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Problem 1. For the feedback control system given, where R(s) G,(s) 1 G.(s) = K(s + 10) and G,(3) =; (s + 1)(s + 2)(s + 6) (a) Sketch the root locus. When sketching the root locus, if necessary, make use of the asymptotes finding ơ, and 8, that are the intersecting point and angles with the real axis, respectively, with the following formula, Efinite poles- E finite zeros afinite poles-#finite pzeros (2k+1)m and 0. = afinite poles-#finite pzeros" -, where k = 0,±1,±2, ... (b) If applies, what are the values of the gain and poles at the imaginary axis crossings? (c) Write the range of the gain making the system stable? (d) It is determined that the dominant poles are at s1,2 = -1t j3.5 when the gain is K = 8. Find the location of the third pole for this value of gain. (e) What is the system type? () Find the steady-state errors for the same gain, K = 8, when r(t) = 0.6u(t) step and 0.6tu(t) ramp inputs are applied, respectively. (g) In order to improve the steady state response of the system add a Pl controller having the same gain and a zero of s = -0.2. Now find the steady-state errors for the same inputs.

Problem 1. For the feedback control system given, where R(s) G,(s) 1 G.(s) = K(s + 10) and G,(3) =; (s + 1)(s + 2)(s + 6) (a) Sketch the root locus. When sketching the root locus, if necessary, make use of the asymptotes finding ơ, and 8, that are the intersecting point and angles with the real axis, respectively, with the following formula, Efinite poles- E finite zeros afinite poles-#finite pzeros (2k+1)m and 0. = afinite poles-#finite pzeros" -, where k = 0,±1,±2, ... (b) If applies, what are the values of the gain and poles at the imaginary axis crossings? (c) Write the range of the gain making the system stable? (d) It is determined that the dominant poles are at s1,2 = -1t j3.5 when the gain is K = 8. Find the location of the third pole for this value of gain. (e) What is the system type? () Find the steady-state errors for the same gain, K = 8, when r(t) = 0.6u(t) step and 0.6tu(t) ramp inputs are applied, respectively. (g) In order to improve the steady state response of the system add a Pl controller having the same gain and a zero of s = -0.2. Now find the steady-state errors for the same inputs.

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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Electrical Engineering course.

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EE350 ( System Dynamics and control )

Efinite poles- E finite zeros and Oa = ainite poles-#finite pzeros where k = 0,±1,±2, ... Problem 1. For the feedback control system given, where R(s) Gę(s) G,(s) 1 G.(s) = K(s + 10) and G„(3) =; (s+ 1)(s + 2)(s + 6) (a) Sketch the root locus. When sketching the root locus, if necessary, make use of the asymptotes finding ơa and 8a that are the intersecting point and angles with the real axis, respectively, with the following formula, (2k+1)m afinite poles-ifinite pzeros (b) If applies, what are the values of the gain and poles at the imaginary axis crossings? (c) Write the range of the gain making the system stable? (d) It is determined that the dominant poles are at s12 = -1 ± j3.5 when the gain is K = 8. Find the location of the third pole for this value of gain. (e) What is the system type? () Find the steady-state errors for the same gain, K = 8, when r(t) = 0.6u(t) step and 0.6tu(t) ramp inputs are applied, respectively. (g) In order to improve the steady state response of the system add a PI controller having the same gain and a zero of s = -0.2. Now find the steady-state errors for the same inputs.
Transcribed Image Text:Efinite poles- E finite zeros and Oa = ainite poles-#finite pzeros where k = 0,±1,±2, ... Problem 1. For the feedback control system given, where R(s) Gę(s) G,(s) 1 G.(s) = K(s + 10) and G„(3) =; (s+ 1)(s + 2)(s + 6) (a) Sketch the root locus. When sketching the root locus, if necessary, make use of the asymptotes finding ơa and 8a that are the intersecting point and angles with the real axis, respectively, with the following formula, (2k+1)m afinite poles-ifinite pzeros (b) If applies, what are the values of the gain and poles at the imaginary axis crossings? (c) Write the range of the gain making the system stable? (d) It is determined that the dominant poles are at s12 = -1 ± j3.5 when the gain is K = 8. Find the location of the third pole for this value of gain. (e) What is the system type? () Find the steady-state errors for the same gain, K = 8, when r(t) = 0.6u(t) step and 0.6tu(t) ramp inputs are applied, respectively. (g) In order to improve the steady state response of the system add a PI controller having the same gain and a zero of s = -0.2. Now find the steady-state errors for the same inputs.
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