Question: For a system with a proportional controller and a 2nd order plant: C(s)=k, P(s) = 1 (S-1)(s + 2) (4) a) Sketch the Nyquist

For a system with a proportional controller and a 2nd order plant: C(s)=k, P(s) = 1 (S-1)(s + 2) (4) a) Sketch the Nyquist plot (assume the Bode plots are monatomic) (Hint: we have 2 repeated poles!) b) Determine the range of values of k (k>0) for which the closed-loop system will be stable. If impossible, state your reason with Nyquist plot. c) Use MATLAB to sketch the root locus, using rlocus(L) function in MATLAB. Verify your range of k found using root locus by MATLAB.

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