ES3011-2324A-Exam04

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Worcester Polytechnic Institute *

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3011

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Mechanical Engineering

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Oct 30, 2023

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pdf

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ES3011 Control Engineering 2324A _____________________________________________________________________________________ EXAM 4 _____________________________________________________________________________________ October 13, 2023 Do All Problems Show All Work This exam is open notes and open book. You have 50 minutes to complete all problems. Only commence the exam when instructed to do so. Student ID: ______________________________ Student Printed Name: ______________________________ Student Signature: ______________________________
ES3011 Control Engineering 2324A Name: _______________________________ ID: _______________________________ Worcester Polytechnic Institute 2 | P a g e 1.) (30 pts) Please draw an appropriate Bode Diagram on the graph below using straight line asymptotes for magnitude and phase for a plant described by the following transfer function: 𝐺(?) = 200 ?(? 2 + 36? + 100) According to your Bode diagram, is this system stable under unity feedback? If we multiply the numerator by 10 (i.e., using a proportional gain 𝐾 𝑝 = 10 ), would the system become more or less stable? Please explain your reasoning.
ES3011 Control Engineering 2324A Name: _______________________________ ID: _______________________________ Worcester Polytechnic Institute 3 | P a g e
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ES3011 Control Engineering 2324A Name: _______________________________ ID: _______________________________ Worcester Polytechnic Institute 4 | P a g e 2.) (40 pts) For an open-loop system with unknown transfer function, the following frequency response is experimentally characterized: a) Is the unity feedback closed-loop system stable? b) Please determine the crossover frequencies and the gain and phase margins approximately. c) What’s the maximum overshoot 𝑀 𝑝 for a unit step reference? d) What is the maximum stable value for a proportional gain 𝐾 𝑝 for this system?
ES3011 Control Engineering 2324A Name: _______________________________ ID: _______________________________ Worcester Polytechnic Institute 5 | P a g e
ES3011 Control Engineering 2324A Name: _______________________________ ID: _______________________________ Worcester Polytechnic Institute 6 | P a g e 3.) (30 pts) The phase margin of a system is found to be 10 degrees and the gain crossover frequency is at 𝜔 𝐺 = 10 ?𝑎𝑑/? . Please design a lead compensator for this system to achieve a phase margin of 40 degrees at the same gain crossover frequency.
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ES3011 Control Engineering 2324A Name: _______________________________ ID: _______________________________ Worcester Polytechnic Institute 7 | P a g e

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