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6. A plant with transfer function G„(s) given by 1 Gp(s) = s(s + 4) is subject to a reference input R(s) and a disturbance input D(s), as shown in Figure Q6. The response C(s) is governed by a controller with transfer function G.(s). 3

6. A plant with transfer function G„(s) given by 1 Gp(s) = s(s + 4) is subject to a reference input R(s) and a disturbance input D(s), as shown in Figure Q6. The response C(s) is governed by a controller with transfer function G.(s). 3

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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6. A plant with transfer function G„(s) given by 1 G„(s) = s(s + 4) is subject to a reference input R(s) and a disturbance input D(s), as shown in Figure Q6. The response C(s) is governed by a controller with transfer function G.(s). 3 Control 3 Section 3 Tutorial: Feedback Control Systems a) For the situation where there is no change in the reference input (i.e. R(s) = 0) derive the closed loop transfer function relating the response C(s) to the disturbance D(s). b) It is proposed to apply a proportional plus derivative controller to the system such that G(s) = Kp + Kas Calculate the values of the gains K, and Ka if the performance requirements for the system response are that it should have a maximum overshoot of 5% and a natural frequency of 5 rad/s. c) Integral action is now added with gain K; to give a PID controller. Using the values of K, and nd calculated in part b) apply Routh's criteria to determine the range of values of K; which ensures system stability. d) When K; = 100 the system has a dominant pair of complex poles with associated damping ratio of 0.152 and natural frequency of 4.22 rad/s. Calculate the value of the third pole. D(s) R(s) C(s) G(s) Gp(s) Figure Q6.
Transcribed Image Text:6. A plant with transfer function G„(s) given by 1 G„(s) = s(s + 4) is subject to a reference input R(s) and a disturbance input D(s), as shown in Figure Q6. The response C(s) is governed by a controller with transfer function G.(s). 3 Control 3 Section 3 Tutorial: Feedback Control Systems a) For the situation where there is no change in the reference input (i.e. R(s) = 0) derive the closed loop transfer function relating the response C(s) to the disturbance D(s). b) It is proposed to apply a proportional plus derivative controller to the system such that G(s) = Kp + Kas Calculate the values of the gains K, and Ka if the performance requirements for the system response are that it should have a maximum overshoot of 5% and a natural frequency of 5 rad/s. c) Integral action is now added with gain K; to give a PID controller. Using the values of K, and nd calculated in part b) apply Routh's criteria to determine the range of values of K; which ensures system stability. d) When K; = 100 the system has a dominant pair of complex poles with associated damping ratio of 0.152 and natural frequency of 4.22 rad/s. Calculate the value of the third pole. D(s) R(s) C(s) G(s) Gp(s) Figure Q6.
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