Lab Report 3_EELE3314

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School

Lakehead University *

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Course

3314L

Subject

Mechanical Engineering

Date

Apr 3, 2024

Type

docx

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33

Uploaded by lisadivona

Running head: EELE3314L LAB FOR CONTROL SYSTEMS 1 EELE3314L Lab for Control Systems LAB #3 Frequency Response Characteristics
2 EELE3314L LAB FOR CONTROL SYSTEMS Results Procedure 4.1 Measured Magnitude M at w = 1rad/s (dB) Calculated Kv =10^M/20 Calculated Kv = sim sG(s) -20.1 0.0989 0.0999 Estimated Ess = 1/kv Measured Ess from response plot 10 9.9 (approximately 10) Procedure 4.2 Required Ess Calculated Kv =1/Ess Calculated K 0.05 20 200.2 Measured Magnitude at w = 1rad/s (dB) Calculated Kv =10^(M/20) Measured Ess from response plot 25.9 19.7 0.05 Procedure 4.3 Bode plot Measured Mr (dB) Measured Magnitude at wr (rad/s) Measured Mr linear 5.28 12.8 1.8365 Calculated ζ Calculated wn (rad/s) 0.2839 13.9759 Calculated Mp (dB) Calculated Ts (s) 39.4494% 1.0081 Procedure 4.3 Response plot Measured Mp (dB) Measured Ts (s) 39.4% 0.994 Procedure 4.3 Root Locus Measured Mp (dB) Calculated Ts (s) (using measured values) 39.8% 1.017 Procedure 4.4 Measured Phase Margin (degrees) Measured Gain Margin (Linear) From Graph 89.4 From Matlab Command 89.3711 1101.1 Procedure and Analysis
3 EELE3314L LAB FOR CONTROL SYSTEMS 1. Unity Feedback System 1.1 Code for all of Part 1 1.2 Kv of Unity Feedback System
4 EELE3314L LAB FOR CONTROL SYSTEMS From the Bode Diagram, the value for magnitude at 1rad/s was approximately -20.1dB. Shown in the calculations below, the Kv that responds to this value of -20.1dB magnitude is 0.0989 (approximately 0.1). This value was verified using the calculation as well and found to be nearly identical. From the Bode Plot Verify using Calculation
5 EELE3314L LAB FOR CONTROL SYSTEMS 1.3 Steady State Error of Unity Feedback System
6 EELE3314L LAB FOR CONTROL SYSTEMS In this part of the lab, the steady state error was found mathematically using the value of Kv and known equation for unit ramp response for a type 1 system, which is 1/Kv. Mathematically, the steady state error was found to be 10. In order to confirm the correctness of this estimate, the unit ramp response of the closed-loop system was plotted on the same graph as the input unit ramp waveform using MatLab. At steady state, the difference in values between the input unit ramp waveform and the unit ramp response of the closed-loop system will be equal to the steady state error. From the MatLab plot, this error was found to be 9.9, i.e. approximately 10, as mathematically expected. Mathematically obtaining steady state error Graphically obtaining steady state error in MatLab
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