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3. The following closed-loop systems in Fig. 1 and Fig. 2 operate with a damping ratio of 0.707 (=0.707). The system in Fig. 1 does not have a PI controller, while the one in Fig. 2 does. R(s): S Gain Plant R(s) + E(s) 1 C(s) K (s+1)(s+2)(s+10) Fig. 1: Closed-loop system without PI controller Compensator Plant R(s) + E(s) K(s+0.1) S 1 (s+1)(s+2)(s+10) C(s) Fig. 2: Closed-loop system with a practical PI controller a. Please use Matlab to find the intersection point between line and the root locus of the system in Fig. 1. Then find the K value and one complex closed-loop pole corresponding to the intersection point. Calculate the steady-state error. Show the Matlab code in your answer sheet. b. Please use Matlab to find the intersection point between § line and the root locus of the system in Fig. 2. Then find the K value and one complex closed-loop pole associated with the intersection point. Compare the complex closed-loop pole with the one you just found in task a. Are they very different from each other? Calculate the steady-state error. Show the Matlab codes in your answer sheet. c. Use Matlab/Simulink to plot the step responses of two systems in Fig. 1 and Fig. 2, respectively.

3. The following closed-loop systems in Fig. 1 and Fig. 2 operate with a damping ratio of 0.707 (=0.707). The system in Fig. 1 does not have a PI controller, while the one in Fig. 2 does. R(s): S Gain Plant R(s) + E(s) 1 C(s) K (s+1)(s+2)(s+10) Fig. 1: Closed-loop system without PI controller Compensator Plant R(s) + E(s) K(s+0.1) S 1 (s+1)(s+2)(s+10) C(s) Fig. 2: Closed-loop system with a practical PI controller a. Please use Matlab to find the intersection point between line and the root locus of the system in Fig. 1. Then find the K value and one complex closed-loop pole corresponding to the intersection point. Calculate the steady-state error. Show the Matlab code in your answer sheet. b. Please use Matlab to find the intersection point between § line and the root locus of the system in Fig. 2. Then find the K value and one complex closed-loop pole associated with the intersection point. Compare the complex closed-loop pole with the one you just found in task a. Are they very different from each other? Calculate the steady-state error. Show the Matlab codes in your answer sheet. c. Use Matlab/Simulink to plot the step responses of two systems in Fig. 1 and Fig. 2, respectively.

Power System Analysis and Design (MindTap Course List)
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 6.15P
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3. The following closed-loop systems in Fig. 1 and Fig. 2 operate with a damping ratio of 0.707 (=0.707). The system in Fig. 1 does not have a PI controller, while the one in Fig. 2 does. R(s): S Gain Plant R(s) + E(s) 1 C(s) K (s+1)(s+2)(s+10) Fig. 1: Closed-loop system without PI controller Compensator Plant R(s) + E(s) K(s+0.1) S 1 (s+1)(s+2)(s+10) C(s) Fig. 2: Closed-loop system with a practical PI controller a. Please use Matlab to find the intersection point between line and the root locus of the system in Fig. 1. Then find the K value and one complex closed-loop pole corresponding to the intersection point. Calculate the steady-state error. Show the Matlab code in your answer sheet. b. Please use Matlab to find the intersection point between § line and the root locus of the system in Fig. 2. Then find the K value and one complex closed-loop pole associated with the intersection point. Compare the complex closed-loop pole with the one you just found in task a. Are they very different from each other? Calculate the steady-state error. Show the Matlab codes in your answer sheet. c. Use Matlab/Simulink to plot the step responses of two systems in Fig. 1 and Fig. 2, respectively.
Transcribed Image Text:3. The following closed-loop systems in Fig. 1 and Fig. 2 operate with a damping ratio of 0.707 (=0.707). The system in Fig. 1 does not have a PI controller, while the one in Fig. 2 does. R(s): S Gain Plant R(s) + E(s) 1 C(s) K (s+1)(s+2)(s+10) Fig. 1: Closed-loop system without PI controller Compensator Plant R(s) + E(s) K(s+0.1) S 1 (s+1)(s+2)(s+10) C(s) Fig. 2: Closed-loop system with a practical PI controller a. Please use Matlab to find the intersection point between line and the root locus of the system in Fig. 1. Then find the K value and one complex closed-loop pole corresponding to the intersection point. Calculate the steady-state error. Show the Matlab code in your answer sheet. b. Please use Matlab to find the intersection point between § line and the root locus of the system in Fig. 2. Then find the K value and one complex closed-loop pole associated with the intersection point. Compare the complex closed-loop pole with the one you just found in task a. Are they very different from each other? Calculate the steady-state error. Show the Matlab codes in your answer sheet. c. Use Matlab/Simulink to plot the step responses of two systems in Fig. 1 and Fig. 2, respectively.
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