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For the PD controlled positioning system, where Ge(s) = K (s+2) and Gp(S) = s(s+1) (a) Plot the root-locus of the system using the Matlab command of "rlocus" for the positive values of gain. (b) Using the root-locus you plotted, write the range of gain for stability of the system. (c) What would be the value of the gain to have a PD Controller Plant closed-loop pole at -2.5? Find it by hand and show it on the root-locus you plotted. (d) Where would be the second pole for the same value of gain? Find it by hand calculations and show it on the root-locus you plotted. R(S) Ge(s) Gp(s) C(s)

For the PD controlled positioning system, where Ge(s) = K (s+2) and Gp(S) = s(s+1) (a) Plot the root-locus of the system using the Matlab command of "rlocus" for the positive values of gain. (b) Using the root-locus you plotted, write the range of gain for stability of the system. (c) What would be the value of the gain to have a PD Controller Plant closed-loop pole at -2.5? Find it by hand and show it on the root-locus you plotted. (d) Where would be the second pole for the same value of gain? Find it by hand calculations and show it on the root-locus you plotted. R(S) Ge(s) Gp(s) C(s)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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s+3 For the PD controlled positioning system, where Ge(s) = K(s + 2) and Gp(S) = s(s+1) (a) Plot the root-locus of the system using the Matlab command of "rlocus" for the positive values of gain. (b) Using the root-locus you plotted, write the range of gain for stability of the system. (c) What would be the value of the gain to have a PD Controller closed-loop pole at -2.5? Find it by hand and show it on the root-locus you plotted. (d) Where would be the second pole for the same value of gain? Find it by hand calculations and show it on the root-locus you plotted. (e) Suppose that the plant has an additional unstable pole at s = +4 and hence looks as follows, R(S) Gc(s) Plant Gp(s) s+3 G₂ (S) = S(S+1)(S-4) Plot the root-locus of this new system, Ge(s)G, (s), for the positive values of gain in Matlab. (f) Write the stability range for gain of this new system by means of the root locus plot and also by hand calculations. (g) What would be the frequency of sustained oscillation in Hz? (h) Plot this response for the first 4-5 periods and show that the response confirms what you found in (g). C(s)
Transcribed Image Text:s+3 For the PD controlled positioning system, where Ge(s) = K(s + 2) and Gp(S) = s(s+1) (a) Plot the root-locus of the system using the Matlab command of "rlocus" for the positive values of gain. (b) Using the root-locus you plotted, write the range of gain for stability of the system. (c) What would be the value of the gain to have a PD Controller closed-loop pole at -2.5? Find it by hand and show it on the root-locus you plotted. (d) Where would be the second pole for the same value of gain? Find it by hand calculations and show it on the root-locus you plotted. (e) Suppose that the plant has an additional unstable pole at s = +4 and hence looks as follows, R(S) Gc(s) Plant Gp(s) s+3 G₂ (S) = S(S+1)(S-4) Plot the root-locus of this new system, Ge(s)G, (s), for the positive values of gain in Matlab. (f) Write the stability range for gain of this new system by means of the root locus plot and also by hand calculations. (g) What would be the frequency of sustained oscillation in Hz? (h) Plot this response for the first 4-5 periods and show that the response confirms what you found in (g). C(s)
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