Download - MA3005 Topic 1 - Introduction
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MA3005: Control TheoryTopic 1: Introduction
Tegoeh Tjahjowidodo
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Controller Plant++
D (s)
U (s) Y (s)
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What is a controller?
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Control Theory
“a is a device, it can be in the form of amicroprocessor or computer, which monitors and
physically alters the operating conditions of a given
dynamical “
controller
Objective: Designing a controller
Definition:
system
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Lecture Arrangement
Part I. (Dynamic) System Asst. Prof. Tegoeh Tjahjowidodo
Office: N3-02c-68
Tel: 6790 4952Email: [email protected]
Recess WeekPart II. Controller Design
Asst. Prof. Pham Quang CuongOffice: N3.2-02-37
Tel: 6790 5597Email: [email protected]
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Textbook/ References
• Textbook – Modern Control Engineering , Katsuhiko Ogata, 4 th ed. or later,
Prentice Hall• Reference Material
– System Dynamics , Katsuhiko Ogata, 4 th ed. or later, PearsonPrentice Hall
– Control Systems Engineering , Nise, 5 th Edition, John Wiley,2008.
– Modeling and Analysis of Dynamic Systems , Close, Charles M.,
3rd edition, John Wiley & Sons, 2002. – Any text on mathematical modelling.
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Course Objectives
Provide background to mathematical modelling ,dynamic response analysis of dynamical systemsExplain basic principles of three term controllers and
their applicationsProvide basics of controller design techniques,performance and stability analysis , in time andfrequency domain for linear feedback controlsystems
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1. Introduction
2. LaplaceTransform
3. Modelling
4. Response andStability
5. Routh Stability
6. First Order
7. Second Order
8. TransientResponse
PART II. CONTROLLER DESIGN
Part 1 Lecture Map
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• Frequency Response: Intro.
Teaching Plan (Before Recess Week)
Week 1 Tue., Jan. 13 • Introduction• Laplace Transforms
Week 2 Tue., Jan. 20 • Mathematical Modeling of DynamicSystems
Week 3 Tue., Jan. 27• System Response
Week 4 Tue., Feb. 17• 1 st order systems
Week 5 Tue., Feb. 10 • 2 nd order systems
Week 6 Tue., Feb. 17 • Transient responses• Basic Control Actions
Week 7 Tue., Feb. 24• QUIZ
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• Frequency Response: Intro.
Teaching Plan (After Recess Week)
Recess Week R E C E S S
Week 8 Tue., Mar. 10 • Introduction to controller
• Basic Control and System TypeWeek 9 Tue., Mar. 17 • Root-Locus: Introduction
• Root-Locus: PD controller
Week 10 Tue., Mar. 24 • Root-Locus: Lead-Lag controller
Week 11 Tue., Mar. 31 • Frequency Response: Intro.• Frequency Response: Property
Week 12 Tue., Apr. 7 • Bode Plot Sketching
Week 13 Tue., Apr. 14 • Stability Analysis
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QUIZ
QUIZ will be provided on the last week before therecess week ( Tue., Feb. 24 )
The quiz comprises all materials before the recessweek
QUIZ contributes 50% of CA grade
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Homework Problems
• Put on NTULearn (was: edveNTUre)
• Homework to be submitted to the tutors inrespective tutorial sessions in the due week
• Contributes to 50% of CA grade• Graded HWs will be returned by tutors• Solution will be provided on NTULearn
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Homework Deadline Schedule
Homework # Assigned Date Due Week1 20 Jan. Week 42 10 Feb. Week 73 17 Mar. Week 114 31 Mar. Week 13
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Prerequisite
• Mathematics I• Mathematics II
Pay more attention on:o Calculus (differentiation-integration)o Complex number operationso
Laplace transform
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1. Introduction
2. LaplaceTransform
3. Modelling
4. Response andStability
5. Routh Stability
6. First Order
7. Second Order
8. TransientResponse
PART II. CONTROLLER DESIGN
Part 1 Lecture Map
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INTRODUCTION
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• Can be any physical, biological, economicmodel.
• Responds to certain inputs by producing output
• Real world example:Pressing on gas pedal , makes vehicle move faster
Here vehicle is system , gas pedal is input and velocity ofvehicle is output
System
SystemInput Output
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In general, can be classified into:• Static System
A system is said to be static if its output y(t ) depends only on theinput u(t ) at the present time t
• Dynamic System A system is said to be static if its output y(t ) will be affected by, notonly by the input u(t ) at the present time but also depends on thepast input u(t )
SystemSystem
u(t ) y(t )
Typically the response will vary in time for a constant(static) input
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Static Systems
Simplest and intuitive example is a ‘function machine’ that we learnt ingrade 3 (or 4?)
10 20 30 time (s)0
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1in
out
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Static Systems
Simplest and intuitive example is a ‘function machine’ that we learnt ingrade 3 (or 4?)
10 20 30 time (s)0
in
out
2
4
1
3
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Dynamic Systems
Characterized mathematically by derivative and/or integrative operators.
Example:
y xdt dx
dt xd
y xdt dx
105
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2
2
Y X s )15(
Y X ss )105( 2
151
sY X
1051
2 ssY X
151
s
Y
X 10 20 30 time (s)0
1 y(t)
x(t)
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Dynamic Systems
Characterized mathematically by derivative and/or integrative operators.
Example:
y xdt dx
dt
xd
y xdt dx
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2
2
Y X s )15(
Y X ss )105( 2
151
sY X
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2 ssY X
151
s
Y
X 10 20 30 time (s)0
1 y(t) x(t)
Tool for evaluating response: Laplace Transform ! 24
System ExamplesWeighing scale
Is the weighing scale a static or dynamic system?
- Identify the input
- Identify the output10 20 30 time (s)0
24 y(t)
2322
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w e i g
h t ( k g
)
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System ExamplesWeighing scale
Is the weighing scale a static or dynamic system?
- Identify the input
- Identify the output10 20 30 time (s)0
24 y(t)
2322
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w e i g
h t ( k g
)
10 20 30 time (s)0
242322
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d i a l p o s i
t i o n
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Light bulb
System Examples
- Identify the input
- Identify the output10 20 30 time (s)0
220 y(t)
v o
l t a g e
Light intensity
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System Examples
Is the light bulb a static or dynamic system?
Light bulb
1. Static2. Dynamics
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in nature are essentially All systems ………
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Reading Assignment
• Modern Control
Engineering, 5th
Ed.Chapter 1
• Refresh differentialequation from MA2006
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