23 The block diagram in figure Q3 shows a plant G, (s) controlled by a controller G.(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 Kp 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 action is added to the controller. Calculate the value of gain Ka which gives an overall system damping ratio of 0.8. 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. (c)

23 The block diagram in figure Q3 shows a plant G, (s) controlled by a controller G.(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 Kp 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 action is added to the controller. Calculate the value of gain Ka which gives an overall system damping ratio of 0.8. 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. (c)

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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Question

Q3
The block diagram in figure Q3 shows a plant G, (s) controlled by a controller
G.(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 Kp 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 action
is added to the controller. Calculate the value of gain Ka which gives an
overall system damping ratio of 0.8.
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.
(c)

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