Consider the following feedback control system. Assume H(s)=F(s)=1 and 4 (s)=D(s)=0. The plant transfer function is: P(s) = Consider a Proportional (P) Control %3D (2s+1)(0.5s+1) (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) Output Reference nput R(s) Control Input Y(s) F(s) C(s) P(s) U(s) + Plant Pre-filter Controller H(s) Noise N(s) Consider the same feedback control system as in Problem 1. Again, assume 4 |(s)=F(s)=l and N(s)=D(s)=0. The plant transfer function is still: P(s) = Now, consider a (2s+1)(0.5s+1) roportional-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?
Consider the following feedback control system. Assume H(s)=F(s)=1 and 4 (s)=D(s)=0. The plant transfer function is: P(s) = Consider a Proportional (P) Control %3D (2s+1)(0.5s+1) (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) Output Reference nput R(s) Control Input Y(s) F(s) C(s) P(s) U(s) + Plant Pre-filter Controller H(s) Noise N(s) Consider the same feedback control system as in Problem 1. Again, assume 4 |(s)=F(s)=l and N(s)=D(s)=0. The plant transfer function is still: P(s) = Now, consider a (2s+1)(0.5s+1) roportional-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?
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Controls practice problem
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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