Problem-3. Given the following open-loop plant, 20(s + 2) G(s) s(s+5)(8 + 7) design a controller to yield a 10% overshoo

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Problem 3 Given The Following Open Loop Plant 20 S 2 G S S S 5 8 7 Design A Controller To Yield A 10 Overshoo 1 (111.84 KiB) Viewed 9 times

Problem-3. Given the following open-loop plant, 20(s + 2) G(s) s(s+5)(8 + 7) design a controller to yield a 10% overshoot and a settling time of 2 seconds. Place the third pole 10 times as far from the imaginary axis as the dominant pole pair. (a) Use the Controllable Canonical Form for state feedback and find the feedback gain vector Kc = [kic kac k3c] by means of coefficient matching method. (b) Find the same gain vector by means of Ackerman's formula. (C) Verify the results in MatLAB with the following function: K=acker(Ac, Bc, D) or K=place(Ac, Bc, D), where D is the vector consisting of the three desired poles, i.e. D= [sl conj(sl) 10*real(sl)] (d) Use the Observable Canonical Form for state feedback and find the feedback gain vector K, = [k10 k20 k3] by means of K=acker(Ao, Bo, D) or K=place(A0, Bo, D) in MatLAB. (e) Find the similarity transformation (from CCF to OCF) matrix P by means of controllability matrices (CM) of the two forms as P = CM, CM; and (1) Find K, = K.P-1 and check if you found the same result of (d). (g) Do the computer simulation of system before and after the full state feedback.