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Given a dynamic system shown in Fig. 3, where K(s) represents a control law: ● ● R(s) + Figure 3 (a) Assume that K(s) is a PD-control given by K(s)= K (s+5): Sketch the root locus of the system as a function of the gain Kc ● K(s) 2 (s+1)(s+3) Y(s) Can the closed-loop system be destabilized by a finite gain Kc? If so, find the minimum value of Kc that destabilizes the system What is the steady-state error to a unit step input? Is this result valid for all the values of Kc? (if needed, the result can be given in terms of Kc) 5 (b) Repeat part (a) assuming that K(s) is a PI-control given by K(s) = K 1+ S 2 (c) Repeat part (a) assuming that K(s) is a PI-control given by K(s)= K₂| 1+ Kc (1+²)

Given a dynamic system shown in Fig. 3, where K(s) represents a control law: ● ● R(s) + Figure 3 (a) Assume that K(s) is a PD-control given by K(s)= K (s+5): Sketch the root locus of the system as a function of the gain Kc ● K(s) 2 (s+1)(s+3) Y(s) Can the closed-loop system be destabilized by a finite gain Kc? If so, find the minimum value of Kc that destabilizes the system What is the steady-state error to a unit step input? Is this result valid for all the values of Kc? (if needed, the result can be given in terms of Kc) 5 (b) Repeat part (a) assuming that K(s) is a PI-control given by K(s) = K 1+ S 2 (c) Repeat part (a) assuming that K(s) is a PI-control given by K(s)= K₂| 1+ Kc (1+²)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Given a dynamic system shown in Fig. 3, where K(s) represents a control law: R(s) + K(s) 2 (s+1)(s+3) Figure 3 (a) Assume that K(s) is a PD-control given by K(s) = K (s+5): Sketch the root locus of the system as a function of the gain Kc Y(s) Can the closed-loop system be destabilized by a finite gain Kc? If so, find the minimum value of Kc that destabilizes the system What is the steady-state error to a unit step input? Is this result valid for all the values of Kc? (if needed, the result can be given in terms of Kc) 5 (b) Repeat part (a) assuming that K(s) is a PI-control given by K(s)= K 1+ S 2 (c) Repeat part (a) assuming that K(s) is a PI-control given by K(s) = K 1+ S
Transcribed Image Text:Given a dynamic system shown in Fig. 3, where K(s) represents a control law: R(s) + K(s) 2 (s+1)(s+3) Figure 3 (a) Assume that K(s) is a PD-control given by K(s) = K (s+5): Sketch the root locus of the system as a function of the gain Kc Y(s) Can the closed-loop system be destabilized by a finite gain Kc? If so, find the minimum value of Kc that destabilizes the system What is the steady-state error to a unit step input? Is this result valid for all the values of Kc? (if needed, the result can be given in terms of Kc) 5 (b) Repeat part (a) assuming that K(s) is a PI-control given by K(s)= K 1+ S 2 (c) Repeat part (a) assuming that K(s) is a PI-control given by K(s) = K 1+ S
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