3. Consider the following feedback system: r(t) y(t) 1 s3+ s2 + 2s +1 (a) Find the entire range of K so that the closed-loop system (i.e., between r(t) and y(t)) is stable. (b) If the step reference input r(t) is given to the system, will y(t) perfectly track the step reference r(t) with zero steady-state error? Why or Why not? Justify your answer.

3. Consider the following feedback system: r(t) y(t) 1 s3+ s2 + 2s +1 (a) Find the entire range of K so that the closed-loop system (i.e., between r(t) and y(t)) is stable. (b) If the step reference input r(t) is given to the system, will y(t) perfectly track the step reference r(t) with zero steady-state error? Why or Why not? Justify your answer.

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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Q1 (A): Sketch the Nyquist plot of the unity feedback system that shown in figure (1). Is the close loop system stable? Find the Gain Margin (GM). R(s) C(s) G(s) = = 120 s(s+2)(s+3) G(s) Figure (1) 10(s² +15 s+56) Q1 (B): For G(s) = = Find ZG (jw) for w = [0.1 1 10 100 1000] " s3-2s²+s-2
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1.) Please consider the system described by the open-loop transfer function: S-2 G(s) = (s + 1)(s² + 6s +25) If this system is controlled by a proportional feedback controller with gain K, determine the range of K for stability of the closed loop system.
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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
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The open-loop transfer function of a unity feedback system is given by G(s)=(5(s+1))/(s2(s+2)). The stability characteristics of the open-loop and closed-loop configuration are respectively: Choices: stable and stable unstable and unstable unstable and stable stable and unstable
(s-2)(s²+16) (s+3)(s²+9) Consider the system G (s) = Assume a unity feedback configuration with D(s)=K. (a) Draw the pole-zero plot for G(s). (b) Draw the 180° root locus against the loop gain K. (i) Show all your calculations for rule 1, 2, 3, 4. (ii) On your plot indicate the approximate angle of departure and angle of arrival. (c) Based on your calculations is the closed loop system stable or unstable? Why?
For the unity feedback system ( Need only handwritten solution please otherwise downvote)
For the unity-feedback system shown above with K find the range of K for stability. K(s+1)}{s^{4}(s+4)}