Answer Happy

c=3
d=4
e=5
Q2. (a) Global Tech is a company that specialises in the design of next generation technology. You have recently been employed as a graduate design engineer to work as part of a team of engineers to develop a low-cost mobility device for a client. Provide a concise discussion on how you would fulfil this task, including any relevant engineering design approach and desirable objectives. [7 marks] Gp(s) R(S) S C(s) (s + 2)(s2 - 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, Peak time < 0.20 seconds, Steady-state error $13.5E%.

(d) Suggest suitable controller(s) that could satisfy the design requirements. Note: maximum marks will be awarded for answers that contain a concise, thoughtful justification of the proposed controller(s). [4 marks] (e) A compensator of the form shown in equation (2.1) is implemented to address the design requirements. (s + Z.)? (2.1) Gc(s) = RC s Design the compensator parameters using the root-locus magnitude and angle criteria technique. [6 marks] (1) Show that the compensator in equation (2.1) satisfies both the transient and steady-state design requirements and, as such, that your boss is pleased with you. [3 marks]