Multi-Stage and Multi-Time Scale Feedback Control of Linear Systems with Applications to Fuel Cells

220 Pages·2019·3.694 MB·English

by  Verica Radisavljević-Gajić, Miloš Milanović, Patrick Rose

Mechanical Engineering Series
Verica Radisavljević-Gajić
Miloš Milanović
Patrick Rose
Multi-Stage and Multi-
Time Scale Feedback
Control of Linear Systems
with Applications to Fuel
Cells
Mechanical Engineering Series
SeriesEditor
FrancisA.Kulacki
DepartmentofMechanicalEngineering,UniversityofMinnesota,
Minneapolis,MN,USA
The Mechanical Engineering Series presents advanced level treatment of topics on
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ć ć (cid:129) š ć (cid:129)
Verica Radisavljevi -Gaji Milo Milanovi
Patrick Rose
Multi-Stage and Multi-Time
Scale Feedback Control of
Linear Systems with
Applications to Fuel Cells
VericaRadisavljević-Gajić MilošMilanović
DepartmentofMechanicalEngineering DepartmentofMechanicalEngineering
VillanovaUniversity VillanovaUniversity
Villanova,PA,USA Villanova,PA,USA
PatrickRose
DepartmentofMechanicalEngineering
VillanovaUniversity
Villanova,PA,USA
ISSN0941-5122 ISSN2192-063X (electronic)
MechanicalEngineeringSeries
ISBN978-3-030-10388-0 ISBN978-3-030-10389-7 (eBook)
https://doi.org/10.1007/978-3-030-10389-7
LibraryofCongressControlNumber:2018966525
©SpringerNatureSwitzerlandAG2019
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“I dedicate this book to my parents
Ljiljana and Miroljub Radisavljević
for their unconditional love and support”
Dr. Verica Radisavljević-Gajić
“To my dear family and Saša,
for endless support and lifelong inspiration”
Miloš Milanović
“To my friends and family
for their endless support and confidence
in me”
Patrick Rose
Preface
This monograph is intended for researchers and practitioners in control systems
interestedin complex, time-invariant, lineardynamicsystems composedofseveral
subsystems and/or large-scale linear, time-invariant, dynamic systems operating in
several time scales. It can be used by engineering graduate students majoring in
control systems and automation, practicing control engineers, as well as all engi-
neering,appliedmathematics,economics,andcomputersciencefacultyinterestedin
controlofdynamicsystems.Duetonumerousapplicationsofthederivedfeedback
controllerdesignalgorithmspresentedinthisbooktofuelcells(cleanelectricenergy
sources), particularly to proton-exchange membrane (PEM) fuel cells, the book is
also of interest for the fuel cell community researchers, graduate students, and
practitioners.Oneofthemostimportantfeaturesofthepresenteddesignmethodol-
ogyisthatdifferenttypesoflinearfeedbackcontrollerscanbedesignedfordifferent
subsystemsand/orindifferenttimescalesofacomplexlineardynamicsystem.
Thisresearch monographpresents completelythetwo-stage feedback controller
design algorithms in both continuous- and discrete-time domains including all
design formulas and algebraic equations for general linear time-invariant dynamic
systems.Theresultspresentedarespecializedandsimplifiedforthetwo-timescale
linear time-invariant dynamic systems (singularly perturbed systems). The
correspondingpresentation iscompletelydonealsoforthe three-stagecontinuous-
timefeedbackcontrollerdesignsforgenerallineartime-invariantdynamicsystems.
Extensions of three-stage feedback controllers to linear dynamic time-invariant
continuous- anddiscrete-time systemsoperating inthethree-time scales havebeen
doneonlyinthecontinuous-time.Thediscrete-timethree-timescalesystemsremain
an open research area for the three-stage design of linear feedback controllers,
mostly due to unsettled issues about the formulations of the three-time scale linear
dynamicsystems.Thefour-stagelinearfeedbackcontrollerdesignispresentedonly
forgeneralclassoflinear,time-invariant,continuous-timedynamicsystems.Howto
extend those results or,more precisely, howtosolve theobtaineddesign algebraic
equations for the four-time scale, time-invariant, continuous-time, linear dynamic
vii
viii Preface
systems is discussed. Hence, the four-stage four-time scale feedback controller
designisleftasanopenfuturechallengingresearcharea.
The designs of linear-quadratic optimal controllers and eigenvalue assignment
(“pole placement”) feedback controllers are fully covered in this research mono-
graph. The book provides opportunities for future research ofother types ofmulti-
stage linear feedback controllers for general and multi-time scale linear dynamic
systems, including observer-based and Kalman filter-based deterministic and sto-
chasticcontrollers.Duetothefactthatdifferenttypesoflinearfeedbackcontrollers
canbedesigned(partialcontrollers)fordifferent subsystemsofalarge-scalelinear
dynamicsystemand/orsystemoperatingindifferenttimescales,producingthedual
resultsforobserversandtheKalmanfilter,itwillbepossible,forexample,todesign
partially optimal Kalman filter and new classes of reduced-order observers. Exten-
sions to other types of existing linear feedback controllers and filters are possible,
includingthedesignofnewhybridlineardynamicfeedbackcontrollersandfilters.
Villanova,PA,USA VericaRadisavljević-Gajić
Villanova,PA,USA MilošMilanović
Villanova,PA,USA PatrickRose
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 GeneralRemarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2 ApplicationstoOtherClassesofDynamicSystems. . . . . . . . . . . 6
1.3 ImprovedSystemRobustness,Reliability,andSecurity. . . . . . . . 7
1.4 BookOrganization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Notes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Continuous-TimeTwo-StageFeedbackControllerDesign. . . . . . . . 11
2.1 Two-StageDesignofLinearFeedbackControllers. . . . . . . . . . . 11
2.2 Two-StageFeedbackDesignforSystemswithSlowandFast
Modes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Two-StageControlofaHydrogenGasReformerSlow-Fast
Dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1 HydrogenGasReformerOperationandModeling. . . . . . 21
2.3.2 EigenvalueAssignmentfortheHydrogenGas
Reformer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.3 OptimalSlowandEigenvalueAssignedFast
Subsystems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4 Two-StageFeedbackControlofaTwo-Time-ScalePEM
FuelCell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4.1 PEMFuelCellDynamicsMathematicalModel. . . . . . . . 30
2.4.2 Two-Time-ScaleStructureofthePEMFuelCell. . . . . . . 33
2.4.3 PEMFuelCellSlow-FastTwo-StageController
DesignSimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.5 PEMFuelCellObserverDesign. . . . . . . . . . . . . . . . . . . . . . . . 42
2.6 Notes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3 Discrete-TimeTwo-StageFeedbackControllerDesign. . . . . . . . . . 47
3.1 Discrete-TimeTwo-StageFeedbackControllerDesign. . . . . . . . 47
3.2 Slow-FastDesignforSystemsDefinedintheSlowTimeScale. . 51
3.2.1 Example:APowerSystem. . . . . . . . . . . . . . . . . . . . . . . 56
ix
x Contents
3.3 Slow-FastDesignforSystemsDefinedintheFastTimeScale. . . 59
3.3.1 Example:ASteamPowerSystem. . . . . . . . . . . . . . . . . . 63
3.4 Notes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4 Three-StageContinuous-TimeFeedbackControllerDesign. . . . . . 71
4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.2 Three-StageDesignofContinuous-TimeFeedback
Controllers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.3 Three-StageThree-TimeScaleLinearControlSystems. . . . . . . . 81
4.4 ApplicationtoaProtonExchangeMembraneFuelCell. . . . . . . . 90
4.5 Notes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5 Three-StageDiscrete-TimeFeedbackControllerDesign. . . . . . . . . 97
5.1 Three-StageDiscrete-TimeLinearFeedbackControllers. . . . . . . 98
5.2 Three-StageThree-TimeScaleDiscreteLinearControl
Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.3 FutureResearchTopics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6 Four-StageContinuous-TimeFeedbackControllerDesign. . . . . . . 109
6.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2 Four-StageDesignofContinuous-TimeFeedbackControllers. . . 111
6.3 Four-StageFour-TimeScaleLinearControlSystems. . . . . . . . . . 123
6.4 FutureResearchTopics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7 ModelingandSystemAnalysisofPEMFuelCells. . . . . . . . . . . . . . 129
7.1 Third-OrderLinearModelofaPEMFuelCell. . . . . . . . . . . . . . 132
7.1.1 ControllabilityoftheLinearPEMFuelCellModel. . . . . 133
7.1.2 SystemAnalysisandConstraintsofthePEMFCModel. . 135
7.2 Third-OrderBilinearPEMFuelCellModel. . . . . . . . . . . . . . . . 138
7.2.1 Steady-StatePEMFuelCellEquilibriumPoints. . . . . . . . 140
7.2.2 FuelCellSystemStabilityAnalysis. . . . . . . . . . . . . . . . . 142
7.2.3 PEMFuelCellControllabilityandObservability
Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
7.2.4 SimulationResults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
7.3 GreenlightInnovationG60StationwithTP50PEMFC. . . . . . . . 150
7.3.1 TP50PEMFCModeling. . . . . . . . . . . . . . . . . . . . . . . . . 153
7.3.2 SimulationResults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
7.4 AFifth-OrderNonlinearPEMFCModel. . .. . . .. . . .. . .. . . .. 161
7.5 Eight-OrderMathematicalModelofaPEMFCUsed
inElectricCars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.6 Notes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
8 ControlofaHydrogenGasProcessingSystem. . . . . . . . . . . . . . . . 167
8.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
8.2 Full-andReduced-OrderObserverandOptimalControllers. . . . 172
8.2.1 Full-OrderObserverDesign. . . . . . . . . . . . . . . . . . . . . . 173
8.2.2 Reduced-OrderObserverDesign. . . . . . . . . . . . . . . . . . . 174