Problem 1. (Proportional Compensator) Suppose C(s) = K with K > 0 and the design objective is to have the dominant closed-loop poles at such locations so that the maximum overshoot of the step response of the closed-loop system is roughtly 16.3%. (a) Use Matlab to plot the root locus of the system; (b) What should be the damping ratio ( for the desired dominant closed-loop poles to meet the design objective? (c) What locations of the dominant closed-loop poles with the above damping ratio can you achieve using the compensator C(s) = K and what value of K should be chosen? You can use Matlab to find the approximate or numerical answers in this part; (d) With the choice of K in (c), what are the settling time (5% criterion) and the steady-state tracking error for ramp input of the compensated closed-loop system?
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