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Q3 The block diagram in figure Q3 shows a plant G,(s) controlled by a controller Ge(s) using a unity negative feedback loop. R(s) C(s) Ge(s) Go(s) Figure Q3

Q3 The block diagram in figure Q3 shows a plant G,(s) controlled by a controller Ge(s) using a unity negative feedback loop. R(s) C(s) Ge(s) Go(s) Figure Q3

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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Q3 The block diagram in figure Q3 shows a plant G„(s) controlled by a controller Gc(s) using a unity negative feedback loop. R(s) C(s) Ge(s) Gp(s) Figure Q3 The dynamics of the plant are described by the transfer function 1 Gp(s) = s² + 2s + 6 If the controller applies proportional action, find the value of gain K, that results in a steady state error of 2% for a unit step input. (a) (b) With proportional gain maintained at the same value as in (a), derivative acuon is added to the controller. Calculate the value of gain Ka which gives an overall system damping ratio of 0.8. (c) Find the transfer function of the system when integral control is added, with the proportional and derivative gains maintained at the same value. Show that the steady-state error is reduced to zero.
Transcribed Image Text:Q3 The block diagram in figure Q3 shows a plant G„(s) controlled by a controller Gc(s) using a unity negative feedback loop. R(s) C(s) Ge(s) Gp(s) Figure Q3 The dynamics of the plant are described by the transfer function 1 Gp(s) = s² + 2s + 6 If the controller applies proportional action, find the value of gain K, that results in a steady state error of 2% for a unit step input. (a) (b) With proportional gain maintained at the same value as in (a), derivative acuon is added to the controller. Calculate the value of gain Ka which gives an overall system damping ratio of 0.8. (c) Find the transfer function of the system when integral control is added, with the proportional and derivative gains maintained at the same value. Show that the steady-state error is reduced to zero.
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