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
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Transcribed Image Text: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.
d(s)
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).
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