Problem 4 [25 marks] Consider again the generic feedback system shown in Figure 4, where G(s) is the plant's transfer fu

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Problem 4 25 Marks Consider Again The Generic Feedback System Shown In Figure 4 Where G S Is The Plant S Transfer Fu 1 (117.45 KiB) Viewed 30 times

Problem 4 [25 marks] Consider again the generic feedback system shown in Figure 4, where G(s) is the plant's transfer function assumed to be stable and its Bode diagram is given in Figure 5 and C(s) is the controller's transfer function. Use the provided Bode plot to answer the following questions. (a) Let C(s) = 1 (unitary static gain), deduce: i) the crossover frequency of the loop transfer function. [2 marks] ii) the phase margin of the loop transfer function. [2 marks] (b) Let C(s) = k (proportional controller): i) find the largest crossover frequency which can be achieved with this type of controller while maintaining a phase margin of at least 30°. [3 marks] ii) find the value of k for which the crossover frequency found in question (b)-i) is attained. [3 marks] (c) Let C(s) = kH(s), where k is a static gain, and H(s) is a phase advance compen- sator in the form: B sta H(s) = Väs+B i) find values of k, a and b such that the cross-over frequency of the resulting loop transfer function is 30 rad/sec and the phase margin is at least 30°. [10 marks] ii) draw the Bode diagram of the so-obtained controller C(s). You can either use Matlab to have the exact Bode plot or you can draw the line approxi- mation of the Bode diagram. [5 marks] Hint: use the following tuning rules to design the phase advance compensator. In order to tune H(s) to attain desired on (0 dB frequency) and on (maximum phase advance) choose: α = a 1-sin(On) 1+ sin(on) Wh, B GV 1+sin(On) 1-sin(on) Wh