blem 8. For the feedback control system -n in the figure on the right, R(s) + (a) Find the closed-loop transfer function, C(s)/R(s). (b) Determine the system's stability range for gain K using Routh-Hurwitz criterion. K 1 s(s+2)(= S (c) What is the type of the system? (Hint: you need to convert the system to a simple unity feedback.) 1 (d) Sketch the root-locus in Matlab (hint: you need to use the open-loop transfer function with K = validate the stability region you found in (b) (e) Plot the step responses up to 10 seconds for the input of 1.5u(t) when the gain K = 22 and ha

Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter12: Power System Controls
Section: Chapter Questions
Problem 12.3P
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Problem 8. For the feedback control system
given in the figure on the right,
R(s)
(a) Find the closed-loop transfer function,
C(s)/R(s).
(b) Determine the system's stability range for gain
Kusing Routh-Hurwitz criterion.
K
1
s(s+ 2)(s + 5)
S
C(s)
(c) What is the type of the system? (Hint: you need to
convert the system to a simple unity feedback.)
(d) Sketch the root-locus in Matlab (hint: you need to use the open-loop transfer function with K = 1) and
validate the stability region you found in (b
(e) Plot the step responses up to 10 seconds for the input of 1.5u(t) when the gain K = 22 and has the value that
makes the system marginally stable on the same plane.
(f) Calculate the steady-state error for the input step of 1.5u(t) for K = 22. Confirm the result with the related
plot you obtained in (e).
(g) Calculate the steady-state error now for an input ramp of 1.5tu(t) for K = 22 and plot this response together
with the input function up to 10 seconds in order to indicate the steady-state error you just computed.
Transcribed Image Text:Problem 8. For the feedback control system given in the figure on the right, R(s) (a) Find the closed-loop transfer function, C(s)/R(s). (b) Determine the system's stability range for gain Kusing Routh-Hurwitz criterion. K 1 s(s+ 2)(s + 5) S C(s) (c) What is the type of the system? (Hint: you need to convert the system to a simple unity feedback.) (d) Sketch the root-locus in Matlab (hint: you need to use the open-loop transfer function with K = 1) and validate the stability region you found in (b (e) Plot the step responses up to 10 seconds for the input of 1.5u(t) when the gain K = 22 and has the value that makes the system marginally stable on the same plane. (f) Calculate the steady-state error for the input step of 1.5u(t) for K = 22. Confirm the result with the related plot you obtained in (e). (g) Calculate the steady-state error now for an input ramp of 1.5tu(t) for K = 22 and plot this response together with the input function up to 10 seconds in order to indicate the steady-state error you just computed.
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