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Toronto Metropolitan University *

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639

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Industrial Engineering

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Apr 3, 2024

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pdf

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10

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ELE639: Control Activity # 7 (Homework # 1) February 26, 2023 1 ELE639 Course Activity Homework # 1 Second Order Model for the Closed Loop - 10 points DUE DATE : Upload to D2L (use “Assignment”) , by February 26, 2023, 11:45 pm. Please note that you are encouraged to complete this activity in PAIRS, to give you the benefit of working, and learning, with a study partner. Also, submissions with more than two names will N OT be marked! N ame 1: Student N umber: YOUR TOTAL IS: /10 N ame 2: Student N umber Consider the following closed loop system under Proportional Control: N OTE: You are encouraged to use Matlab whenever it helps, but do not submit Matlab code, or a Matlab printout of results – these have to be handwritten, together with any conclusions. 1. Find the critical gain value ࠵? ࠵?࠵?࠵?࠵? (for marginal stability), then find an operational gain ࠵? ࠵?࠵? such that the Gain Margin is equal to 2.5. N OTE: Since the emphasis of the homework is on models, you can skip doing the full Routh Array by hand if you know how to find the Critical Gain by using the Root Locus (“rlocus” and “rlocfind” – see lecture slides on Stability) or by using the symbolic Matlab script for the Routh Array. 2. Find the open loop transfer function of the system at that value of the Operational Gain ࠵? ࠵?࠵? and perform the steady state error analysis of the system performance, i.e. find position, velocity & acceleration constants and the corresponding errors. 3. Find the closed loop transfer function of the system at that value of the Operational Gain ࠵? ࠵?࠵? and decide if a reduced order model can be used. If yes, find the model parameters using TWO approaches you were introduced to: Using the pole-zero map of the closed loop transfer function, determine the second order model based on the dominant closed loop poles. Using the step response of the original system – get the transient response specs (PO, Settling Time (2%), Rise Time (0-100%), etc.) and estimate the parameters of the second order model. 4. Include a Matlab plot of the system response vs. BOTH model responses – your plot should have three traces in it, all properly labeled. 5. Tabulate and compare the specs for both models and the original system: PO, Settling Time (2%), Rise Time (0-100%), Steady State Error for Step. 6. Provide a brief discussion of how the actual system response differs from the models, and which model, in your opinion, is better, and why. ⑦ ° @ ° °@°@ -
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