Consider the feedback control system in Figure 1: R(s) + Σ Y(s) G(s) D(s) Figure 1 Let G(s) A and D(s) = Ks +1 s(s+2) (a) Derive, step by step, the closed-loop transfer function- Y(s) R(s)' (b) What is the characteristic equation of this system? What information is contained in the characteristic equation? Please explain. E(s) (c) Define E(s) = R(s) – Y(s). Derive the transfer function R(s)'

Consider the feedback control system in Figure 1: R(s) + Σ Y(s) G(s) D(s) Figure 1 Let G(s) A and D(s) = Ks +1 s(s+2) (a) Derive, step by step, the closed-loop transfer function- Y(s) R(s)' (b) What is the characteristic equation of this system? What information is contained in the characteristic equation? Please explain. E(s) (c) Define E(s) = R(s) – Y(s). Derive the transfer function R(s)'

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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=. The block diagram of a multiple-loop feedback control system is shown in the following figure, please find the transfer function of C(s)/ R(s) H,(s) R(s) G,(s) G,(s) C(s) G,(s) H,(s)
1. For the unitary feedback closed-loop system with a proportional K gain controller C below R P(s) + 1 (s + 1)(s + 2) (s + 9) (s + 10) E C P Assuming the properties of the closed-loop system are determined by the two dominant poles, what is the range of K to make the overshoot smaller than 10%?
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. (c) What is the type of the system? (Hint: you need to convert the system to a simple unity feedback.) K 1 s(s+2)(s+5) C(s) (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…
(Stability of a Feedback System) The open-loop transfer function of a system is given as: G(s) 2s3 + s² + 14s a) Draw a unity feedback system with a gain K and open-loop transfer function G(s). Indicate the name (e.g. E(s),..) of each arrow. Find the closed-loop transfer function T(s). b) of terms. Build the Routh table for the closed-loop system by clearly showing the calculation c) Analyze the stability of the closed-loop system and find the range of K for stable operation. Justify your answer.
Explain how the Nyquist stability criterion can be used to determine the stability of a closed-loop feedback system. Formulate the criterion for a system with no right-half plane open-loop poles. (a) (b) Consider the Nyquist plot of the frequency response of the system G(jw) = 500 shown in Figure Q4 below. (jw+1)(jw+10)² i. Explain how the gain margin can be obtained from the Nyquist plot and determine its approximate value from Figure Q4. What is the maximum value of an additional gain K for which the closed loop would still be stable? 0.5 -0.5 -0.5 0.5 Real Axis Figure Q4 i. Explain how the phase margin can be obtained from the Nyquist plot and determine its approximate value from Figure Q4. Assuming that the corresponding point on the plot occurs at 4rad/s, what is the maximum delay which can be added to the system before the closed loop would become unstable? Sketch the approximate Bode diagram for the system in part (b) of the question, clearly showing the asymptotes and corner…
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A second-order system has an open-loop transfer function (pictured in images) A closed-loop system is constructed using a proportional controller in front of the second-order system, and the then a unity negative feedback loop applied. Use a root-locus plotter by entering the transfer function G(s), so that the plot shows the position of the closed-loop poles as the proportional gain is varied from 0 to 100. Use a screenshot of the root locus plot as your answer. Remember that you cannot use brackets when you enter the transfer function into the root-locus plotter, so the first step is the mathematical manipulation of the transfer function to remove the brackets
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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…
(a) Consider following differential equation. d³y d²y +3. dt3 dy d³x d²x dx +6 + 8x dt +5 +y = +4 dt² dt dt3 dt2 Y(s) i) Find the transfer function of X(s)' ii) Consider that the system in i) has a unity feedback. For this system identify parameters below. 1) Open loop transfer function 2) Open loop poles 3) Open loop zeros 4) Real axis segment 5) Break away or break in point 6) Sketch of the root locus
Consider the feedback system is shown in following figure. The system has one parameters R(s) C(s) 10 s(s+1) TS (1) Find the transfer function. (2) When 70 determine the overshoot M, and setting time t at A = +2%. (3) Find the value to determine the overshoot Mp = 10% and tp = 1s