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Robust Control Toolbox™ 3.pdf

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    Introduction
    Product Overview
    Required Software
    Modeling Uncertainty
    Example: ACC Benchmark Problem
    Worst-Case Performance
    Example: ACC Two-Cart Benchmark Problem
    Synthesis of Robust MIMO Controllers
    Example: Designing a Controller with LOOPSYN
    Model Reduction and Approximation
    Example: NASA HiMAT Controller Order Reduction
    LMI Solvers
    Extends Control System Toolbox™ Capabilities
    About the Authors
    Bibliography
    Multivariable Loop Shaping
    Tradeoff Between Performance and Robustness
    Norms and Singular Values
    Typical Loop Shapes, S and T Design
    Singular Values
    Guaranteed Gain/Phase Margins in MIMO Systems
    Using LOOPSYN to Do H-Infinity Loop Shaping
    Example: NASA HiMAT Loop Shaping
    Design Specifications
    MATLAB® Commands for a LOOPSYN Design
    Using MIXSYN for H-Infinity Loop Shaping
    Example: NASA HiMAT Design Using MIXSYN
    Loop-Shaping Commands
    Model Reduction for Robust Control
    Introduction
    Hankel Singular Values
    Overview of Model Reduction Techniques
    Approximating Plant Models — Additive Error Methods
    Approximating Plant Models — Multiplicative Error Method
    Using Modal Algorithms
    Rigid Body Dynamics
    Reducing Large-Scale Models
    Using Normalized Coprime Factor Methods
    References
    Robustness Analysis
    Uncertainty Modeling
    Creating Uncertain Models of Dynamic Systems
    Creating Uncertain Parameters
    Quantifying Unmodeled Dynamics
    Robustness Analysis
    Multiinput, Multioutput Robustness Analysis
    Adding Independent Input Uncertainty toEachChannel
    Closed-Loop Robustness Analysis
    Nominal Stability Margins
    Robustness of Stability Model Uncertainty
    Worst-Case Gain Analysis
    Summary of Robustness Analysis Tools
    H-Infinity and Mu Synthesis
    H-Infinity Performance
    Performance as Generalized Disturbance Rejection
    Robustness in the H-Infinity Framework
    Application of H-Infinity and Mu to Active Suspension Control
    Quarter Car Suspension Model
    Linear H-Infinity Controller Design
    H-Infinity Control Design 1
    H-Infinity Control Design 2
    Control Design via Mu Synthesis
    Functions for Control Design
    Interpretation of H-Infinity Norm
    Norms of Signals and Systems
    Using Weighted Norms to Characterize Performance
    References
    Index
    www.matlab.org.cn MATLAB 研究与探索 说明：本资料仅供MATLAB 学习者及相关技术人员研究参考使用。获取更丰富资料请登录：www.matlab.org.cn
    Robust Control Toolbox™ 3 Getting Started Guide Gary Balas Richard Chiang Andy Packard Michael Safonov
    How to Contact The MathWorks www.mathworks.com comp.soft-sys.matlab Web Newsgroup support@mathworks.com suggest@mathworks.com bugs@mathworks.com doc@mathworks.com service@mathworks.com info@mathworks.com Technical support Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information 508-647-7000 508-647-7001 Phone Fax The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 For contact information about worldwide offices, see the MathWorks Web site. Mail Robust Control Toolbox™ Getting Started Guide © COPYRIGHT 2005–2009 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 repro- duced 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 The MathWorks products are protected by one or more U.S. patents. Please see www.mathworks.com/patents for more information.
    Revision History September 2005 First printing March 2006 Online only September 2006 Online only March 2007 Online only September 2007 Online only Online only March 2008 Online only October 2008 March 2009 Online only New for Version 3.0.2 (Release 14SP3) Revised for Version 3.1 (Release 2006a) Revised for Version 3.1.1 (Release 2006b) Revised for Version 3.2 (Release 2007a) Revised for Version 3.3 (Release 2007b) Revised for Version 3.3.1 (Release 2008a) Revised for Version 3.3.2 (Release 2008b) Revised for Version 3.3.3 (Release 2009a)
    1 2 Contents Introduction Product Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2 Required Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2 Modeling Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3 Example: ACC Benchmark Problem . . . . . . . . . . . . . . . . . . . . . 1-3 Worst-Case Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7 Example: ACC Two-Cart Benchmark Problem . . . . . . . . . . . . . 1-7 Synthesis of Robust MIMO Controllers . . . . . . . . . . . . . . . . 1-10 Example: Designing a Controller with LOOPSYN . . . . . . . . . 1-10 Model Reduction and Approximation . . . . . . . . . . . . . . . . . . 1-14 Example: NASA HiMAT Controller Order Reduction . . . . . . . 1-14 LMI Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-18 Extends Control System Toolbox™ Capabilities . . . . . . . . 1-19 About the Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-20 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-21 Multivariable Loop Shaping Tradeoff Between Performance and Robustness . . . . . . . . . 2-2 Norms and Singular Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3 Typical Loop Shapes, S and T Design . . . . . . . . . . . . . . . . . . . 2-5 Singular Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5 v
    Guaranteed Gain/Phase Margins in MIMO Systems . . . . . . . . 2-9 Using LOOPSYN to Do H-Infinity Loop Shaping . . . . . . . . 2-11 Example: NASA HiMAT Loop Shaping . . . . . . . . . . . . . . . . . . 2-11 Design Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-13 MATLAB® Commands for a LOOPSYN Design . . . . . . . . . . . 2-13 Using MIXSYN for H-Infinity Loop Shaping . . . . . . . . . . . . 2-17 Example: NASA HiMAT Design Using MIXSYN . . . . . . . . . . 2-18 Loop-Shaping Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-20 Model Reduction for Robust Control 3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2 Hankel Singular Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2 Overview of Model Reduction Techniques . . . . . . . . . . . . . . . 3-4 Approximating Plant Models — Additive Error Methods . . 3-6 Approximating Plant Models — Multiplicative Error Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-8 Using Modal Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10 Rigid Body Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10 Reducing Large-Scale Models . . . . . . . . . . . . . . . . . . . . . . . . . 3-13 Using Normalized Coprime Factor Methods . . . . . . . . . . . . 3-14 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-15 vi Contents
    4 5 Robustness Analysis Uncertainty Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2 Creating Uncertain Models of Dynamic Systems . . . . . . . . . . . 4-2 Creating Uncertain Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 4-3 Quantifying Unmodeled Dynamics . . . . . . . . . . . . . . . . . . . . . . . 4-5 Robustness Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8 Multiinput, Multioutput Robustness Analysis . . . . . . . . . . . 4-12 Adding Independent Input Uncertainty to Each Channel . . . 4-13 Closed-Loop Robustness Analysis . . . . . . . . . . . . . . . . . . . . . . . 4-15 Nominal Stability Margins . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-17 Robustness of Stability Model Uncertainty . . . . . . . . . . . . . . . 4-18 Worst-Case Gain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-20 Summary of Robustness Analysis Tools . . . . . . . . . . . . . . . . 4-23 H-Infinity and Mu Synthesis H-Infinity Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2 Performance as Generalized Disturbance Rejection . . . . . . . . . 5-2 Robustness in the H-Infinity Framework . . . . . . . . . . . . . . . . . . 5-8 Application of H-Infinity and Mu to Active Suspension Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-10 Quarter Car Suspension Model . . . . . . . . . . . . . . . . . . . . . . . . . 5-10 Linear H-Infinity Controller Design . . . . . . . . . . . . . . . . . . . . . 5-12 H-Infinity Control Design 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-13 H-Infinity Control Design 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-14 Control Design via Mu Synthesis . . . . . . . . . . . . . . . . . . . . . . . 5-19 Functions for Control Design . . . . . . . . . . . . . . . . . . . . . . . . . 5-26 vii
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