Suppose you are to design a unity feedback controller for a first-order plant depicted in Fig. 3.59. (As you will learn in Chapter 4, the configuration shown is referred to as a proportional-integral controller.) You are to design the controller so that the closed-loop poles lie within the shaded regions shown in Fig. 3.60. (a) What values of n and correspond to the shaded regions in Fig. 3.59? (A simple estimate from the figure is sufficient.) (b) Let K = = 2. Find values for K and KI so that the poles of the closed-loop system lie within the shaded regions. Figure 3.59 Unity feedback system for 3.28 Figure 3.60 Desired closed-loop pole locations for 3.28 (c) Prove that no matter what the values of K and are, the controller provides enough flexibility to place the poles anywhere in the complex (left-half) plane.

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