s+3Problem 8. For the PD controlled positioning system, where Ge(s) = K(s + 2) and G,(s) :s(s+1)(a) Plot the root-locus of the system using the Matlab command of "rlocus" for the positive values of gain.(b) Using the root-locus you plotted, write the range of gain for stability of the system(c) What would be the value of the gainto have a closed-loop pole at -2.5?PD ControllerPlantFind it by hand and show it on theroot-locus you plotted.(d) Where would be the second pole forthe same value of gain?Find it by hand and show it on theR(s)C(s)G(s)Gp(s)root-locus you plotted.(e) Suppose that the plant has an additional unstable pole at +4 and hence looks as follows,s+ 3Gp(s) = s(s + 1)(s – 4)Plot the root-locus of this new system, Ge(s)G(s), for the positive values of gain in Matlab.() Using this root locus, write the stability range for gain of this new system.(g) What would be the frequency of sustained oscillation in Hz?(h) Plot this response for the first 4-5 periods and show that the response confims what you found in (g).

Problem 8. For the PD controlled positioning system, where Ge(s) = K(s+ 2) and Gp(s) =+1) (a) Plot the root-locus of the system using the Matlab command of "tlocus" for the positive values of gain. (b) Using the root-locus you plotted, write the range of gain for stability of the system (c) What would be the value of the gain to have a closed-loop pole at -2.5? Find it by hand and show it on the root-locus you plotted. (d) Where would be the second pole for the same value of gain? Find it by hand and show it on the PD Controller Plant R(s) C(s) G(s) Gp(8)

Problem 8. For the PD controlled positioning system, where Ge(s) = K(s+ 2) and Gp(s) =+1) (a) Plot the root-locus of the system using the Matlab command of "tlocus" for the positive values of gain. (b) Using the root-locus you plotted, write the range of gain for stability of the system (c) What would be the value of the gain to have a closed-loop pole at -2.5? Find it by hand and show it on the root-locus you plotted. (d) Where would be the second pole for the same value of gain? Find it by hand and show it on the PD Controller Plant R(s) C(s) G(s) Gp(8)

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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Concept explainers

Compensation Techniques

The compensation techniques are the methods that are employed in the electrical control systems to enhance the performance of the system. The performance are generally affected by the factors like lag in the compensating devices, slow response of the system of the components like sensors used in the control system. The basic compensation technique involves lag compensation, lead compensation or the combination of the both.

Question

s+3
Problem 8. For the PD controlled positioning system, where Ge(s) = K(s + 2) and G,(s) :
s(s+1)
(a) Plot the root-locus of the system using the Matlab command of "rlocus" for the positive values of gain.
(b) Using the root-locus you plotted, write the range of gain for stability of the system
(c) What would be the value of the gain
to have a closed-loop pole at -2.5?
PD Controller
Plant
Find it by hand and show it on the
root-locus you plotted.
(d) Where would be the second pole for
the same value of gain?
Find it by hand and show it on the
R(s)
C(s)
G(s)
Gp(s)
root-locus you plotted.
(e) Suppose that the plant has an additional unstable pole at +4 and hence looks as follows,
s+ 3
Gp(s) = s(s + 1)(s – 4)
Plot the root-locus of this new system, Ge(s)G(s), for the positive values of gain in Matlab.
() Using this root locus, write the stability range for gain of this new system.
(g) What would be the frequency of sustained oscillation in Hz?
(h) Plot this response for the first 4-5 periods and show that the response confims what you found in (g).

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