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Problem 1. controller, and G(s) = Consider the control system shown in Fig. 1, where De(s) is the 1 (s - 1)(s+5) 1) (5 points) Is the open-loop system stable? 2) (15 points) Assume that De(s) = K. Rewrite the closed-loop characteristic equation in the root-locus form 1 + KL(s) = 0. Sketch the root locus for L(s). Is it possible to stabilize the system using a proportional controller? == 3) (10 points) Assume that a PD-controller is used to control the system, i.e., De(s) KpKDs. Utilize the Routh-Hurwitz criterion to derive stability conditions for the closed-loop system. + Ro Σ Dc(s) G(s) -OY Figure 1: Control system in Problem 1.

Problem 1. controller, and G(s) = Consider the control system shown in Fig. 1, where De(s) is the 1 (s - 1)(s+5) 1) (5 points) Is the open-loop system stable? 2) (15 points) Assume that De(s) = K. Rewrite the closed-loop characteristic equation in the root-locus form 1 + KL(s) = 0. Sketch the root locus for L(s). Is it possible to stabilize the system using a proportional controller? == 3) (10 points) Assume that a PD-controller is used to control the system, i.e., De(s) KpKDs. Utilize the Routh-Hurwitz criterion to derive stability conditions for the closed-loop system. + Ro Σ Dc(s) G(s) -OY Figure 1: Control system in Problem 1.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Problem 1. controller, and G(s) = Consider the control system shown in Fig. 1, where De(s) is the 1 (s - 1)(s+5) 1) (5 points) Is the open-loop system stable? 2) (15 points) Assume that De(s) = K. Rewrite the closed-loop characteristic equation in the root-locus form 1 + KL(s) = 0. Sketch the root locus for L(s). Is it possible to stabilize the system using a proportional controller? == 3) (10 points) Assume that a PD-controller is used to control the system, i.e., De(s) KpKDs. Utilize the Routh-Hurwitz criterion to derive stability conditions for the closed-loop system. + Ro Σ Dc(s) G(s) -OY Figure 1: Control system in Problem 1.
Transcribed Image Text:Problem 1. controller, and G(s) = Consider the control system shown in Fig. 1, where De(s) is the 1 (s - 1)(s+5) 1) (5 points) Is the open-loop system stable? 2) (15 points) Assume that De(s) = K. Rewrite the closed-loop characteristic equation in the root-locus form 1 + KL(s) = 0. Sketch the root locus for L(s). Is it possible to stabilize the system using a proportional controller? == 3) (10 points) Assume that a PD-controller is used to control the system, i.e., De(s) KpKDs. Utilize the Routh-Hurwitz criterion to derive stability conditions for the closed-loop system. + Ro Σ Dc(s) G(s) -OY Figure 1: Control system in Problem 1.
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