Question: Problem 3. Pole placement with PI Control (10 pts.) Consider the closed-loop system involving a first-order plant shown in the figure below. e(t) RO

Problem 3. Pole placement with PI Control (10 pts.) Consider the closed-loop system involving a first-order plant shown in the figure below. e(t) RO Ka K sta You will be asked to design the controller for this system, i.e. identify the PI control gains K and Kr. In this problem you will design the closed-loop poles of this system so that they fall within the shaded region of the s-plane shown below. Use the values: 0 = 30 0 = 60 1 = 3+ 2 Im(s) Re(s) a. What values of w and 3 correspond to the shaded regions (5 pts)? b. Let Ka = = 2. Find the values for K and K, such that the poles of the closed-loop system fall in the center of the shaded regions. Take the centers to be at -2 2i (5 pts).

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