Nonlinear H 2/H ∞ Constrained Feedback Control: A Practical Design Approach Using Neural Networks PDF
Preview Nonlinear H 2/H ∞ Constrained Feedback Control: A Practical Design Approach Using Neural Networks
Advances in Industrial Control OthertitlespublishedinthisSeries: DigitalControllerImplementation RudderandFinShipRollStabilization andFragility TristanPerez RobertS.H.Istepanianand HardDiskDriveServoSystems(2nd JamesF.Whidborne(Eds.) Edition) OptimisationofIndustrialProcesses BenM.Chen,TongH.Lee,KemaoPeng atSupervisoryLevel andVenkatakrishnanVenkataramanan DorisSáez,AldoCiprianoand Measurement,Control,and AndrzejW.Ordys CommunicationUsingIEEE1588 RobustControlofDieselShipPropulsion JohnEidson NikolaosXiros PiezoelectricTransducersforVibration HydraulicServo-systems ControlandDamping MohieddineJelaliandAndreasKroll S.O.RezaMoheimaniandAndrewJ. Fleming StrategiesforFeedbackLinearisation FreddyGarces,VictorM.Becerra, WindupinControl ChandrasekharKambhampatiand PeterHippe KevinWarwick ManufacturingSystemsControlDesign RobustAutonomousGuidance StjepanBogdan,FrankL.Lewis,Zdenko AlbertoIsidori,LorenzoMarconiand Kovaˇci´candJoséMirelesJr. AndreaSerrani PracticalGrey-boxProcessIdentification DynamicModellingofGasTurbines TorstenBohlin GennadyG.KulikovandHaydnA. ModernSupervisoryandOptimalControl Thompson(Eds.) SandorA.Markon,HajimeKita,Hiroshi ControlofFuelCellPowerSystems KiseandThomasBartz-Beielstein JayT.Pukrushpan,AnnaG.Stefanopoulou PublicationdueJuly2006 andHueiPeng WindTurbineControlSystems FuzzyLogic,IdentificationandPredictive FernandoD.Bianchi,HernánDeBattista Control andRicardoJ.Mantz JairoEspinosa,JoosVandewalleand PublicationdueAugust2006 VincentWertz SoftSensorsforMonitoringandControlof OptimalReal-timeControlofSewer IndustrialProcesses Networks LuigiFortuna,SalvatoreGraziani, MagdaleneMarinakiandMarkos AlessandroRizzoandMariaGabriella Papageorgiou Xibilia ProcessModellingforControl PublicationdueAugust2006 BenoîtCodrons AdvancedFuzzyLogicTechnologiesin ComputationalIntelligenceinTimeSeries IndustrialApplications Forecasting YingBai,HanqiZhuangandDaliWang AjoyK.PalitandDobrivojePopovic (Eds.) PublicationdueSeptember2006 ModellingandControlofmini-Flying Machines PracticalPIDControl PedroCastillo,RogelioLozanoand AntonioVisioli AlejandroDzul PublicationdueNovember2006 MuradAbu-Khalaf,JieHuangandFrankL.Lewis H H Nonlinear / ∞ 2 Constrained Feedback Control APracticalDesignApproachUsingNeuralNetworks With47Figures 123 MuradAbu-Khalaf,PhD JieHuang,PhD FrankL.Lewis,PhD Automation&Robotics DepartmentofAutomation Automation&Robotics ResearchInstitute andComputer-aided ResearchInstitute TheUniversityofTexas Engineering TheUniversityofTexas atArlington ChineseUniversityof atArlington FortWorth,Texas HongKong FortWorth,Texas USA Shatin,NewTerritories USA HongKong BritishLibraryCataloguinginPublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary LibraryofCongressControlNumber:2006925302 AdvancesinIndustrialControlseriesISSN1430-9491 ISBN-10: 1-84628-349-3 e-ISBN 1-84628-350-7 Printedonacid-freepaper ISBN-13: 978-1-84628-349-9 ©Springer-VerlagLondonLimited2006 MATLAB®andSimulink®areregisteredtrademarksofTheMathWorks,Inc.,3AppleHillDrive,Natick, MA01760-2098,U.S.A.http://www.mathworks.com Apartfromanyfairdealingforthepurposes ofresearchorprivatestudy,orcriticismorreview,as permittedundertheCopyright,DesignsandPatentsAct1988,thispublicationmayonlybereproduced, storedortransmitted,inanyformorbyanymeans,withthepriorpermissioninwritingofthepublishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the CopyrightLicensingAgency.Enquiriesconcerningreproductionoutsidethosetermsshouldbesentto thepublishers. Theuseofregisterednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofa specificstatement,thatsuchnamesareexemptfromtherelevantlawsandregulationsandthereforefree forgeneraluse. Thepublishermakesnorepresentation,expressorimplied,withregardtotheaccuracyoftheinformation containedinthisbookandcannotacceptanylegalresponsibilityorliabilityforanyerrorsoromissions thatmaybemade. PrintedinGermany 9 8 7 6 5 4 3 2 1 SpringerScience+BusinessMedia springer.com AdvancesinIndustrialControl SeriesEditors ProfessorMichaelJ.Grimble,ProfessorofIndustrialSystemsandDirector ProfessorMichaelA.Johnson,Professor(Emeritus)ofControlSystems andDeputyDirector IndustrialControlCentre DepartmentofElectronicandElectricalEngineering UniversityofStrathclyde GrahamHillsBuilding 50GeorgeStreet GlasgowG11QE UnitedKingdom SeriesAdvisoryBoard ProfessorE.F.Camacho EscuelaSuperiordeIngenieros UniversidaddeSevilla CaminodelosDescobrimientoss/n 41092Sevilla Spain ProfessorS.Engell LehrstuhlfürAnlagensteuerungstechnik FachbereichChemietechnik UniversitätDortmund 44221Dortmund Germany ProfessorG.Goodwin DepartmentofElectricalandComputerEngineering TheUniversityofNewcastle Callaghan NSW2308 Australia ProfessorT.J.Harris DepartmentofChemicalEngineering Queen’sUniversity Kingston,Ontario K7L3N6 Canada ProfessorT.H.Lee DepartmentofElectricalEngineering NationalUniversityofSingapore 4EngineeringDrive3 Singapore117576 ProfessorEmeritusO.P.Malik DepartmentofElectricalandComputerEngineering UniversityofCalgary 2500,UniversityDrive,NW Calgary Alberta T2N1N4 Canada ProfessorK.-F.Man ElectronicEngineeringDepartment CityUniversityofHongKong TatCheeAvenue Kowloon HongKong ProfessorG.Olsson DepartmentofIndustrialElectricalEngineeringandAutomation LundInstituteofTechnology Box118 S-22100Lund Sweden ProfessorA.Ray PennsylvaniaStateUniversity DepartmentofMechanicalEngineering 0329ReberBuilding UniversityPark PA16802 USA ProfessorD.E.Seborg ChemicalEngineering 3335EngineeringII UniversityofCaliforniaSantaBarbara SantaBarbara CA93106 USA DoctorK.K.Tan DepartmentofElectricalEngineering NationalUniversityofSingapore 4EngineeringDrive3 Singapore117576 ProfessorIkuoYamamoto KyushuUniversityGraduateSchool MarineTechnologyResearchandDevelopmentProgram MARITEC,Headquarters,JAMSTEC 2-15NatsushimaYokosuka Kanagawa237-0061 Japan To my parents Suzan and Muhammad Samir M. Abu-Khalaf To Qingwei, Anne and Jane J. Huang To Galina F. L. Lewis Series Editors’ Foreword The seriesAdvancesin IndustrialControlaimsto report and encourage technology transfer in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. New theory, new controllers, actuators, sensors, new industrial processes, computer methods, new applications, new philosophies(cid:125), new challenges. Much of this development work resides in industrial reports, feasibility study papers and the reports of advanced collaborative projects. The series offers an opportunity for researchers to present an extended exposition of such new work in all aspects of industrial control for wider and rapid dissemination. Almost all physical systems are nonlinear and the success of linear control techniques depends on the extent of the nonlinear system behaviour and the careful attention given to switching linear controllers through the range of nonlinear system operations. In many industrial and process-control applications, good engineering practice, linear control systems and classical PID control can give satisfactory performance because the process nonlinearity is mild and the control system performance specification is not particularly demanding; however, there are other industrial system applications where the requirement for high-performance control can only be achieved if nonlinear control design techniques are used. Thus, in some industrial and technological domains there is a strong justification for more applications of nonlinear methods. One prevailing difficulty with nonlinear control methods is that they are not so easily understood nor are they easy to reduce to formulaic algorithms for routine application. The abstract and often highly mathematical tools needed for nonlinear control systems design means that there is often an “education gap” between the control theorist and the industrial applications engineer; a gap that is difficult to bridge and that prevents the widespread implementation of many nonlinear control methods. The theorist/applications engineer “education gap” is only one aspect of the complex issues involved in the technology transfer of nonlinear control systems into industry. A second issue lies in the subject itself and involves the question of whether nonlinear control design methods are sufficiently mature actually to make the transfer to industry feasible and worthwhile. A look at the nonlinear control literature reveals many novel approaches being developed by the theorist but often x Series Editors’ Foreword these methods are neither tractable nor feasible nor has sufficient attention been given to the practical relevance of the techniques for industrial application. We hope through the Advances in Industrial Control series to explore these themes through suitable volumes and to try to create a corpus of monograph texts on applicable nonlinear control methods. Typically such volumes will make contributions to the range of applicable nonlinear-control-design tools, will provide reviews of industrially applicable techniques that try to unify groups of nonlinear control design methods and will provide detailed presentations of industrial applications of nonlinear control methods and system technology. This particular volume in Advances in Industrial Control by M. Abu-Khalaf, J. Huang and F.L. Lewis makes a contribution to increasing the range of applicable nonlinear control design tools. It starts from a very classical viewpoint that performance can be captured by a suitably constructed cost function and that the appropriate control law emerges from the optimisation of the cost function. The difficulty is that the solution of these optimal control problems for the class of nonlinear state-space systems selected leads to intractable equations of the Hamilton–Jacobi type. The authors then propose and develop a solution route that exploits the approximation properties of various levels of complexity within nonlinear network structures. Namely, they use neural networks and exploit their “universal function approximation property” to compute tractable solutions to the posed nonlinear H - and H -optimal-control problems. Demonstrations of the 2 (cid:146) methods devised are given for various numerical examples in Chapter 3; these include a nonlinear oscillator, a minimum-time control problem and a parabolic tracking system. Later in the volume, the nonlinear benchmark problem of a Rotational–Translational Actuator (RTAC) system is used to illustrate the power of the methods devised. An aerospace example using the control design for the F-16 aircraft normal acceleration regulator illustrates a high-performance output feedback control system application. Thus, the volume has an interesting set of applications examples to test the optimal control approximation techniques and demonstrate the performance enhancements possible. This welcome entry to the Advances in Industrial Control monograph series will be of considerable interest to the academic research community particularly those involved in developing applicable nonlinear-control-system methods. Research fellows and postgraduate students should find many items giving research inspiration or requiring further development. The industrial engineer will be able to use the volume’s examples to see what the nonlinear control laws look like and by how much levels of performance can be improved by the use of nonlinear optimal control. M.J. Grimble and M.A. Johnson Industrial Control Centre Glasgow, Scotland, U.K. Preface Modern Control Theory has revolutionized the design of control systems for aerospace systems, vehicles including automobiles and ships, industrial processes, and other highly complex systems in today’s world. Modern Control Theory was introduced during the late 1950s and 1960s. Key features of Modern Control are the use of matrices, optimality design conditions, and probabilistic methods. It allows the design of control systems with guaranteed performance for multi- input/multi-output systems through the solution of formal matrix design equations. For linear state-space systems, the design equations are quadratic in form and belong to the general class known as Riccati equations. For systems in polynomial form, the design equations belong to the class known as Diophantine equations. The availability of excellent solution techniques for the Riccati and Diophantine design equations has brought forward a revolution in the design of control systems for linear systems. Moreover, mathematical analysis techniques have been effectively used to provide guaranteed performance and closed-loop stability results for these linear system controllers. This has provided confidence in modern control systems designed for linear systems, resulting in their general acceptance in communities including aerospace, process control, military systems, and vehicle systems, where performance failures can bring catastrophic disasters. Physical systems are nonlinear. The push to extend the operating envelopes of such systems, for instance hyper-velocity and super-maneuverability performance in aerospace systems and higher data storage densities for computer hard disk drive systems, means that linear approximation techniques for controls design no longer work effectively. Therefore the design of efficient modern control systems hinges on the ability to use nonlinear system models. It is known that control systems design for general nonlinear systems can be performed by solving equations that are in the Hamilton–Jacobi (HJ) class. Unfortunately, control design for modern- day nonlinear systems is hampered because the HJ equations are impossible to solve exactly for general nonlinear systems. This book presents computationally effective and rigorous methods for solving control design equations in the HJ class for nonlinear systems. The approach taken
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