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SoC Presentation Title 2004
ME2142 - Feedback Control Systems
Tutorial Problem Set 1
Tutor: Li Jinfu, PhD Office: EA 04-06 Control and Mechatronics Lab 1 Email: [email protected]
SoC Presentation Title 2004
Before the lecture
Teach and explain the tutorial questions in the tutorial lectures
Consultation of tutorial questions and lecture notes after class
Consultation of previous exam papers before exams
Three ways to communicate:
Ask questions in and after the tutorial lectures
Send emails: simple questions
Approach to my office: complex questions
SoC Presentation Title 2004
Open-Loop
Plant Controller u, control effort r, reference input y, actual output
Closed-Loop
Plant Controller u r y
Sensor
e, error
_
+
Feedback Loop
Introduction to Feedback Control Systems
Control Systems
SoC Presentation Title 2004
Some Reviews
Laplace Transform
Differential equation Transfer function
Control Systems Description
Time domain f(t) vs. Frequency domain F(s)
By definition The table of transformation pairs => Most useful
f(t) F(s) Laplace Transform
Inverse Laplace Transform
Why need frequency domain: Analyze Systems and Design Controller
SoC Presentation Title 2004
Some Reviews
Two ways to use exponential function Method 1
Method 2
Translation Property
Frequency Shift Property
SoC Presentation Title 2004
Question 1
( Table of Laplace Transform Pairs )
SoC Presentation Title 2004
Question 1 Solution
time t = 2
f(t)=g(t-2)
g(t) G(s)=
SoC Presentation Title 2004
Question 1 Solution
By Laplace Transform Definition
f(t)=1
f(t)=0
SoC Presentation Title 2004
Question 1 Solution
minus
Built by Basic Functions
SoC Presentation Title 2004
Question 1 Solution
SoC Presentation Title 2004
Question 2
SoC Presentation Title 2004
Question 2 Solution
(Using Partial Fractions)
SoC Presentation Title 2004
Question 2 Solution
(frequency domain)
(time domain)
SoC Presentation Title 2004
Question 2 Solution
(Using Partial Fractions)
SoC Presentation Title 2004
Question 2 Solution
(From Table of Laplace Transform Pairs)
We also could solve it using Final Value Theorem in frequency domain!
SoC Presentation Title 2004
Question 2 Solution
SoC Presentation Title 2004
Question 2 Solution
b
SoC Presentation Title 2004 Question 3a
Procedures: 1. First find the differential equation of motion 2. Time domain to frequency domain via Laplace Transform 3. Transfer function
SoC Presentation Title 2004
Question 3a Solution
Free body diagram at point A:
A
(Note: direction force will determine the equation!)
SoC Presentation Title 2004
Question 3a Solution
Free body diagram
Using Newton’s Law:
SoC Presentation Title 2004 Question 3b
SoC Presentation Title 2004 Question 3b Solution
SoC Presentation Title 2004 Question 3b Solution
SoC Presentation Title 2004 Question 3c
c)
SoC Presentation Title 2004 Question 3c Solution
Recap that Zi
Zf
SoC Presentation Title 2004 Question 3c Solution
Therefore,