To improve the transient performance of the feedback loop discussed in Question 1, you instead choose to implement the P

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To Improve The Transient Performance Of The Feedback Loop Discussed In Question 1 You Instead Choose To Implement The P 1 (149.6 KiB) Viewed 49 times

QUESTION 1 for REFERENCE:

To Improve The Transient Performance Of The Feedback Loop Discussed In Question 1 You Instead Choose To Implement The P 2 (143.92 KiB) Viewed 49 times

To improve the transient performance of the feedback loop discussed in Question 1, you instead choose to implement the PI compensator Ks- 2) HS) = Kp+Ki/s = where K = Kp and z= -K/Kp. a.) Relative to the system poles, there are three possible regions for where the (real) compensator zero can be placed: i. to the left of the plant poles at -2, ii. between the poles at -2 and the origin, and iii. to the right of the origin. Sketch the root locus for each of these three cases. b.) Identify which of the above cases will result in the closed-loop system being unstable for any K > 0. c.) Determine values of Kp and Kj so that the closed-loop transfer function T(S) is an "ideal” second- order system (i.e., no zeros or other poles) with damping ratio 2/2 and the fastest possible settling time. Would you expect better or worse transient response characteristics as compared to the closed-loop system in Question 1 part a?
The transfer function for the dynamics of a particular system is given by 7 G(s) = (s + 2)2 To accurately track at least constant step inputs ya(t), you initially decide to try an integral control strategy with H(s) = K/s. Use MATLAB® to generate the root locus using the rlocus.n command. a.) Use the data cursor in the plot window (although you could more accurately call the function with output arguments and either specify a fine grid of gains or interpolate the result) to find the approximate value of K for which the closed-loop system will have poles with a damping ratio of V2/2. What would you approximate the corresponding settling time to a step input to be? b.) Find the largest value of K for which the closed-loop system will be stable. How does the point at which the locus intersects the imaginary axis relate to the margin/crossover characteristics of L(jw)?