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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clearly hand write， As soon as possible！
Q2 The block diagram in figure Q2 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 Q2 The dynamics of the plant are described by the trans fer function 1 Gp(s) = 2s2 + s + 4 If the controller applies proportional action, find the value of gain K, that results in a steady state error of 4% for a unit step input. (a) (b) With proportional gain maintained at the same value from part (a), derivative action is added to the controller. Calculate the value of gain Ka which gives an overall system damping ratio of 0.8. (c) The controller is redesigned with new gains so that the system has a settling time of 2s and maximum overshoot of 7.5% in response to a unit step input. Find the new values of K, and Ka.
Do b)
In the feedback system shown in Figure Q3, the controller and the plant have the following transfer functions respectively: (s+4) (s+1)(s+2)(s+3) G.(s) = K>0 and G,(s) = Answer the following for this feedback configuration: a) Calculate the closed-loop transfer function. b) By using the Routh-Hurwitz criterion find the values of the controller gain K such that the closed-loop system is BIBO stable. c) Compute the steady-state error to a unit step reference input as a function of the controller gain K. d) Assume now a PI controller G.(s)=K, 1+ is used instead of the constant gain K. Ts Calculate the steady-state error to a unit step reference input. Is your result in agreement with the "internal model principle"? R(s)+ E(s) Y(s) G.(s) G,(s) Figure Q3: Unity feedback system
Must solve all 4 questions. Otherwise dont attempt. Dont solve only 3 .