Question

Question 1 (60 points) Consider the following block diagram where G(s)- Controller R(s) G(s) (a) Sketch the root locus assuming a proportional controller is used. [25 points] (b) Design specifications require a closed-loop pole at (-3+j1). Design a lead compensator to make sure the root locus goes through this point. For the design, pick the pole of the compensator at-23 and analytically find its zero. (Hint: Lead compensator transfer function will be Ge (s)$+23 First plot the poles and zeros of both G(s) and Ge (s) on the s-plane. Then find the appropriate value of 'z' by writing the phase condition equation with (-3 +j1) being the test point) [20 points] (c) Sketch the root locus with the lead compensator in place. [15 points] (d) Determine the K value that places a closed-loop pole at the desired location (by letting s-3+ji in the characteristic equation and solving for K) [5 points extra credit]

Answer 1

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