Consider the following feedback control system. Assume H(s)=F(s)=1 and 4 N(s)=D(s)=0. The plant transfer function is: P(s) = Consider a Proportional (P) Control %3D (2s+1)(0.5s+1) C(s) = Kp. (a) What is the closed-loop transfer function? What are the expressions of the closed-loop poles? (b) What is the allowed region of the closed-loop poles on the complex plane such that the %OS is less than 10% and that the 2% settling time is less than 6 sec? What is the corresponding range of K,? (c) Plot the step response of the closed-loop system when K, = 0.5. (d) Does the response obtained in (c) satisfy the requirements in (b)? Is the steady-state error zero? Disturbance D (s) Actuating Signal EA(S) Reference Control Output Input R(s) Input + Y(s) F(s) C(s) P(s) U(s) + Pre-filter Controller Plant H(s) + Noise N(s) Considor the gome faodhool, oontrel syatom og in Problom 1 A goin
Consider the following feedback control system. Assume H(s)=F(s)=1 and 4 N(s)=D(s)=0. The plant transfer function is: P(s) = Consider a Proportional (P) Control %3D (2s+1)(0.5s+1) C(s) = Kp. (a) What is the closed-loop transfer function? What are the expressions of the closed-loop poles? (b) What is the allowed region of the closed-loop poles on the complex plane such that the %OS is less than 10% and that the 2% settling time is less than 6 sec? What is the corresponding range of K,? (c) Plot the step response of the closed-loop system when K, = 0.5. (d) Does the response obtained in (c) satisfy the requirements in (b)? Is the steady-state error zero? Disturbance D (s) Actuating Signal EA(S) Reference Control Output Input R(s) Input + Y(s) F(s) C(s) P(s) U(s) + Pre-filter Controller Plant H(s) + Noise N(s) Considor the gome faodhool, oontrel syatom og in Problom 1 A goin
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Question
![Consider the following feedback control system. Assume H(s)=F(s)=1 and
4
N(s)=D(s)=0. The plant transfer function is: P(s) =
Consider a Proportional (P) Control
(2s+1)(0.5s+1)
C(s) = Kp.
(a) What is the closed-loop transfer function? What are the expressions of the closed-loop poles?
(b) What is the allowed region of the closed-loop poles on the complex plane such that the %OS is less
than 10% and that the 2% settling time is less than 6 sec? What
the corresponding range of Kp?
(c) Plot the step response of the closed-loop system when Kp
= 0.5.
(d) Does the response obtained in (c) satisfy the requirements in (b)? Is the steady-state error zero?
Disturbance D (s)
Actuating
Signal
EA(S)
Reference
Control
Output
Input R(s)
Input
+
Y(s)
F (s)
C(s)
P(s)
U(s) +
Pre-filter
Controller
Plant
H(s)
+
Noise N(s)
Consider the same feedback control system as in Problem 1. Again, assume
4
H(s)=F(s)=1 and N(s)=D(s)=D0. The plant transfer function is still: P(s) =
Now, consider a
(2s+1)(0.5s+1)
Proportional-Integral (PI) Control C(s) = Kp + K; -.
(a) What is the closed-loop transfer function?
(b) Plot the step response of the closed-loop system when Kp = 5 and K
= 3.
%3D
(c) From the plot, is the steady-state error zero?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf587696-7abc-4430-8e78-96c282a0430a%2F2a1d460c-d41e-4cd3-9488-b5f913e3e98f%2Fni2vyab_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following feedback control system. Assume H(s)=F(s)=1 and
4
N(s)=D(s)=0. The plant transfer function is: P(s) =
Consider a Proportional (P) Control
(2s+1)(0.5s+1)
C(s) = Kp.
(a) What is the closed-loop transfer function? What are the expressions of the closed-loop poles?
(b) What is the allowed region of the closed-loop poles on the complex plane such that the %OS is less
than 10% and that the 2% settling time is less than 6 sec? What
the corresponding range of Kp?
(c) Plot the step response of the closed-loop system when Kp
= 0.5.
(d) Does the response obtained in (c) satisfy the requirements in (b)? Is the steady-state error zero?
Disturbance D (s)
Actuating
Signal
EA(S)
Reference
Control
Output
Input R(s)
Input
+
Y(s)
F (s)
C(s)
P(s)
U(s) +
Pre-filter
Controller
Plant
H(s)
+
Noise N(s)
Consider the same feedback control system as in Problem 1. Again, assume
4
H(s)=F(s)=1 and N(s)=D(s)=D0. The plant transfer function is still: P(s) =
Now, consider a
(2s+1)(0.5s+1)
Proportional-Integral (PI) Control C(s) = Kp + K; -.
(a) What is the closed-loop transfer function?
(b) Plot the step response of the closed-loop system when Kp = 5 and K
= 3.
%3D
(c) From the plot, is the steady-state error zero?
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