LabVIEW Control Design Toolkit User Manual.pdf

LabVIEW TM

Control Design Toolkit User Manual

September 2004 Edition

Part Number 371057B-01

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Contents

About This Manual

Conventions ...................................................................................................................xi

Related Documentation..................................................................................................xii

Chapter 1

Introduction to Control Design

Model-Based Control Design Process ...........................................................................1-2

Analyzing and Modeling a Plant .....................................................................1-2

Designing a Controller ....................................................................................1-3

Simulating the Dynamic System .....................................................................1-4

Deploying the Controller .................................................................................1-4

Designing a Controller with the Toolkit ........................................................................1-5

Control Design Assistant .................................................................................1-5

Control Design VIs..........................................................................................1-5

Chapter 2

Creating Dynamic System Models

Introduction to Modeling ...............................................................................................2-2

Linear versus Nonlinear Models .....................................................................2-3

Time-Variant versus Time-Invariant Models ..................................................2-3

Continuous versus Discrete Models ................................................................2-3

LabVIEW Control Design Toolkit Model Representations ............................2-4

RLC Circuit Example ....................................................................................................2-5

Transfer Function Model ...............................................................................................2-5

Creating Transfer Function Models.................................................................2-6

SISO Transfer Function Model.........................................................2-6

MIMO Transfer Function Model ......................................................2-8

Symbolic Transfer Function Model ..................................................2-10

Zero-Pole-Gain Model ...................................................................................................2-11

Creating Zero-Pole-Gain Models ....................................................................2-11

SISO Zero-Pole-Gain Model ............................................................2-12

MIMO Zero-Pole-Gain Model..........................................................2-12

Symbolic Zero-Pole-Gain Model......................................................2-13

Control Design Toolkit User Manual

Contents

State-Space Model......................................................................................................... 2-13

Creating State-Space Models .......................................................................... 2-14

SISO State-Space Model .................................................................. 2-14

MIMO State-Space Model................................................................ 2-15

Symbolic State-Space Model............................................................ 2-16

Model Information......................................................................................................... 2-16

Chapter 3

Model Conversion

Changing System Representation.................................................................................. 3-1

Converting State-Space Models to Transfer Function Models ....................... 3-1

Converting Transfer Function Models to Zero-Pole-Gain Models................. 3-2

Converting Zero-Pole-Gain Models to State-Space Models........................... 3-3

Minimal Realization........................................................................................ 3-4

Converting between Continuous and Discrete Systems ................................................ 3-4

Continuous to Discrete Conversions............................................................... 3-5

Forward Rectangular Method ........................................................... 3-7

Backward Rectangular Method ........................................................ 3-7

Tustin’s Method................................................................................ 3-8

Prewarp Conversion Method ............................................................ 3-9

Zero-Order-Hold and First-Order-Hold Methods............................. 3-10

Z Transform Conversion Method ..................................................... 3-11

Matched Pole Zero Conversion Method........................................... 3-11

Discrete to Continuous Conversions............................................................... 3-11

Discrete to Discrete Conversions .................................................................... 3-12

Chapter 4

Connecting Models

Connecting Models in Series......................................................................................... 4-1

SISO Systems in Series................................................................................... 4-1

MIMO Systems in Series ................................................................................ 4-3

SIMO Systems in Series ................................................................................. 4-4

Appending Models ........................................................................................................ 4-6

Connecting Models in Parallel ...................................................................................... 4-8

Placing Models in a Closed-Loop ................................................................................. 4-11

One Model in a Closed-Loop Configuration .................................................. 4-12

Feedback Connections Undefined .................................................... 4-12

Feedback Connections Defined ........................................................ 4-13

Control Design Toolkit User Manual

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