Problem 1: [50 points] Consider the unity feedback control system Controller Process R(s) G (s) G(s) Assume that the pla

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Problem 1 50 Points Consider The Unity Feedback Control System Controller Process R S G S G S Assume That The Pla 1 (67.24 KiB) Viewed 47 times

Problem 1: [50 points] Consider the unity feedback control system Controller Process R(s) G (s) G(s) Assume that the plant is the system R₁ R₂ www ww u(t) Cy(t) where L = 1.1765H, C = 0.0170F, R₁ = 50, and R₂ = 50. a) Derive the transfer function G(s) of the plant from the input u(t) to the output y(t). b) It is required that the closed loop system has a steady state error which is less than 10% and the overshoot is less than 13% for a step input. Design a first order controller which satisfies these requirements. Explain why your controller will perform the job. Plot the response and verify that the requirements are satisfied. c) Implement the controller as an op-amp circuit. In other words, design an op-amp circuit and choose the values of its components such that it has the TF of the controller you designed in part b). Y(s)