Matlab Control System Toolbox User’s Guide (The MathWorks, Inc.) (z-library.sk, 1lib.sk, z-lib.sk)
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Control System Toolbox™ User's Guide R2018b
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How to Contact MathWorks Latest news: www.mathworks.com Sales and services: www.mathworks.com/sales_and_services User community: www.mathworks.com/matlabcentral Technical support: www.mathworks.com/support/contact_us Phone: 508-647-7000 The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 Control System Toolbox™ User's Guide © COPYRIGHT 2001–2018 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or reproduced in any form without prior written consent from The MathWorks, Inc. FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation by, for, or through the federal government of the United States. By accepting delivery of the Program or Documentation, the government hereby agrees that this software or documentation qualifies as commercial computer software or commercial computer software documentation as such terms are used or defined in FAR 12.212, DFARS Part 227.72, and DFARS 252.227-7014. Accordingly, the terms and conditions of this Agreement and only those rights specified in this Agreement, shall pertain to and govern the use, modification, reproduction, release, performance, display, and disclosure of the Program and Documentation by the federal government (or other entity acquiring for or through the federal government) and shall supersede any conflicting contractual terms or conditions. If this License fails to meet the government's needs or is inconsistent in any respect with federal procurement law, the government agrees to return the Program and Documentation, unused, to The MathWorks, Inc. Trademarks MATLAB and Simulink are registered trademarks of The MathWorks, Inc. See www.mathworks.com/trademarks for a list of additional trademarks. Other product or brand names may be trademarks or registered trademarks of their respective holders. Patents MathWorks products are protected by one or more U.S. patents. Please see www.mathworks.com/patents for more information.
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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)
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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 Identified LTI Models . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14 Identified 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 Coefficients . . . . . . . . . . . . . . . . . . 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 Contents
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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 Coefficients . . . . . . . . . . . . . . . . . . . . . . 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
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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 Different Delays with Different Approximation Orders . . . . . . . . . . . . . . . . . . . . . . . . . . 2-60 Convert Time Delay in Discrete-Time Model to Factors of 1/z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-64 vii
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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
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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 Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . 3-6 Functions for Extracting Model Coefficients . . . . . . . . . . 3-6 Extracting Coefficients of Different 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 Different 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 Configure Transfer Function Display Variable . . . . . . . . 3-17 ix
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Configure 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
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Model Transformation 5 Conversion Between Model Types . . . . . . . . . . . . . . . . . . . 5-2 Explicit Conversion Between Model Types . . . . . . . . . . . 5-2 Automatic Conversion Between Model Types . . . . . . . . . 5-2 Recommended Working Representation . . . . . . . . . . . . . 5-3 Convert From One Model Type to Another . . . . . . . . . . . . 5-4 Get Current Value of Generalized Model by Model Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-6 Decompose a 2-DOF PID Controller into SISO Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-8 Discretize a Compensator . . . . . . . . . . . . . . . . . . . . . . . . . 5-13 Improve Accuracy of Discretized System with Time Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-19 Convert Discrete-Time System to Continuous Time . . . . 5-23 Continuous-Discrete Conversion Methods . . . . . . . . . . . 5-26 Choosing a Conversion Method . . . . . . . . . . . . . . . . . . . 5-26 Zero-Order Hold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-27 First-Order Hold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-28 Impulse-Invariant Mapping . . . . . . . . . . . . . . . . . . . . . . 5-29 Tustin Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . 5-30 Zero-Pole Matching Equivalents . . . . . . . . . . . . . . . . . . 5-34 Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-34 Upsample Discrete-Time System . . . . . . . . . . . . . . . . . . . 5-36 Choosing a Resampling Command . . . . . . . . . . . . . . . . . . 5-40 xi
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Model Simplification 6 Model Reduction Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-2 When to Reduce Model Order . . . . . . . . . . . . . . . . . . . . . 6-2 Choosing a Model Reduction Method . . . . . . . . . . . . . . . 6-4 Reduce Model Order Using the Model Reducer App . . . . 6-6 Balanced Truncation Model Reduction . . . . . . . . . . . . . . 6-17 Balanced Truncation in the Model Reducer App . . . . . . 6-17 Approximate Model by Balanced Truncation at the Command Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-26 Compare Truncated and DC Matched Low-Order Model Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-30 Approximate Model with Unstable or Near-Unstable Pole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-35 Frequency-Limited Balanced Truncation . . . . . . . . . . . . 6-40 Pole-Zero Simplification . . . . . . . . . . . . . . . . . . . . . . . . . . 6-47 Pole-Zero Simplification in the Model Reducer App . . . . 6-47 Pole-Zero Cancellation at the Command Line . . . . . . . . 6-53 Mode-Selection Model Reduction . . . . . . . . . . . . . . . . . . 6-57 Mode Selection in the Model Reducer App . . . . . . . . . . 6-57 Mode Selection at the Command Line . . . . . . . . . . . . . . 6-63 Visualize Reduced-Order Models in the Model Reducer App . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-67 Error Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-67 Response Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-68 Plot Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-70 Plot Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-72 xii Contents
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Linear Analysis Time Domain Analysis 7 Plotting System Responses . . . . . . . . . . . . . . . . . . . . . . . . . 7-2 Time-Domain Responses . . . . . . . . . . . . . . . . . . . . . . . . . . 7-20 Time-Domain Response Data and Plots . . . . . . . . . . . . . . 7-21 Time-Domain Characteristics on Response Plots . . . . . . 7-24 Numeric Values of Time-Domain System Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-29 Time-Domain Responses of Discrete-Time Model . . . . . . 7-31 Time-Domain Responses of MIMO Model . . . . . . . . . . . . 7-34 Time-Domain Responses of Multiple Models . . . . . . . . . 7-36 Joint Time-Domain and Frequency-Domain Analysis . . . 7-40 Response from Initial Conditions . . . . . . . . . . . . . . . . . . . 7-45 Import LTI Model Objects into Simulink . . . . . . . . . . . . . 7-48 Simulate LTI Model in Simulink . . . . . . . . . . . . . . . . . . 7-48 Import MIMO LTI Model into Simulink . . . . . . . . . . . . . 7-50 Analysis of Systems with Time Delays . . . . . . . . . . . . . . . 7-53 Considerations to Keep in Mind when Analyzing Systems with Internal Time Delays . . . . . . . . . . . . . . . . . . . . . 7-56 xiii
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Frequency Domain Analysis 8 Frequency-Domain Responses . . . . . . . . . . . . . . . . . . . . . . 8-2 Frequency Response of a SISO System . . . . . . . . . . . . . . . 8-4 Frequency Response of a MIMO System . . . . . . . . . . . . . . 8-6 Frequency-Domain Characteristics on Response Plots . 8-10 Numeric Values of Frequency-Domain Characteristics of SISO Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-13 Pole and Zero Locations . . . . . . . . . . . . . . . . . . . . . . . . . . 8-16 Assessing Gain and Phase Margins . . . . . . . . . . . . . . . . . 8-19 Analyzing Control Systems with Delays . . . . . . . . . . . . . . 8-32 Analyzing the Response of an RLC Circuit . . . . . . . . . . . 8-50 Sensitivity Analysis 9 Model Array with Single Parameter Variation . . . . . . . . . . 9-2 Model Array with Variations in Two Parameters . . . . . . . . 9-6 Study Parameter Variation by Sampling Tunable Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-9 Sensitivity of Control System to Time Delays . . . . . . . . . 9-12 xiv Contents
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Passivity and Conic Sectors 10 About Passivity and Passivity Indices . . . . . . . . . . . . . . . 10-2 About Sector Bounds and Sector Indices . . . . . . . . . . . . 10-9 Passivity Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-19 Parallel Interconnection of Passive Systems . . . . . . . . . 10-24 Series Interconnection of Passive Systems . . . . . . . . . . 10-27 Feedback Interconnection of Passive Systems . . . . . . . 10-31 Control Design PID Controller Design 11 PID Controller Design at the Command Line . . . . . . . . . 11-2 Designing Cascade Control System with PI Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-9 Tune 2-DOF PID Controller (Command Line) . . . . . . . . 11-15 Tune 2-DOF PID Controller (PID Tuner) . . . . . . . . . . . . 11-21 PID Controller Types for Tuning . . . . . . . . . . . . . . . . . . . 11-31 Specifying PID Controller Type . . . . . . . . . . . . . . . . . . 11-31 1-DOF Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-33 2-DOF Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-33 2-DOF Controllers with Fixed Setpoint Weights . . . . . 11-34 PID Controller Tuning in Simulink . . . . . . . . . . . . . . . . 11-37 xv
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Design PID Controller Using Estimated Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-46 Design Family of PID Controllers for Multiple Operating Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-56 Design PID Controller Using Simulated I/O Data . . . . . 11-65 Classical Control Design 12 Choosing a Control Design Approach . . . . . . . . . . . . . . . 12-2 Control System Designer Tuning Methods . . . . . . . . . . . 12-4 Graphical Tuning Methods . . . . . . . . . . . . . . . . . . . . . . 12-4 Automated Tuning Methods . . . . . . . . . . . . . . . . . . . . . 12-5 Effective Plant for Tuning . . . . . . . . . . . . . . . . . . . . . . . 12-6 Select a Tuning Method . . . . . . . . . . . . . . . . . . . . . . . . 12-7 Design Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-9 Add Design Requirements . . . . . . . . . . . . . . . . . . . . . 12-10 Edit Design Requirements . . . . . . . . . . . . . . . . . . . . . 12-13 Root Locus and Pole-Zero Plot Requirements . . . . . . . 12-14 Open-Loop and Closed-Loop Bode Diagram Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-16 Open-Loop Nichols Plot Requirements . . . . . . . . . . . . 12-17 Step and Impulse Response Requirements . . . . . . . . . 12-18 Feedback Control Architectures . . . . . . . . . . . . . . . . . . . 12-21 Design Multiloop Control System . . . . . . . . . . . . . . . . . 12-24 Multimodel Control Design . . . . . . . . . . . . . . . . . . . . . . 12-35 Control Design Overview . . . . . . . . . . . . . . . . . . . . . . 12-35 Model Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-35 Nominal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-37 Frequency Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-39 Design Controller for Multiple Plant Models . . . . . . . . 12-40 xvi Contents
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Bode Diagram Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-49 Tune Compensator For DC Motor Using Bode Diagram Graphical Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . 12-49 Root Locus Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-64 Tune Electrohydraulic Servomechanism Using Root Locus Graphical Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . 12-64 Nichols Plot Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-80 Tune Compensator For DC Motor Using Nichols Plot Graphical Design . . . . . . . . . . . . . . . . . . . . . . . . . . 12-80 Edit Compensator Dynamics . . . . . . . . . . . . . . . . . . . . . . 12-93 Compensator Editor . . . . . . . . . . . . . . . . . . . . . . . . . . 12-93 Graphical Compensator Editing . . . . . . . . . . . . . . . . . 12-96 Poles and Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-97 Lead and Lag Networks . . . . . . . . . . . . . . . . . . . . . . . 12-97 Notch Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-98 Design Compensator Using Automated Tuning Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-100 Select Tuning Method . . . . . . . . . . . . . . . . . . . . . . . 12-100 Select Compensator and Loop to Tune . . . . . . . . . . . 12-101 PID Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-102 Optimization-Based Tuning . . . . . . . . . . . . . . . . . . . . 12-108 LQG Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-110 Loop Shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-112 Internal Model Control Tuning . . . . . . . . . . . . . . . . . 12-113 Analyze Designs Using Response Plots . . . . . . . . . . . . 12-117 Analysis Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-117 Editor Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-120 Plot Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 12-121 Plot Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-122 Design Requirements . . . . . . . . . . . . . . . . . . . . . . . . 12-124 Compare Performance of Multiple Designs . . . . . . . . 12-127 Design Hard-Disk Read/Write Head Controller . . . . . 12-133 Design Compensator for Plant Model with Time Delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-147 xvii
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Design Compensator for Systems Represented by Frequency Response Data . . . . . . . . . . . . . . . . . . . . . 12-155 Design Internal Model Controller for Chemical Reactor Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-161 Design LQG Tracker Using Control System Designer 12-176 Export Design to MATLAB Workspace . . . . . . . . . . . . . 12-188 Generate Simulink Model for Control Architecture . . 12-191 Tune Simulink Blocks Using Compensator Editor . . . 12-193 Single Loop Feedback/Prefilter Compensator Design 12-201 Cascaded Multiloop Feedback Design . . . . . . . . . . . . . 12-211 Reference Tracking of DC Motor with Parameter Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-222 State-Space Control Design 13 Extended and Unscented Kalman Filter Algorithms for Online State Estimation . . . . . . . . . . . . . . . . . . . . . . . . 13-2 Extended Kalman Filter Algorithm . . . . . . . . . . . . . . . . 13-2 Unscented Kalman Filter Algorithm . . . . . . . . . . . . . . . 13-5 Generate Code for Online State Estimation in MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-11 Tunable and Nontunable Object Properties . . . . . . . . . 13-13 Validate Online State Estimation at the Command Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-15 Examine Output Estimation Error . . . . . . . . . . . . . . . . 13-15 Examine State Estimation Error for Simulated Data . . 13-16 Validate Online State Estimation in Simulink . . . . . . . . 13-18 Examine Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-18 xviii Contents
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Examine State Estimation Error for Simulated Data . . 13-19 Compute Residuals and State Estimation Errors . . . . . 13-19 Troubleshoot Online State Estimation . . . . . . . . . . . . . . 13-22 Nonlinear State Estimation Using Unscented Kalman Filter and Particle Filter . . . . . . . . . . . . . . . . . . . . . . . 13-24 Estimate States of Nonlinear System with Multiple, Multirate Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-45 Regulate Pressure in Drum Boiler . . . . . . . . . . . . . . . . . 13-59 Control System Tuning Control System Tuning 14 Automated Tuning Overview . . . . . . . . . . . . . . . . . . . . . . . 14-3 Choosing an Automated Tuning Approach . . . . . . . . . . . 14-5 Automated Tuning Workflow . . . . . . . . . . . . . . . . . . . . . . . 14-7 Specify Control Architecture in Control System Tuner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-9 About Control Architecture . . . . . . . . . . . . . . . . . . . . . . 14-9 Predefined Feedback Architecture . . . . . . . . . . . . . . . . 14-9 Arbitrary Feedback Control Architecture . . . . . . . . . . 14-11 Control System Architecture in Simulink . . . . . . . . . . 14-12 Open Control System Tuner for Tuning Simulink Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-13 Command-Line Equivalents . . . . . . . . . . . . . . . . . . . . 14-14 xix
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Specify Operating Points for Tuning in Control System Tuner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-15 About Operating Points in Control System Tuner . . . . 14-15 Linearize at Simulation Snapshot Times . . . . . . . . . . . 14-15 Compute Operating Points at Simulation Snapshot Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-17 Compute Steady-State Operating Points . . . . . . . . . . . 14-21 Specify Blocks to Tune in Control System Tuner . . . . . 14-24 View and Change Block Parameterization in Control System Tuner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-26 View Block Parameterization . . . . . . . . . . . . . . . . . . . 14-26 Fix Parameter Values or Limit Tuning Range . . . . . . . 14-28 Custom Parameterization . . . . . . . . . . . . . . . . . . . . . . 14-30 Block Rate Conversion . . . . . . . . . . . . . . . . . . . . . . . . 14-31 Setup for Tuning Control System Modeled in MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-35 How Tuned Simulink Blocks Are Parameterized . . . . . . 14-36 Blocks With Predefined Parameterization . . . . . . . . . . 14-36 Blocks Without Predefined Parameterization . . . . . . . . 14-37 View and Change Block Parameterization . . . . . . . . . . 14-38 Specify Goals for Interactive Tuning . . . . . . . . . . . . . . . 14-39 Quick Loop Tuning of Feedback Loops in Control System Tuner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-48 Quick Loop Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-58 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-58 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-58 Feedback Loop Selection . . . . . . . . . . . . . . . . . . . . . . 14-58 Desired Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-59 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-60 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-61 Step Tracking Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-62 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-62 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-62 Step Response Selection . . . . . . . . . . . . . . . . . . . . . . . 14-63 Desired Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-64 xx Contents
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AI Reading Assistant
Whole-book reading guide from stratified index samples; jump to passages in the text
AI guide
【One-Line Pitch】
A practical, task-oriented manual for engineers and students who want to model, analyze, and tune linear control systems in MATLAB without wading through theory textbooks. Best for readers who already know basic control concepts and need to get real work done in the Control System Toolbox.
【Book Arc】
- **Opening (~0%–12%)**: Front matter, revision history, and the conceptual overview of linear system model objects — what they represent, how model data is stored, and the taxonomy of dynamic, static, numeric, identified, and generalized models. Solves the "what am I actually manipulating?" question before any commands appear.
- **Early (~13%–31%)**: Model creation in depth — transfer functions, state-space (explicit and descriptor), frequency response data, PID controllers (continuous, discrete, 2-DOF), MIMO models, and time delays including internal delays and approximation strategies. This is the construction toolkit.
- **Middle (~38%–56%)**: Working with models once built — storing/retrieving properties, extracting coefficients, metadata and units, subsystem extraction, model interconnections (feedback loops, multi-loop, MIMO), then model transformation (type conversion, discretization methods like ZOH and Tustin) and model simplification (balanced truncation, pole-zero cancellation, mode selection, Model Reducer app).
- **Late (~63%–75%)**: Linear analysis — time-domain responses (step, impulse, initial conditions, discrete and MIMO cases, Simulink import) and frequency-domain analysis (Bode/Nyquist-style responses, margins, pole-zero maps, delay handling, an RLC circuit worked example).
- **Ending (~75%+)**: Sensitivity analysis via model arrays with parameter variation; excerpts do not cover the remaining chapters in detail.
【Key Takeaways】
- **Model objects are the central abstraction** (Opening): everything in the toolbox operates on typed model objects (tf, ss, frd, pid, genss), and understanding their data structure and type hierarchy is the prerequisite for every later workflow.
- **Creation is representation-driven** (Early): the same physical system can be built from numerator/denominator coefficients, poles-zeros-gain, or state matrices — choosing the right representation early saves conversion pain later.
- **Time delays are a first-class concern** (Early): the manual treats delays seriously, covering input/output delays, internal delays, and Padé-style approximation, because delays break many standard assumptions and must be handled deliberately.
- **Interconnection rules determine model type** (Middle): when you combine models arithmetically or in feedback, the software infers the resulting type by fixed rules — knowing these rules prevents surprises in large block diagrams.
- **Discretization method choice matters** (Middle): ZOH, FOH, Tustin, impulse-invariant, and zero-pole matching each have trade-offs; the guide explicitly frames "choosing a conversion method" as a decision, not a default.
- **Model reduction is a workflow, not a single command** (Middle): balanced truncation, pole-zero simplification, and mode selection are presented with both app-based and command-line paths, plus error/response plots to validate the reduced model.
- **Analysis spans time and frequency domains** (Late): response plots, numeric characteristics, and margins are treated as complementary views, with explicit support for MIMO, discrete-time, and delayed systems.
- **Parameter variation is handled through model arrays** (Ending): arrays and LPV models let you sweep parameters and simulate multi-mode dynamics without rewriting your model from scratch.
【Reading Tips】
- **Skim the front matter and revision history** — it is pure boilerplate; jump straight to the model-objects chapter if you are new to the toolbox.
- **Deep-read Chapters 2 and 4** (creation and interconnection): these are the load-bearing chapters; almost every later workflow assumes fluency here.
- **Treat the discretization and model-reduction chapters as reference**, not linear reading — consult the method-comparison tables when you actually face a conversion or reduction decision.
- **Work the RLC circuit and jet transport aircraft examples** as hands-on anchors; they connect abstract commands to physical systems.
- **Keep the analysis chapters (time/frequency domain) nearby while modeling** — they are where you verify that what you built behaves as intended.
【Coverage Limits】
This guide is based on a table-of-contents-heavy sample; chapter contents beyond headings (especially the sensitivity-analysis and later chapters) are not covered in detail, so specific command syntax and worked examples should be verified against the manual itself.
Passage locations
Page 2
nd Simulink are registered trademarks of The MathWorks, Inc. See www.mathworks.com/trademarks for a list of additional trademarks. Other product or brand nam...
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ntations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-16 2-DOF Control Architectures . . . . . . . . . . . . . . . . . . . . 2-18 Discrete-Time...
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Page 8
and Tuning . . . . . . 2-95 Model Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-100 What Are Model Arrays? . . . . . . . . . ....
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Page 12
osing a Model Reduction Method . . . . . . . . . . . . . . . 6-4 Reduce Model Order Using the Model Reducer App . . . . 6-6 Balanced Truncation Model Reducti...
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