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Excercise 2: Ideal PID controllers. Consider the systems represented by the block diagrams below r ki/s ki/s Σ у P(s) kp Σ Σ) P(s) kp Σ kas kas Controller -1 -1 Controller Assume that the plant has the transfer function P(s) = b/(s + a) (a) Show that the transfer functions from r to y are bk4s2 bkpsbki (1bkd)s2(a + bkp)s + bki Gyr(s) bki Gyr(s) (1 bkd)s2(a +bkp)s+ bki (b) Pick the parameters: b = 1, a 5, kd = 2, ki = 4, and kp = 3, and compare the step responses of the systems. What are the main differences between the two PID controllers?

Excercise 2: Ideal PID controllers. Consider the systems represented by the block diagrams below r ki/s ki/s Σ у P(s) kp Σ Σ) P(s) kp Σ kas kas Controller -1 -1 Controller Assume that the plant has the transfer function P(s) = b/(s + a) (a) Show that the transfer functions from r to y are bk4s2 bkpsbki (1bkd)s2(a + bkp)s + bki Gyr(s) bki Gyr(s) (1 bkd)s2(a +bkp)s+ bki (b) Pick the parameters: b = 1, a 5, kd = 2, ki = 4, and kp = 3, and compare the step responses of the systems. What are the main differences between the two PID controllers?

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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Excercise 2: Ideal PID controllers. Consider the systems represented by the block diagrams below r ki/s ki/s Σ у P(s) kp Σ Σ) P(s) kp Σ kas kas Controller -1 -1 Controller Assume that the plant has the transfer function P(s) = b/(s + a) (a) Show that the transfer functions from r to y are bk4s2 bkpsbki (1bkd)s2(a + bkp)s + bki Gyr(s) bki Gyr(s) (1 bkd)s2(a +bkp)s+ bki (b) Pick the parameters: b = 1, a 5, kd = 2, ki = 4, and kp = 3, and compare the step responses of the systems. What are the main differences between the two PID controllers?
Transcribed Image Text:Excercise 2: Ideal PID controllers. Consider the systems represented by the block diagrams below r ki/s ki/s Σ у P(s) kp Σ Σ) P(s) kp Σ kas kas Controller -1 -1 Controller Assume that the plant has the transfer function P(s) = b/(s + a) (a) Show that the transfer functions from r to y are bk4s2 bkpsbki (1bkd)s2(a + bkp)s + bki Gyr(s) bki Gyr(s) (1 bkd)s2(a +bkp)s+ bki (b) Pick the parameters: b = 1, a 5, kd = 2, ki = 4, and kp = 3, and compare the step responses of the systems. What are the main differences between the two PID controllers?
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