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

2

4

1in

out

3

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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

5

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

105

5

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)

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

25

w e i g

h t ( k g

)

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System ExamplesWeighing scale

Is the weighing scale a static or dynamic system?



24 y(t)

2322

25

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



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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ma3005 topic 1 - introduction

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