MECE3350U-ControlSystems-Assignment4

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University of Ontario Institute of Technology *

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3350U

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Mechanical Engineering

Date

Apr 3, 2024

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docx

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4

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MECE 3350U: Control Systems - Assignment 4 Page 1 of 4 MECE 3350U: Control Systems - Assignment 4 Student Name: Student ID #: I, undersigned, certify that this assignment is my own work, based on personal study and/or research. I also certify that I have not copied in part or whole or otherwise plagiarized the work of other students. We are aware that posting this material to or copying the solution from any website constitutes a breach of Ontario Tech regulations and constitutes a form of academic misconduct. Student Signature: Question 1 -The bode plot of a system was determined experimentally using the sinusoidal wave excitation. Given the Bode plot below, find the transfer function. (20 Marks)
MECE 3350U: Control Systems - Assignment 4 Page 2 of 4 Question 2- Consider a unit feedback system, which has the following open-loop transfer function 2-1) Draw Bode plot of the open-loop system for 𝑘 = 1 . Identify the components of the open- loop transfer function for which you know the Bode plot. Then add them up to find the Bode plot of 𝐺(𝑠) . (15 Marks)
MECE 3350U: Control Systems - Assignment 4 Page 3 of 4 2-2) Based on the Bode diagram, sketch the Nyquist plot of the system for k = 1. Specify the points where the Nyquist plot crosses the real axis. (15 Marks) 2-3) Based on the Nyquist stability criterion, determine the maximum value of k before instability. (5 marks). 2-4) If k is set higher than the maximum value determined in (2-3), determine the number of unstable roots of the closed-loop system. Confirm your answer with an approximate sketch of the root-locus. (20 Marks)
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MECE 3350U: Control Systems - Assignment 4 Page 4 of 4 2-5) Without using the Bode plot, calculate the phase and magnitude of 𝐺(𝑠) at 5 𝑟𝑎𝑑/𝑠 for k = 1. (10 Marks) 2-6) Determine the cross-over frequency, and the phase and gain margins for k = 20. (15 Marks)