matlab模型预测控制
介绍MPC，简介预测控制动态矩阵能直接处理带有纯滞后的对象，对大惯性有很强的适应能力，又有良好的跟踪性能和较强的鲁棒性，并且对模型精度要求低，所以在工业过程中有很强的适用性。本文针对DMC算法进行研究，并在此基础上用matlab进行了系统仿真验证了该算法的优点。口经验交流口仪器仪表用户P已知的情况下,控制时域长度M越小,越难保证输出在各采能的 Window标准图形用户界面,使优化问题操作简单方便。样点紧密跟踪期望输出值,系统的响应速度比较慢,但容易得在 Matlab制作图形用户界而(GUI)的设计环境下,用M文件到稳定的控制和较好的鲁棒性;控制时域长度M越大,控制来进行CU编程,使GU设计变得简单、快捷。的机动性越强,能够改善系统的动态响应,增大了系统的灵活首先在Meab的命令窗下输人 guide命令或者利用文件性和快速性,提高控制的灵敏度,但是系统的稳定性和鲁棒性菜单中的new选项下的GUI,即可以进入CUI设计窗口。从变差。因此,控制时域长度的选择应兼顾快速性和稳定性。窗口的左侧工具栏中选取需要的控件,绘制在右侧锥形窗口;4)控制加权系数双击各控件图标,即打开该控件属性对话框,对其进行属性设控制加权系数主要用于限制控制增量的剧烈变化,使控置。保存图形界面时,系统将直动生成一个同名的m文件,打制量的变化趋于平缓,以防止超出限制范围或发生剧烈振荡,开此程序文件,对图形界面各控廾的回调函数 Callback()增减少对系统的过大冲击。增加控制值加权系数的值,控制作加所需的程序代码,以完成各种操作。设计完成之后的得到用减弱,闭环系统稳定,输出响应速度减慢,有益于增加系统的界面如图4所示。的稳定性;但过人的控制加权系数会使控制量的变化极为缓动态矩阵控制算法仿真慢,系统得不到及时的调节,反而会使动态特性变坏7。拴制牌出图积样周期预測时域斑度「F动态矩阵控制算法的优点I)直接在控制算法中考虑预测变量和控制变量的约束条控制时域长度M=1件,用满足约束条件的范围求出最优预测值输入戏象横型控淛权系数2)把控制变量与预测变量的权系数矩阵作为设计参数,系统设定值在设计过程中通过仿真调节鲁棒性好的参数值。3)预测变量和控制变量较多的场合,或者控制变量的的设定在给出的目标值范围内,只是具有自由度,预测变量的定图4动态矩阵控制算法界面设计常状态值被认为是有无数组组合。5结束语4)从受控对象动态特性设定到最后作为仿真来确定控制性由上述仿真结果可以知道,动态矩阵控制效果比传统能为止。DMC算法以直接作为控制量,在控制中包含了数字积PID的控制效果好。动态矩阵控制采用工程上容易得到的阶分环节,因此,即使在模型失配的情况下,也能得到无静差控制。跃响应作为数学模型、运算量小、算法简单、在线实时方便,具4仿真研究有良好的调节品质和很强的鲁棒性,能抑制被控对象的大迟针对被控对象C(s)=12滞特性,能够满足生产现场的需要,获得满意的控制效果,因17.2s+进行仿真,取采样周期而有良好的应用前景。同时基于 Matlab汝计实现了动态矩阵T=2s,模型时域长度为N=90,预测时域长度P=6,控制时控制算法图形用户界面,为动态矩阵控制算法提供了一个简域长度M=1,控制权系数A=1,系统设定值y,=1。对模型在单实用的平台。由于 Matlab具有良好、开放的可扩展性,在应用阶跃扰动下进行仿真,得到如图2所示的控制曲线,可以知道中,用户可以根据实际问题编写相应的函数文件,在CU平台输控制效果较好。入要修改的参数即可完成优化求解操作简单、非常实用。口与传统的PID控制器的控制效果进行比较,其中传统参考文献PD的参数采用工程整定法中的动态特性参数法(又称Z-NL1]李国勇.智能控制及其 MATLAB实现[M]北京:电子工业整定法),得到的参数为Kp=1.5,T1=1,T=0.5,仿真结果出版社,2005:285-289如图3所示。2]席裕庚预测控制[M].北京:国防工业出版社,1993[3]周福恩,毕效辉.动态矩阵控制算法在过程控制中的应用研究[J].南通航运职业技术学院学报,2005,4(1)4345[4]何同祥,常宁青.动态矩阵控制算法在工业电加热炉温度控制中的应用[J.仪器仪表用户,2011,(01):28-3004[5}李玉红,刘红军,王东风,韩璞.一种新型的动态矩阵控制算法及仿真研究[J]计算机学报,2005,22(2):103-1091015公23[6]周忠海,张涛,陈哓高.基于动态矩阵控制算法的电加热炉图2DMC仿真纬果图图3传统Pm仿真结果图温度控制系统[J].山东科学,2005,18(5):7073我们知道传统的PID控制超调量过大,稳定时间长,控制7]触晓红,周佳精通GUI图形界面编程[M].北京:北京大学模型和参数需要比较精确,否则控制性能不会很好,而采用动出版社,2003作者简介:杨丽华(1987-),女,在读硕士研究生,主要从事预测控制方态矩阵控制算法则大大地抑制了超调量,消除了振荡,也缩短面的研究工作;赵文杰(1969-),男,华北电力大学控制科学与工程学了平衡时间,控制效果好。院副教授,主要从事热工过程的信息融合与先进控制方面的研究根据上述动态矩阵控制算法的基本流程及其操作编制成工作相应的m函数文件。这个设计包含动态矩阵控制算法优化功收稿日期2012041866EcVo.192012No,4欢迎光临本刊网站http://www.yqybyh.com
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MATLAB在卡尔曼滤波器中应用的理论与实践Kalman
MATLAB在卡尔曼滤波器中应用的理论与实践KalmanKALMAN FILTERINGTheory and Practice Using MATLABThird editionMOHINDER S GREWALCalifornia State University at FullertonANGUS P. ANDREWSRockwell Science Center (retired)WILEYA JOHN WILEY & SONS, INC. PUBLICATIONCopyright 2008 by John Wiley sons, Inc. All rights reservedPublished by John Wiley sons, InC, Hoboken, New JerseyPublished simultaneously in CanadaNo part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or byany means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permittedunder Section 107 or 108 of the 1976 United States Copyright Act, without either the prior writtenpermission of the Publisher, or authorization through payment of the appropriate per-copy fee to theCopyright Clearance Center, Inc, 222 Rosewood Drive, Danvers, MA 01923,(978)750-8400, fax(978)750-4470,oronthewebatwww.copyright.com.RequeststothePublisherforpermissionshouldbe addressed to the Permissions Department, John Wiley Sons, Inc, lll River Street, Hoboken, NJ07030,(201)748-6011,fax(201)748-6008,oronlineathttp://www.wiley.com/go/permissionimit of liability Disclaimer of Warranty: While the publisher and author have used their best efforts inpreparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability orfitness for a particular purpose. No warranty may be created or extended by sales representatives orwritten sales materials. The advice and strategies contained herein may not be suitable for your situationYou should consult with a professional where appropriate. Neither the publisher nor author shall be liablefor any loss of profit or any other commercial damages, including but not limited to special, incidentalconsequential, or other damagesFor general information on our other products and services or for technical support, please contact ourCustomer Care Department within the United States at(800)762-2974, outside the United States at(317)572-3993 or fax(317)572-4002Wiley also publishes its books in a variety of electronic formats. Some content that appears in print maynot be available in electronic format. For more information about wiley products, visit our web site atwww.wiley.comLibrary of Congress Cataloging- in-Publication DataGrewal. Mohinder sKalman filtering: theory and practice using MATLAB/Mohinder S. GrewalAngus p. andrews. 3rd edIncludes bibliographical references and indexISBN978-0-470-17366-4( cloth)1. Kalman filtering. 2. MATLAB. I. Andrews, Angus P. II. TitleQA402.3.G69520086298312—dc22200803733Printed in the United States of america10987654321CONTENTSPrefaceAcknowledgmentsXIIIList of abbreviationsXV1 General Information1.1 On Kalman Filtering1.2 On Optimal Estimation Methods, 51. 3 On the notation Used In This book 231. 4 Summary, 25Problems. 262 Linear Dvnamic Systems2. 1 Chapter focus, 312.2 Dynamic System Models, 362. 3 Continuous Linear Systems and Their Solutions, 402.4 Discrete Linear Systems and Their Solutions, 532.5 Observability of Linear Dynamic System Models, 552.6 Summary, 61Problems. 643 Random Processes and Stochastic Systems3.1 Chapter Focus, 673.2 Probability and random Variables (rvs), 703.3 Statistical Properties of RVS, 78CONTEN3.4 Statistical Properties of Random Processes(RPs),803.5 Linear rp models. 883.6 Shaping Filters and State Augmentation, 953.7 Mean and Covariance propagation, 993.8 Relationships between Model Parameters, 1053.9 Orthogonality principle 1143.10 Summary, 118Problems. 1214 Linear Optimal Filters and Predictors1314.1 Chapter Focus, 1314.2 Kalman Filter. 1334.3 Kalman-Bucy filter, 1444.4 Optimal Linear Predictors, 1464.5 Correlated noise Sources 1474.6 Relationships between Kalman-Bucy and wiener Filters, 1484.7 Quadratic Loss Functions, 1494.8 Matrix Riccati Differential Equation. 1514.9 Matrix Riccati Equation In Discrete Time, 1654.10 Model equations for Transformed State Variables, 1704.11 Application of Kalman Filters, 1724.12 Summary, 177Problems. 1795 Optimal Smoothers5.1 Chapter Focus, 1835.2 Fixed-Interval Smoothing, 1895.3 Fixed-Lag Smoothing, 2005.4 Fixed-Point Smoothing, 2135.5 Summary, 220Problems. 226 Implementation Methods2256. 1 Chapter Focus, 2256.2 Computer Roundoff, 2276.3 Effects of roundoff errors on Kalman filters 2326.4 Factorization Methods for Square-Root Filtering, 2386. 5 Square-Root and UD Filters, 2616.6 Other Implementation Methods, 2756.7 Summary, 288Problems. 2897 Nonlinear Filtering2937.1 Chapter Focus, 2937.2 Quasilinear Filtering, 296CONTENTS7.3 Sampling Methods for Nonlinear Filtering, 3307.4 Summary, 345Problems. 3508 Practical Considerations3558.1 Chapter Focus. 3558.2 Detecting and Correcting Anomalous behavior, 3568.3 Prefiltering and Data Rejection Methods, 3798.4 Stability of Kalman Filters, 3828. 5 Suboptimal and reduced- Order Filters, 3838.6 Schmidt-Kalman Filtering, 3938.7 Memory, Throughput, and wordlength Requirements, 4038.8 Ways to Reduce Computational requirements 4098.9 Error Budgets and Sensitivity Analysis, 4148.10 Optimizing Measurement Selection Policies, 4198.11 Innovations analysis, 4248.12 Summary, 425Problems. 4269 Applications to Navigation4279.1 Chapter focus, 4279.2 Host vehicle dynamics, 4319.3 Inertial Navigation Systems(INS), 4359. 4 Global Navigation Satellite Systems(GNSS), 4659.5 Kalman Filters for GNSS. 4709.6 Loosely Coupled GNSS/INS Integration, 4889.7 Tightly Coupled GNSS /INS Integration, 4919. 8 Summary, 507Problems. 508Appendix A MATLAB Software511A 1 Notice. 511A 2 General System Requirements, 511A 3 CD Directory Structure, 512A 4 MATLAB Software for Chapter 2, 512A. 5 MATLAB Software for Chapter 3, 512A6 MATLAB Software for Chapter 4, 512A. 7 MATLAB Software for Chapter 5, 513A 8 MATLAB Software for Chapter 6, 513A 9 MATLAB Software for Chapter 7, 514A10 MATLAB Software for Chapter 8, 515A 11 MATLAB Software for Chapter 9, 515A 12 Other Sources of software 516CONTENAppendix b A Matrix Refresher519B. 1 Matrix Forms. 519B 2 Matrix Operations, 523B 3 Block matrix Formulas. 527B 4 Functions of Square Matrices, 531B 5 Norms. 538B6 Cholesky decomposition, 541B7 Orthogonal Decompositions of Matrices, 543B 8 Quadratic Forms, 545B 9 Derivatives of matrices. 546Bibliography549Index565PREFACEThis book is designed to provide familiarity with both the theoretical and practicalaspects of Kalman filtering by including real-world problems in practice as illustrativeexamples. The material includes the essential technical background for Kalman filter-ing and the more practical aspects of implementation: how to represent the problem ina mathematical model, analyze the performance of the estimator as a function ofsystem design parameters, implement the mechanization equations in numericallystable algorithms, assess its computational requirements, test the validity of resultsitor the filteThetant attributes ofthe subject that are often overlooked in theoretical treatments but are necessary forapplication of the theory to real-world problemsIn this third edition, we have included important developments in the implemen-tation and application of Kalman filtering over the past several years, including adaptations for nonlinear filtering, more robust smoothing methods, and develelopingapplications in navigationWe have also incorporated many helpful corrections and suggefrom ourreaders, reviewers, colleagues, and students over the past several years for theoverall improvement of the textbookAll software has been provided in MatLab so that users can take advantage ofits excellent graphing capabilities and a programming interface that is very close tothe mathematical equations used for defining Kalman filtering and its applicationsSee Appendix a for more information on MATLAB softwareThe inclusion of the software is practically a matter of necessity because Kalmanfiltering would not be very useful without computers to implement it. It provides aMATLAB is a registered trademark of The Mathworks, IncEFACEbetter learning experience for the student to discover how the Kalman filter works byobserving it in actionThe implementation of Kalman filtering on computers also illuminates some of thepractical considerations of finite-wordlength arithmetic and the need for alternativealgorithms to preserve the accuracy of the results. If the student wishes to applywhat she or he learns, then it is essential that she or he experience its workingsand failings--and learn to recognize the differenceThe book is organized as a text for an introductory course in stochastic processes atthe senior level and as a first-year graduate-level course in Kalman filtering theory andapplicationIt can also be used for self-instruction or for purposes of review by practi-cing engineers and scientists who are not intimately familiar with the subject. Theorganization of the material is illustrated by the following chapter-level dependencygraph, which shows how the subject of each chapter depends upon material in otherchapters. The arrows in the figure indicate the recommended order of study. Boxesabove another box and connected by arrows indicate that the material represented bythe upper boxes is background material for the subject in the lower boxAPPENDIX B: A MATRIX REFRESHERGENERAL INFORMATION2. LINEAR DYNAMIC SYSTEMSRANDOM PROCESSES AND STOCHASTIC SYSTEMS4. OPTIMAL LINEAR FILTERS AND PREDICTORS5. OPTIMAL SMOOTHERS6. IMPLEMENTATIONMETHODS7. NONLINEAR8. PRACTICAL9. APPLICATIONSFILTERINGCONSIDERATIONSTO NAVIGATIONAPPENDIX A: MATLAB SOFTWAREChapter l provides an informal introduction to the general subject matter by wayof its history of development and application. Chapters 2 and 3 and Appendix b coverthe essential background material on linear systems, probability, stochastic processesand modeling. These chapters could be covered in a senior-level course in electricalcomputer, and systems engineeringChapter 4 covers linear optimal filters and predictors, with detailed examples ofapplications. Chapter 5 is a new tutorial-level treatment of optimal smoothing
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