To find K using Routh criterion Figure Q2(a) shows a unity feedback control system.(i) Assume that the system is controlled by a proportional controller given by G₁(s) = K. Findthe range of value of K for which the system is stable by applying the Routh-Hurwitz stabilitycriterion.(ii) If a proportional-plus-derivative controller Ge(s) = Kp + Kps is used instead, find theminimum control gains Ke and Ko so that the system will be stable as well as achieve a steady-state error es <2% for a unit step input.ControllerR(s) +Plant2C(s)G₁(s)3s³ + 4s² + 5s + 2

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Answered: Figure Q2(a) shows a unity feedback…

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter12: Power System Controls

Section: Chapter Questions

Problem 12.2P

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4. Suppose you are to design a unity feedback controller for a first-order plant depicted in Figure Ba, You are to design the controller so that the closed-loop poles lie within the shaded regions shown in Figure 3b, ↑ Im(s) 4 8, F2 e(1) RO K OY S+ a -4 -2 Re(s) (a) (ь) Figure 3: a) Unity feedback system and b) desired closed-loop pole locations. (а) What values of wn and § correspond to the shaded regions in Figure 3b? Let Ka = a = 2. Find values for K and K1 so that the poles of the closed-loop system lie within the shaded (b) regions. (c) anywhere in the complex (left-half) plane. Prove that no matter what the values of Ka and a are, the controller provides enough flexibility to place the poles

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