Tutorial 1

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: li.jinfu@nus.edu.sg

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,

SoC Presentation Title 2004

Li Jinfu

Email: li.jinfu@nus.edu.sg

THANK YOU