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Liu, MuhammadShahzad,XiulongLiuandKeqiuLi Design of Embedded Robust Control Systems Using ® ® MATLAB /Simulink Petko H. Petkov, Tsonyo N. Slavov and Jordan K. Kralev The Institution of Engineering and Technology PublishedbyTheInstitutionofEngineeringandTechnology,London,UnitedKingdom TheInstitutionofEngineeringandTechnologyisregisteredasaCharityinEngland& Wales(no.211014)andScotland(no.SC038698). ©TheInstitutionofEngineeringandTechnology2018 Firstpublished2018 ThispublicationiscopyrightundertheBerneConventionandtheUniversalCopyright Convention.Allrightsreserved.Apartfromanyfairdealingforthepurposesofresearch orprivatestudy,orcriticismorreview,aspermittedundertheCopyright,Designsand PatentsAct1988,thispublicationmaybereproduced,storedortransmitted,inany formorbyanymeans,onlywiththepriorpermissioninwritingofthepublishers,orin thecaseofreprographicreproductioninaccordancewiththetermsoflicencesissued bytheCopyrightLicensingAgency.Enquiriesconcerningreproductionoutsidethose termsshouldbesenttothepublisherattheundermentionedaddress: TheInstitutionofEngineeringandTechnology MichaelFaradayHouse SixHillsWay,Stevenage Herts,SG12AY,UnitedKingdom www.theiet.org Whiletheauthorsandpublisherbelievethattheinformationandguidancegiveninthis workarecorrect,allpartiesmustrelyupontheirownskillandjudgementwhenmaking useofthem.Neithertheauthorsnorpublisherassumesanyliabilitytoanyoneforany lossordamagecausedbyanyerrororomissioninthework,whethersuchanerroror omissionistheresultofnegligenceoranyothercause.Anyandallsuchliability isdisclaimed. 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BritishLibraryCataloguinginPublicationData AcataloguerecordforthisproductisavailablefromtheBritishLibrary ISBN978-1-78561-330-2(hardback) ISBN978-1-78561-331-9(PDF) TypesetinIndiabyMPSLimited PrintedintheUKbyCPIGroup(UK)Ltd,Croydon Toourteachersandstudents This page intentionally left blank Contents Preface xiii 1 Embeddedcontrolsystems 1 1.1 Introduction 1 1.2 Structureandelementsofembeddedcontrolsystems 2 1.2.1 Typicalblockdiagram 2 1.2.2 A/DandD/Aconversion 4 1.2.3 Sensors 5 1.2.4 Actuators 6 1.2.5 Processors 7 1.2.6 Software 8 1.3 Samplingandaliasing 10 1.4 Fixed-pointarithmetic 12 1.4.1 Fixed-pointnumbers 12 1.4.2 Scaling 15 1.4.3 Rangeandprecision 18 1.4.4 Fixed-pointarithmeticoperations 19 1.5 Floating-pointarithmetic 22 1.5.1 Floating-pointnumbers 22 1.5.2 IEEEarithmetic 23 1.5.3 Floating-pointarithmeticoperations 25 1.6 Quantizationeffects 25 1.6.1 Truncationandroundoff 25 1.6.2 QuantizationerrorsinA/Dconversion 28 1.7 Designstages 29 1.7.1 Controllerdesign 32 1.7.2 Closed-loopsystemsimulation 34 1.7.3 Embeddedcodegeneration 36 1.8 Hardwareconfiguration 36 1.8.1 Microprocessingarchitectures 37 1.8.2 Hardwaredescriptionlanguage 41 1.8.3 Moduleleveldevelopment 44 1.8.4 Systemleveldevelopment 48 1.9 Softwareconfiguration 54 1.9.1 Boardsupportpackage 54 1.9.2 Applicationprograminginterface 56 viii DesignofembeddedrobustcontrolsystemsusingMATLAB®/Simulink® 1.9.3 Codegeneration 56 1.9.4 Codevalidation 60 1.10 Notesandreferences 61 2 Systemmodeling 63 2.1 Plantmodeling 63 2.2 Linearization 66 2.2.1 Analyticlinearization 66 2.2.2 Symboliclinearization 68 2.2.3 Numericlinearization 71 2.3 Discretization 71 2.3.1 Discrete-timemodels 73 2.3.2 Discrete-timefrequencyresponses 74 2.3.3 Discretizationofcontinuous-timemodels 76 2.3.4 Discretizationoftimedelaysystems 80 2.3.5 Choiceofthesamplingperiod 81 2.3.6 Discretizationofnonlinearmodels 82 2.4 Stochasticmodeling 84 2.4.1 Stochasticlinearsystems 84 2.4.2 Discretizationofstochasticmodels 86 2.4.3 Optimalestimation 88 2.5 Plantidentification 91 2.5.1 Identificationofblackboxmodel 92 2.5.2 Identificationofgray-boxmodel 102 2.6 Uncertaintymodeling 111 2.6.1 Structureduncertaintymodels 111 2.6.2 RepresentinguncertainmodelsbyLFT 117 2.6.3 Derivinguncertainstate-spacemodelsfrom Simulink®models 119 2.6.4 Unstructureduncertaintymodels 120 2.6.5 Mixeduncertaintymodels 124 2.6.6 Discretizationofuncertainmodels 125 2.6.7 Derivinguncertaintymodelsbyidentification 128 2.7 Sensormodeling 131 2.7.1 Allanvariance 132 2.7.2 Stochasticgyromodel 133 2.7.3 Stochasticaccelerometermodel 138 2.7.4 Sensordatafiltering 142 2.8 Notesandreferences 145 3 Performancerequirementsanddesignlimitations 147 3.1 SISOclosed-loopsystems 147 3.2 PerformancespecificationsofSISOsystems 151 3.2.1 Time-domainspecifications 151 3.2.2 Frequency-domainspecifications 152 Contents ix 3.3 Trade-offsinthedesignofSISOsystems 155 3.3.1 LimitationsonS andT 155 3.3.2 Righthalf-planepolesandzeros 156 3.3.3 Limitationsimposedbytimedelays 158 3.3.4 Limitationsimposedbymeasurementnoise 159 3.3.5 Limitations,imposedbydisturbances 160 3.3.6 Limitationsoncontrolaction 160 3.3.7 Limitationsduetomodelerrors 161 3.4 MIMOclosed-loopsystems 168 3.5 PerformancespecificationsofMIMOsystems 171 3.5.1 Usingsingularvaluesforperformanceanalysis 171 3.5.2 H∞Normofasystem 174 3.5.3 Hankelnorm 176 3.6 Trade-offsinthedesignofMIMOsystems 176 3.6.1 Disturbancerejection 177 3.6.2 Noisesuppression 178 3.6.3 Modelerrors 178 3.7 Uncertainsystems 180 3.8 Robust-stabilityanalysis 182 3.8.1 Unstructureduncertainty 183 3.8.2 Structuredsingularvalue 183 3.8.3 Robust-stabilityanalysiswithμ 185 3.9 Robustperformanceanalysis 188 3.9.1 Usingμforrobustperformanceanalysis 189 3.9.2 Worstcasegain 194 3.9.3 Worstcasemargin 196 3.10 Numericalissuesinrobustnessanalysis 197 3.11 Notesandreferences 201 4 Controllerdesign 203 4.1 PIDcontroller 204 4.2 LQGcontrollerwithintegralaction 219 4.2.1 Discrete-timeLQGcontroller 220 4.2.2 Coloredmeasurementnoise 223 4.2.3 LQGcontrollerwithbiascompensation 233 4.3 LQregulatorwithH∞filter 240 4.3.1 Discrete-timeH∞filter 241 4.3.2 H∞Filterwithbiascompensation 247 4.4 H∞Design 252 4.4.1 TheH∞designproblem 252 4.4.2 Mixed-sensitivityH∞control 258 4.4.3 Twodegrees-of-freedomcontrollers 261 4.4.4 NumericalissuesinH∞design 263 4.5 μSynthesis 272 4.5.1 Theμsynthesisproblem 273