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A laboratory experiment can be modelled as a system with an open-loop transfer function: 04 P(s) = (s2 + s) with a controller C(s) which has the transfer function: K(s + 2,) s+4 C(s) = (а) For the controller C(s) with z = 6: 2 = 6: Determine the open-loop transfer function G(s) = C(s)P(s), and identify the open-loop poles and open-loop zeros of the system. (i) (ii) For the root-locus of G(s), determine the number of asymptotes and where they meet, and calculate the location of any double point(s). (iii) Sketch the root-locus for this system, using the information derived in (i)-(ii) and comment on the characteristics of this system for different values of K, e.g. for small K and for larger values of K. Hint: You may find it useful to know that the equation x* + 11.5x + 30x + 12 = 0 has the solutions x, = -7.89, x, = -3.12, and x = -0.49. (b) For the plant P(s) and controller C(s) given above: Choose the value of z, so that the closed-loop system remains stable for all values of K. Sketch a corresponding root-locus diagram and discuss the differences to the diagram which you have obtained in (a). (1) What is the largest value of z, for which the system can be guaranteed to remain stable? (ii) The Bode diagram of G(s) from (a), part (i), is shown in Figure Q4 over the page. Determine approximate values for the gain and phase margins from this plot. (c) Bode Diagram 20 -20 -40 -60 -90 .135 -180 100 Frequency (rad/s) 101 101 Figure 04 (ap) apruubew

A laboratory experiment can be modelled as a system with an open-loop transfer function: 04 P(s) = (s2 + s) with a controller C(s) which has the transfer function: K(s + 2,) s+4 C(s) = (а) For the controller C(s) with z = 6: 2 = 6: Determine the open-loop transfer function G(s) = C(s)P(s), and identify the open-loop poles and open-loop zeros of the system. (i) (ii) For the root-locus of G(s), determine the number of asymptotes and where they meet, and calculate the location of any double point(s). (iii) Sketch the root-locus for this system, using the information derived in (i)-(ii) and comment on the characteristics of this system for different values of K, e.g. for small K and for larger values of K. Hint: You may find it useful to know that the equation x* + 11.5x + 30x + 12 = 0 has the solutions x, = -7.89, x, = -3.12, and x = -0.49. (b) For the plant P(s) and controller C(s) given above: Choose the value of z, so that the closed-loop system remains stable for all values of K. Sketch a corresponding root-locus diagram and discuss the differences to the diagram which you have obtained in (a). (1) What is the largest value of z, for which the system can be guaranteed to remain stable? (ii) The Bode diagram of G(s) from (a), part (i), is shown in Figure Q4 over the page. Determine approximate values for the gain and phase margins from this plot. (c) Bode Diagram 20 -20 -40 -60 -90 .135 -180 100 Frequency (rad/s) 101 101 Figure 04 (ap) apruubew

Introductory Circuit Analysis (13th Edition)
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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A laboratory experiment can be modelled as a system with an open-loop transfer function: 04 P(s) = (s2 + s) with a controller C(s) which has the transfer function: K(s + 2,) s+4 C(s) = (а) For the controller C(s) with z = 6: 2 = 6: Determine the open-loop transfer function G(s) = C(s)P(s), and identify the open-loop poles and open-loop zeros of the system. (i) (ii) For the root-locus of G(s), determine the number of asymptotes and where they meet, and calculate the location of any double point(s). (iii) Sketch the root-locus for this system, using the information derived in (i)-(ii) and comment on the characteristics of this system for different values of K, e.g. for small K and for larger values of K. Hint: You may find it useful to know that the equation x* + 11.5x + 30x + 12 = 0 has the solutions x, = -7.89, x, = -3.12, and x = -0.49. (b) For the plant P(s) and controller C(s) given above: Choose the value of z, so that the closed-loop system remains stable for all values of K. Sketch a corresponding root-locus diagram and discuss the differences to the diagram which you have obtained in (a). (1) What is the largest value of z, for which the system can be guaranteed to remain stable? (ii) The Bode diagram of G(s) from (a), part (i), is shown in Figure Q4 over the page. Determine approximate values for the gain and phase margins from this plot. (c) Bode Diagram 20 -20 -40 -60 -90 .135 -180 100 Frequency (rad/s) 101 101 Figure 04 (ap) apruubew
Transcribed Image Text:A laboratory experiment can be modelled as a system with an open-loop transfer function: 04 P(s) = (s2 + s) with a controller C(s) which has the transfer function: K(s + 2,) s+4 C(s) = (а) For the controller C(s) with z = 6: 2 = 6: Determine the open-loop transfer function G(s) = C(s)P(s), and identify the open-loop poles and open-loop zeros of the system. (i) (ii) For the root-locus of G(s), determine the number of asymptotes and where they meet, and calculate the location of any double point(s). (iii) Sketch the root-locus for this system, using the information derived in (i)-(ii) and comment on the characteristics of this system for different values of K, e.g. for small K and for larger values of K. Hint: You may find it useful to know that the equation x* + 11.5x + 30x + 12 = 0 has the solutions x, = -7.89, x, = -3.12, and x = -0.49. (b) For the plant P(s) and controller C(s) given above: Choose the value of z, so that the closed-loop system remains stable for all values of K. Sketch a corresponding root-locus diagram and discuss the differences to the diagram which you have obtained in (a). (1) What is the largest value of z, for which the system can be guaranteed to remain stable? (ii) The Bode diagram of G(s) from (a), part (i), is shown in Figure Q4 over the page. Determine approximate values for the gain and phase margins from this plot. (c) Bode Diagram 20 -20 -40 -60 -90 .135 -180 100 Frequency (rad/s) 101 101 Figure 04 (ap) apruubew
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