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Stability of Linear Systems

Design a proportional and integral controller, G= k_p ((a+1/T_1)/s) for the plant,

P = 1/((X+1)(S+3)) to have dominant poled with (see attachment)

i) Use rough sketches of the root locus to determine the location of the controller zero (i.e. find T_1)

ii) Calculate the required controller gain Kp, (An accurate root locus is not required)

Question 1: Nyquist Analysis

Consider the following open loop system: L= (s+3)/(s^2+2)

a) Make a rough sketch of the Bode plot
b) Sketch the full Nyquist diagram
c) Determine if the closed loop system is stable or not
d) Sketch the positive gain root locus of the system with open loop transfer function, kL(s) and comment on your answer in corresponding to A - 1

Plot the root locus for the following system: L= k (s^2+2s+2)/(s(s+1)(s+2)) as the feedback gain is varied from -infinity to positive infinity. 1/L(s) has turning points at s= -1.49 and s=-0.51

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