the plant's natural response is unstable. [4 marks] In a desperate attempt to stabilise the plant in Figure Q2a, a novice control engineer designed a unity feedback control system that includes a proportional controller, Ge(s) = K, connected in cascade to the inverted pendulum plant. (c) With the aid of the root locus technique and the Routh-Hurwitz stability criterion, show that the feedback system is not stable for all positive values of K. [6 marks] You have recently been employed to salvage the situation. Your boss has informed you that the objective of the task is to design a new controller that guarantees the stability of the unity feedback system while satisfying the following transient and steady-state performance requirements: Settling time < 0.50 seconds, C=5 • Peak time < 0.2D seconds, 4 Steady-state error 5 +3.5E%. E: 1 D:4