316 and controller C(s), as shown in the3. Consider a unity-feedback control system with plant G(s)following figure.ReferenceError ControllerPlantr(t)e(t)u(t)y(1)C(s)G(s)(a) Determine the poles, zeros, order, type, relative degree, and de gain of the plant G(s) and showusing the Routh-Hurwitz criterion that G(s) is not stable.= Kp stabilize the plant G(s)? If so, find the values of Kp that are(b) Can a P controller C(s)necessary and sufficient.(c) Show using the Final Value Theorem that the system with the P controller from (b) can track aunit-step reference r(t) = 1 with zero steady-state error limo e(t) = 0.(d) Show that it however cannot track a unit-ramp reference r(t) =t with zero steady-state error.Can the error be made arbitrarily small with Kp without losing stability?(e) Can a PI controller C(s) = Kp + AL stabilize the plant G(8) and, at the same time, yield zerosteady-state error to both unit-step and unit-ramp references? If so, find the values of Kp andKi that are necessary and sufficient.Reconsider the unity-feedback control system shown in Problem 3 and let the controller C(s) and plantG(s) be defined as follows.(a) Let C(s) = Kp and G(s) = : Find the value of Kp that yields 10% of overshoot in y(t)when r(t) is a unit-step input. Hint: 2nd-order system.(b) Let C(s) = Kp and G(s) = S+21ASL5): Sketch the root locus of the open-loop transferfunction C(s)G(s) by hand and using MATLAB's rlocus. Derive a condition that Kp mustsatisfy in order for the closed-loop system to be asymptotically stable.(s+3)%3D

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lowing figure. Reference Error Controller Plant r(1) e(t) u(t) y(1) C(s) G(s) (a) Determine the poles, zeros, order, type, relative degree, and de gain of the plant G(s) and show using the Routh-Hurwitz criterion that G(s) is not stable. (b) Can a P controller C(s) = Kp stabilize the plant G(s)? If so, find the values of Kp that are necessary and sufficient. (c) Show using the Final Value Theorem that the system with the P controller from (b) can track a unit-step reference r(t) = 1 with zero steady-state error lim-+00 e(t) = 0. (1) t with goro stoady ate error

lowing figure. Reference Error Controller Plant r(1) e(t) u(t) y(1) C(s) G(s) (a) Determine the poles, zeros, order, type, relative degree, and de gain of the plant G(s) and show using the Routh-Hurwitz criterion that G(s) is not stable. (b) Can a P controller C(s) = Kp stabilize the plant G(s)? If so, find the values of Kp that are necessary and sufficient. (c) Show using the Final Value Theorem that the system with the P controller from (b) can track a unit-step reference r(t) = 1 with zero steady-state error lim-+00 e(t) = 0. (1) t with goro stoady ate error

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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