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1. Consider a plant that you want to control. The input u(t) and output y(t) of the plant are related by y(t) = 7 u(t) + w(t) where w(t) is an additive disturbance at the output which is bounded by -0.5 w(t) ≤0.5 for all time t. You want to build a controller so that the output follows a constant reference signal r(t) = where -15 ≤≤ 15. You will consider both open-loop and closed-loop for this problem. a) Sketch the block diagram of the plant. b) Please build an open-loop controller that sets the output to 7, assuming the disturbance is ignored. Please show your controller both as an equation and a block diagram. c) Say that you use the open-loop controller in part b, but now the disturbance w(t) is present. What is the maximum possible magnitude of error in the output for the reference signal? Suppose you have designed a feedback control for the plant where the controller has the form u(t) = K(r(t) − y(t)). Here K is the gain constant of the controller that you will design. d) Please draw the full control system when the feedback control is used. e) Please find the expression of output and error in terms of F, w(t) and K. f) Please design K so that the absolute value of the error is at most 0.05.

1. Consider a plant that you want to control. The input u(t) and output y(t) of the plant are related by y(t) = 7 u(t) + w(t) where w(t) is an additive disturbance at the output which is bounded by -0.5 w(t) ≤0.5 for all time t. You want to build a controller so that the output follows a constant reference signal r(t) = where -15 ≤≤ 15. You will consider both open-loop and closed-loop for this problem. a) Sketch the block diagram of the plant. b) Please build an open-loop controller that sets the output to 7, assuming the disturbance is ignored. Please show your controller both as an equation and a block diagram. c) Say that you use the open-loop controller in part b, but now the disturbance w(t) is present. What is the maximum possible magnitude of error in the output for the reference signal? Suppose you have designed a feedback control for the plant where the controller has the form u(t) = K(r(t) − y(t)). Here K is the gain constant of the controller that you will design. d) Please draw the full control system when the feedback control is used. e) Please find the expression of output and error in terms of F, w(t) and K. f) Please design K so that the absolute value of the error is at most 0.05.

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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1. Consider a plant that you want to control. The input u(t) and output y(t) of the plant are related by y(t) = 7 u(t) + w(t) where w(t) is an additive disturbance at the output which is bounded by -0.5 w(t) ≤0.5 for all time t. You want to build a controller so that the output follows a constant reference signal r(t) = where -15 ≤≤ 15. You will consider both open-loop and closed-loop for this problem. a) Sketch the block diagram of the plant. b) Please build an open-loop controller that sets the output to 7, assuming the disturbance is ignored. Please show your controller both as an equation and a block diagram. c) Say that you use the open-loop controller in part b, but now the disturbance w(t) is present. What is the maximum possible magnitude of error in the output for the reference signal? Suppose you have designed a feedback control for the plant where the controller has the form u(t) = K(r(t) − y(t)). Here K is the gain constant of the controller that you will design. d) Please draw the full control system when the feedback control is used. e) Please find the expression of output and error in terms of F, w(t) and K. f) Please design K so that the absolute value of the error is at most 0.05.
Transcribed Image Text:1. Consider a plant that you want to control. The input u(t) and output y(t) of the plant are related by y(t) = 7 u(t) + w(t) where w(t) is an additive disturbance at the output which is bounded by -0.5 w(t) ≤0.5 for all time t. You want to build a controller so that the output follows a constant reference signal r(t) = where -15 ≤≤ 15. You will consider both open-loop and closed-loop for this problem. a) Sketch the block diagram of the plant. b) Please build an open-loop controller that sets the output to 7, assuming the disturbance is ignored. Please show your controller both as an equation and a block diagram. c) Say that you use the open-loop controller in part b, but now the disturbance w(t) is present. What is the maximum possible magnitude of error in the output for the reference signal? Suppose you have designed a feedback control for the plant where the controller has the form u(t) = K(r(t) − y(t)). Here K is the gain constant of the controller that you will design. d) Please draw the full control system when the feedback control is used. e) Please find the expression of output and error in terms of F, w(t) and K. f) Please design K so that the absolute value of the error is at most 0.05.
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