Q4) Consider the system shown in Figure Q3. This is a PID control of a second-order plant G(s). Assume that disturbances d(s) enter the system as shown in the diagram. It is assumed that the reference input F(s) is normally held constant, and the response characteristics to disturbances are a very important consideration in this system. (s)p f(s) C(s) G(s) y(s) H(s) Figure Q3 1 K(as + 1)(bs + 1) G(s) C(s) = H(s) = 1 s² + 7s + 10' In the absence of the reference input i.e. F(s) = 0, derive the closed-loop transfer function between y(s) and d(s). a) b) The performance specification requires that the unit step disturbance response be such that the settling time be approximately half a second and the system has reasonable damping. We may interpret the specification as 3 = 0.8 and wn = 8 for the dominant closed-loop poles. We may choose the third pole at s = - 10 so that the effect of this real pole on the response is small. Derive the required characteristic polynomial that satisfies the above performance specification. c) Using the result in a) and b), calculate the controller parameters ab, a + b and K. Hence write down the controller transfer function C(s).

Q4) Consider the system shown in Figure Q3. This is a PID control of a second-order plant G(s). Assume that disturbances d(s) enter the system as shown in the diagram. It is assumed that the reference input F(s) is normally held constant, and the response characteristics to disturbances are a very important consideration in this system. (s)p f(s) C(s) G(s) y(s) H(s) Figure Q3 1 K(as + 1)(bs + 1) G(s) C(s) = H(s) = 1 s² + 7s + 10' In the absence of the reference input i.e. F(s) = 0, derive the closed-loop transfer function between y(s) and d(s). a) b) The performance specification requires that the unit step disturbance response be such that the settling time be approximately half a second and the system has reasonable damping. We may interpret the specification as 3 = 0.8 and wn = 8 for the dominant closed-loop poles. We may choose the third pole at s = - 10 so that the effect of this real pole on the response is small. Derive the required characteristic polynomial that satisfies the above performance specification. c) Using the result in a) and b), calculate the controller parameters ab, a + b and K. Hence write down the controller transfer function C(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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