R(s)(i)(ii)(iii)A system, G(s) =(s² +45+4)S³+45²-s-4¹feedback as shown in Figure 3.1.KG(s)Figure 3.1is to be controlled by a proportional controller with unityY(s)w [Rad/s] 0.01 0.02 0.04Gain [dB] 24.5 12.2 12.2Phase [Deg] -95 -100 -109Derive the closed-loop characteristic equation (CLCE) of the system.With K = 2, is the closed-loop system stable?Find the range of value of K such that all its CLCE roots have real partless than -1.[Hint: Routh-Hurwitz Stability Criterion](b)Table 4.1 shows the experimentally measured frequency response of an open-loopprocess plant G(s). It is decided that a proportional controller with gain K is to be usedas the controller for this plant in the unity feedback configuration. (Note: Graph paperis provided on Page 19.)Table 4.10.08 0.1 0.2 0.3 0.4 0.8 15.4 3.0 -6.1 -12.7 -18.0 -33.4 -39.2-127-135 -167 -189 -206-249-262(i) Plot the Bode plot of the open-loop transfer function using K=1.What is the Gain Margin and Phase Margin of the system?(ii)(iii)It is decided to increase the system's phase margin to 72°, what should be thevalue of K and the new Gain Margin?

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R(S) (i) (ii) (iii) K G(s) Figure 3.1 A system, G(s) = (s² +4s+4) is to be controlled by a proportional controller with unity S³+45²-s-4¹ feedback as shown in Figure 3.1. [Hint: Routh-Hurwitz Stability Criterion] Y(s) Derive the closed-loop characteristic equation (CLCE) of the system. With K = 2, is the closed-loop system stable? Find the range of value of K such that all its CLCE roots have real part less than -1.

R(S) (i) (ii) (iii) K G(s) Figure 3.1 A system, G(s) = (s² +4s+4) is to be controlled by a proportional controller with unity S³+45²-s-4¹ feedback as shown in Figure 3.1. [Hint: Routh-Hurwitz Stability Criterion] Y(s) Derive the closed-loop characteristic equation (CLCE) of the system. With K = 2, is the closed-loop system stable? Find the range of value of K such that all its CLCE roots have real part less than -1.

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

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.22P

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