Matlab Control System Toolbox User’s Guide

1816 Pages·2018·28.37 MB·English

Control System Toolbox™
User's Guide
R2018b
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Control System Toolbox™ User's Guide
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Revision History
June 2001 Online only New for Version 5.1 (Release 12.1)
July 2002 Online only Revised for Version 5.2 (Release 13)
June 2004 Online only Revised for Version 6.0 (Release 14)
March 2005 Online only Revised for Version 6.2 (Release 14SP2)
September 2005 Online only Revised for Version 6.2.1 (Release 14SP3)
March 2006 Online only Revised for Version 7.0 (Release 2006a)
September 2006 Online only Revised for Version 7.1 (Release 2006b)
March 2007 Online only Revised for Version 8.0 (Release 2007a)
September 2007 Online only Revised for Version 8.0.1 (Release 2007b)
March 2008 Online only Revised for Version 8.1 (Release 2008a)
October 2008 Online only Revised for Version 8.2 (Release 2008b)
March 2009 Online only Revised for Version 8.3 (Release 2009a)
September 2009 Online only Revised for Version 8.4 (Release 2009b)
March 2010 Online only Revised for Version 8.5 (Release 2010a)
September 2010 Online only Revised for Version 9.0 (Release 2010b)
April 2011 Online only Revised for Version 9.1 (Release 2011a)
September 2011 Online only Revised for Version 9.2 (Release 2011b)
March 2012 Online only Revised for Version 9.3 (Release 2012a)
September 2012 Online only Revised for Version 9.4 (Release 2012b)
March 2013 Online only Revised for Version 9.5 (Release 2013a)
September 2013 Online only Revised for Version 9.6 (Release 2013b)
March 2014 Online only Revised for Version 9.7 (Release 2014a)
October 2014 Online only Revised for Version 9.8 (Release 2014b)
March 2015 Online only Revised for Version 9.9 (Release 2015a)
September 2015 Online only Revised for Version 9.10 (Release 2015b)
March 2016 Online only Revised for Version 10.0 (Release 2016a)
September 2016 Online only Revised for Version 10.1 (Release 2016b)
March 2017 Online only Revised for Version 10.2 (Release 2017a)
September 2017 Online only Revised for Version 10.3 (Release 2017b)
March 2018 Online only Revised for Version 10.4 (Release 2018a)
September 2018 Online only Revised for Version 10.5 (Release 2018b)
Contents
Linear System Modeling
Linear System Model Objects
1
What Are Model Objects? . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2
Model Objects Represent Linear Systems . . . . . . . . . . . . 1-2
About Model Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2
Control System Modeling with Model Objects . . . . . . . . . 1-4
Types of Model Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7
Dynamic System Models . . . . . . . . . . . . . . . . . . . . . . . . . . 1-10
Static Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-12
Numeric Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-13
Numeric Linear Time Invariant (LTI) Models . . . . . . . . . 1-13
Identifed LTI Models . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14
Identifed Nonlinear Models . . . . . . . . . . . . . . . . . . . . . 1-14
Generalized Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-16
Generalized and Uncertain LTI Models . . . . . . . . . . . . . 1-16
Control Design Blocks . . . . . . . . . . . . . . . . . . . . . . . . . 1-16
Generalized Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . 1-18
Models with Tunable Coeficients . . . . . . . . . . . . . . . . . . 1-19
Tunable Generalized LTI Models . . . . . . . . . . . . . . . . . . 1-19
Modeling Tunable Components . . . . . . . . . . . . . . . . . . . 1-19
Modeling Control Systems with Tunable Components . . 1-20
Internal Structure of Generalized Models . . . . . . . . . . . 1-20
v
Using Model Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-23
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-24
Model Creation
2
Transfer Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3
Transfer Function Representations . . . . . . . . . . . . . . . . . 2-3
Commands for Creating Transfer Functions . . . . . . . . . . 2-4
Create Transfer Function Using Numerator and
Denominator Coeficients . . . . . . . . . . . . . . . . . . . . . . 2-4
Create Transfer Function Model Using Zeros, Poles, and
Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
State-Space Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6
State-Space Model Representations . . . . . . . . . . . . . . . . 2-6
Explicit State-Space Models . . . . . . . . . . . . . . . . . . . . . . 2-6
Descriptor (Implicit) State-Space Models . . . . . . . . . . . . 2-7
Commands for Creating State-Space Models . . . . . . . . . . 2-7
Create State-Space Model From Matrices . . . . . . . . . . . . 2-7
Frequency Response Data (FRD) Models . . . . . . . . . . . . . 2-10
Frequency Response Data . . . . . . . . . . . . . . . . . . . . . . 2-10
Commands for Creating FRD Models . . . . . . . . . . . . . . 2-10
Create Frequency-Response Model from Data . . . . . . . . 2-11
Proportional-Integral-Derivative (PID) Controllers . . . . 2-13
Continuous-Time PID Controller Representations . . . . . 2-13
Create Continuous-Time Parallel-Form PID Controller . . 2-14
Create Continuous-Time Standard-Form PID
Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-14
Two-Degree-of-Freedom PID Controllers . . . . . . . . . . . . . 2-16
Continuous-Time 2-DOF PID Controller
Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-16
2-DOF Control Architectures . . . . . . . . . . . . . . . . . . . . 2-18
Discrete-Time Numeric Models . . . . . . . . . . . . . . . . . . . . 2-23
Create Discrete-Time Transfer Function Model . . . . . . . 2-23
vi Contents
Other Model Types in Discrete Time Representations . . 2-23
Discrete-Time Proportional-Integral-Derivative (PID)
Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-24
Discrete-Time PID Controller Representations . . . . . . . 2-24
Create Discrete-Time Standard-Form PID Controller . . . 2-26
Discrete-Time 2-DOF PI Controller in Standard Form . . 2-26
MIMO Transfer Functions . . . . . . . . . . . . . . . . . . . . . . . . . 2-28
Concatenation of SISO Models . . . . . . . . . . . . . . . . . . . 2-28
Using the tf Function with Cell Arrays . . . . . . . . . . . . . 2-29
MIMO State-Space Models . . . . . . . . . . . . . . . . . . . . . . . . 2-31
MIMO Explicit State-Space Models . . . . . . . . . . . . . . . . 2-31
MIMO Descriptor State-Space Models . . . . . . . . . . . . . 2-32
State-Space Model of Jet Transport Aircraft . . . . . . . . . 2-33
MIMO Frequency Response Data Models . . . . . . . . . . . . 2-37
Select Input/Output Pairs in MIMO Models . . . . . . . . . . 2-39
Time Delays in Linear Systems . . . . . . . . . . . . . . . . . . . . . 2-40
First Order Plus Dead Time Model . . . . . . . . . . . . . . . . 2-40
Input and Output Delay in State-Space Model . . . . . . . . 2-41
Transport Delay in MIMO Transfer Function . . . . . . . . . 2-43
Discrete-Time Transfer Function with Time Delay . . . . . 2-43
Closing Feedback Loops with Time Delays . . . . . . . . . . . 2-45
Time-Delay Approximation . . . . . . . . . . . . . . . . . . . . . . . . 2-48
Time-Delay Approximation in Discrete-Time Models . . . 2-48
Time-Delay Approximation in Continuous-Time Open-Loop
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-50
Time-Delay Approximation in Continuous-Time Closed-
Loop Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-55
Approximate Diferent Delays with Diferent
Approximation Orders . . . . . . . . . . . . . . . . . . . . . . . . . . 2-60
Convert Time Delay in Discrete-Time Model to Factors of
1/z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-64
vii
Frequency Response Data (FRD) Model with Time
Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-69
Internal Delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-73
Why Internal Delays Are Necessary . . . . . . . . . . . . . . . 2-73
Behavior of Models With Internal Delays . . . . . . . . . . . 2-74
Inside Time Delay Models . . . . . . . . . . . . . . . . . . . . . . . 2-75
Functions That Support Internal Time Delays . . . . . . . . 2-76
Functions That Do Not Support Internal Time Delays . . 2-76
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-77
Create Tunable Low-Pass Filter . . . . . . . . . . . . . . . . . . . . 2-78
Create Tunable Second-Order Filter . . . . . . . . . . . . . . . . 2-79
Create State-Space Model with Both Fixed and Tunable
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-81
Control System with Tunable Components . . . . . . . . . . . 2-83
Control System with Multichannel Analysis Points . . . . 2-85
Mark Signals of Interest for Control System Analysis and
Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-89
Analysis Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-89
Specify Analysis Points for MATLAB Models . . . . . . . . . 2-90
Specify Analysis Points for Simulink Models . . . . . . . . . 2-91
Refer to Analysis Points for Analysis and Tuning . . . . . . 2-95
Model Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-100
What Are Model Arrays? . . . . . . . . . . . . . . . . . . . . . . . 2-100
Uses of Model Arrays . . . . . . . . . . . . . . . . . . . . . . . . . 2-100
Visualizing Model Arrays . . . . . . . . . . . . . . . . . . . . . . 2-101
Visualizing Selection of Models From Model Arrays . . 2-101
Select Models from Array . . . . . . . . . . . . . . . . . . . . . . . . 2-103
Query Array Size and Characteristics . . . . . . . . . . . . . . 2-106
Linear Parameter-Varying Models . . . . . . . . . . . . . . . . . 2-109
What are Linear Parameter-Varying Models? . . . . . . . . 2-109
Regular vs. Irregular Grids . . . . . . . . . . . . . . . . . . . . . 2-112
viii Contents
Use Model Arrays to Create Linear Parameter-Varying
Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-114
Approximate Nonlinear Systems using LPV Models . . . 2-115
Applications of Linear Parameter-Varying Models . . . . 2-116
Using LTI Arrays for Simulating Multi-Mode
Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-118
Working with Linear Models
Data Manipulation
3
Store and Retrieve Model Data . . . . . . . . . . . . . . . . . . . . . . 3-2
Model Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2
Specify Model Properties at Model Creation . . . . . . . . . . 3-2
Examine and Change Properties of an Existing Model . . . 3-3
Extract Model Coeficients . . . . . . . . . . . . . . . . . . . . . . . . . 3-6
Functions for Extracting Model Coeficients . . . . . . . . . . 3-6
Extracting Coeficients of Diferent Model Type . . . . . . . 3-6
Extract Numeric Model Data and Time Delay . . . . . . . . . 3-6
Extract PID Gains from Transfer Function . . . . . . . . . . . 3-8
Attach Metadata to Models . . . . . . . . . . . . . . . . . . . . . . . . . 3-9
Specify Model Time Units . . . . . . . . . . . . . . . . . . . . . . . . 3-9
Interconnect Models with Diferent Time Units . . . . . . . . 3-9
Specify Frequency Units of Frequency-Response Data
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10
Extract Subsystems of Multi-Input, Multi-Output (MIMO)
Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10
Specify and Select Input and Output Groups . . . . . . . . . 3-11
Query Model Characteristics . . . . . . . . . . . . . . . . . . . . . . 3-14
Customize Model Display . . . . . . . . . . . . . . . . . . . . . . . . . 3-17
Confgure Transfer Function Display Variable . . . . . . . . 3-17
ix
Confgure Display Format of Transfer Function in
Factorized Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-18
Model Interconnections
4
Why Interconnect Models? . . . . . . . . . . . . . . . . . . . . . . . . . 4-2
Catalog of Model Interconnections . . . . . . . . . . . . . . . . . . 4-3
Model Interconnection Commands . . . . . . . . . . . . . . . . . 4-3
Arithmetic Operations . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4
Numeric Model of SISO Feedback Loop . . . . . . . . . . . . . . 4-6
Control System Model With Both Numeric and Tunable
Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8
Multi-Loop Control System . . . . . . . . . . . . . . . . . . . . . . . . 4-10
Mark Analysis Points in Closed-Loop Models . . . . . . . . . 4-13
MIMO Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-19
MIMO Feedback Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-22
How the Software Determines Properties of Connected
Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-27
Rules That Determine Model Type . . . . . . . . . . . . . . . . . . 4-29
Recommended Model Type for Building Block
Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-31
x Contents