LECTUREFIVE-5State-space modeling and control of ship propulsion1LEARNINGOBJECTIVES:To understand the use of neural nets toward developing marinepropulsion engine state-space modelsTo develop state-space marine propulsion models for control·usingnumerical simulationresults andneural nets:To decompose marine propulsion state-spacemodels and signals.To design supervisory setpoint control filters for elimination ofproblemsduringfastengineloadchangesTodesign full statefeedback controllersofmarine propulsionenginesfordisturbance rejection usingpoleplacementand robustcontrolconcepts21
1 LECTURE FIVE – 5 State-space modeling and control of ship propulsion 1 LEARNING OBJECTIVES • To understand the use of neural nets toward developing marine propulsion engine state-space models • To develop state-space marine propulsion models for control using numerical simulation results and neural nets • To decompose marine propulsion state-space models and signals • To design supervisory setpoint control filters for elimination of problems during fast engine load changes • To design full state feedback controllers of marine propulsion engines for disturbance rejection using pole placement and robust control concepts 2
Neural nets as approximators of engine andturbocharger torque mapsNik.Xiros-MARINEDIESELENGINETHERMODYNAMICS中CONCLUSIONS.Enginetorquedevelopmentdemonstratessignificantandvariable delays due to turbocharging dynamics· Marine powerplant dynamics are highly nonlinear due tothe thermal power and torque delivery processes·Propeller law loading guarantees open-loop stability of theplantENGINE&TURBOCHARGERTORQUEMAPSSolutionofthethermodynamicmodel'salgebraic part for triad value gridX=(Ne,NTc,FR)2
2 Neural nets as approximators of engine and turbocharger torque maps Nik. Xiros 3 CONCLUSIONS • Engine torque development demonstrates significant and variable delays due to turbocharging dynamics • Marine powerplant dynamics are highly nonlinear due to the thermal power and torque delivery processes • Propeller law loading guarantees open-loop stability of the plant X = ( , , ) N N F E TC R Solution of the thermodynamic model’s algebraic part for triad value grid ENGINE & TURBOCHARGER TORQUE MAPS 4 MARINE DIESEL ENGINE THERMODYNAMICS
NEURALTORQUEAPPROXIMATORSActivationfunction@Φ(x)=1/(l+e-")=e"/(1+e*)2feed-forward neural torqueapproximatorsEnginetorqueapproximatorQe(Ng,NTec.FR)=QEmar.(w(We.Ng+WreNre+W. F,+W.)+Wo)i=lTurbochargertorqueapproximatorQrc(Ne,Nrc,Fr)=Qrmax:(Zv,.O(Ve,Ng+Ve.Nre+VR.,-Fr+Vb.)+Vo)+Qcmaxi=lNEURALTORQUEAPPROXIMATORSMANB&W6L60MarineEngine-9,177kW@114.6rpmNeuralTorqueApproximatorsWeightsWWWreW.W.-Engine Torque2.13190.07150.00375.19571.57981231Approximator0.17366.65960.12960.00148.7201-4.23170.01670.00010.30450.185545Qm=900kNm-0.29690.11920.001814.363010.2347-1.08800.06220.00108.9268-8.0251Woo=4.272360.00980.0001-7.03620.70850.47977-0.22030.16640.091312.6202-13.7209[TurbochargerVAAVNTorque3.25140.02720.00030.2592-9.03491Approximator2-1.95190.0233-0.0001-1.53994.5981Qtmx=3000Nm3:0.06720.02560.99170.0008-6.24380.03520.000243.72741.4856-9.8138Qcn=-2000Nm567-3.79180.0218-0.00001.4235-4.9183Voo=1.55990.49510.01710.0003-1.10224.71280.6192-0.0059-0.00044.22281.642063
3 Engine torque approximator Activation function 2 feed-forward neural torque approximators Emax 7 , , , , 00 1 ( , , ) Q { Φ( ) } E E TC R i E i E TC i TC R i R b i i Q N N F W W N W N W F W W = = ⋅ ∑ ⋅ ⋅ + ⋅ + ⋅ + + Tmax 7 , , , , 00 Cmax 1 ( , , ) Q { Φ( ) } Q TC E TC R i E i E TC i TC R i R b i i Q N N F V V N V N V F V V = = ⋅ ∑ ⋅ ⋅ + ⋅ + ⋅ + + + Turbocharger torque approximator ( ) 1/ (1 e ) e / (1 e ) x x x Φ x − = + = + 5 NEURAL TORQUE APPROXIMATORS MAN B&W 6L60 Marine Engine – 9,177kW @ 114.6rpm Neural Torque Approximators Weights NEURAL TORQUE APPROXIMATORS 6
NEURALTORQUEAPPROXIMATORSMANB&W6L60MarineEngine-9,177kW@114.6rpmTraining and Propeller-curvesteady-state point validationP, (%)N,NrEng. Torq.T/C Torg.2700Approx.Approx,Min3012014000103103Max100Learn.rateStep5fo5007.5x1053.0x10-6MSEachvdEngine loadEngine torque ez(kNm)Tubocharger torqueCre (Nm)(%)ThermoNeuralErrorThermoNeuralError450.600450.02780.57223.55042.64910.90136065489.8090.47388.61397.31381.3001489.335470529.061528.66060.400910.51169.05471.456975568.442568.07990.36289.87079.24720.623580607.73860735530.382611.302311.29840.003985647.119646.86050.25870.15370.01460.139190686.586686.22470.36164.65043.93710.713395726.053725.78650.2669-6.1997-7.66911.4694100765.5200.55022.5965764.97046.24893.6524NEURALTOROUEAPPROXIMATORSMANB&W6L60MarineEngine-9,177kW@114.6rpmTransienttorquemapvalidationRPM=110200000%index=90ant20200F086000200RPM=115t200Sooormnl馆:%index=9000.OL400Nieus6120001400Ceo4
4 MAN B&W 6L60 Marine Engine – 9,177kW @ 114.6rpm Training and Propeller-curve steady-state point validation NEURAL TORQUE APPROXIMATORS 7 MAN B&W 6L60 Marine Engine – 9,177kW @ 114.6rpm Transient torque map validation 6000 8000 10000 12000 14000 TC rpm -800 -600 -400 -200 0 200 400 TC Balance Torque (Nm) -24 -16 -8 0 8 16 24 Approximation Error (Nm) 6000 8000 10000 12000 14000 TC rpm 0 200 400 600 800 Engine Torque (kNm) -32 -16 0 16 32 Approximation Error (kNm) Thermo Neural Error Thermo Neural Error RPM = 115 %index = 90 6000 8000 10000 12000 TC rpm -600 -400 -200 0 200 400 TC Balance Torque (Nm) -16 -8 0 8 16 24 Approximation Error (Nm) 6000 8000 10000 12000 TC rpm 0 200 400 600 800 Engine Torque (kNm) -32 -16 0 16 32 Approximation Error (kNm) Thermo Neural Error Thermo Neural Error RPM = 110 %index = 90 0 ( ) ( ) E L E Q Q N t N t J J ∆ − = = + ( ) T C TC TC Q Q N t J + = NEURAL TORQUE APPROXIMATORS 8
SIMULATIONRESULTSTransientStepResponsebybothmodels-35to100%loadSIMULATIONRESULTSResponseofNeuralState-spacemodelvs.Thermodynamicone-
5 SIMULATION RESULTS Transient Step Response by both models – 35 to 100% load 0 20 40 60 80 50 60 70 80 90 100 110 120 Time (sec) Engine speed (rpm) Neural Thermo 0 20 40 60 80 2 4 6 8 10 12 14 Time (sec) Turbo speed (1000rpm) 0 20 40 60 80 -400 -200 0 200 400 600 800 Time (sec) Engine torque (kNm) 0 20 40 60 80 -100 0 100 200 300 400 500 Time (sec) Turbocharger torque (Nm) 9 SIMULATION RESULTS Response of Neural State-space model vs. Thermodynamic one 0 20 40 60 80 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Time (sec) Shaft speed (rpm) 0 20 40 60 80 0 20 40 60 80 100 120 Time (sec) Turbo speed (rpm) 0 20 40 60 80 -20 -10 0 10 20 30 40 Time (sec) Engine Torque (kNm) 0 20 40 60 80 -20 -10 0 10 20 30 Time (sec) Turbocharger Torque (Nm) 10
UNCERTAINTYANALYSISSignaldecompositionschemeN=N+n,Nre=Nrco+nc.F,=Fro+frEngine&turbochargertorque linearapproximationQ=Qeo+[ge] qe.][n nte+e.o frQre=Qrco+[qre qrc.2][n nic]'+qrc.of,aQ(N,NeF)=Qmatqe=ON=N,@'(We.-N+Wrc.Nreo+Wr.Fro+W.)ZwWe.exp(We.-N。+Wre.Nrco +W.-Fro +W.)i=lqe,=qeo,+4qqrc;=rco, +4qrc.i1/DISTURBANCEANALYSISSignal decomposition schemeN=N+n, Nrc=Nreo+nc,Fr=Fro+frLoad torque &shaft inertia signalprocessingQ,(t) = Koo-N +2KgoN。-n(t)+Ng-ke(t) =QLo+2KooN-n(t)+N-ko(t)d,(t)=-N-kg(t)/I(t)(I-N)=N.2(4I)+1-N=didtN.(4I)+1, N, +41 N +1.i=dtI-N,+I-n+I.d.de()=-4()-N()+ N()(4(0)1()12at6
6 UNCERTAINTY ANALYSIS Signal decomposition scheme Engine & turbocharger torque linear approximation 0 0 0 , , N N n N N n F F f = + = + = + TC TC TC R R R [ ] [ ] 0 ,1 ,2 ,0 0 ,1 ,2 ,0 T E E E E TC E R T TC TC TC TC TC TC R Q Q q q n n q f Q Q q q n n q f ≈ + ⋅ + ⋅ ≈ + ⋅ + ⋅ 0 ,1 Emax 2 7 , 0 , 0 , 0 , , 1 , 0 , 0 , 0 , ( , , ) Q ( ) exp( ) E E TC R N N E i TC i TC R i R b i i E i i E i TC i TC R i R b i q Q N N F N W N W N W F W WW W N W N W F W Φ = = ∂ = = ⋅ ∂ ⋅ + ⋅ + ⋅ + ⋅ ⋅ + ⋅ + ⋅ + ∑ , 0, , , 0, , , E i E i E i TC i TC i TC i q q q q q q = + = + ∆ ∆ 11 DISTURBANCE ANALYSIS Signal decomposition scheme Load torque & shaft inertia signal processing 0 0 0 , , N N n N N n F F f = + = + = + TC TC TC R R R 2 2 0 0 0 0 0 2 0 0 0 0 ( ) 2 ( ) ( ) 2 ( ) ( ) L Q Q Q L Q Q Q t K N K N n t N k t Q K N n t N k t ≈ ⋅ + ⋅ + ⋅ = + ⋅ + ⋅ 2 ss 0 ( ) ( ) / ( ) Q d t N k t I t = − ⋅ ( ) tr 0 ( ) ( ) ( ) ( ) ( ) / ( ) d d t I t N t N t I t I t dt ∆ ∆ = − ⋅ + ⋅ ( ) ( ) ( ) 0 0 0 0 0 tr d d I N N I I N dt dt d N I I N I N I n dt I N I n I d ∆ ∆ ∆ ⋅ = ⋅ + ⋅ = ⋅ + ⋅ + ⋅ + ⋅ = ⋅ + ⋅ + ⋅ 12
POWER-PLANTMODELDECOMPOSITIONSignaldecompositionschemeN=N。+n,Nre=Nrco+ntcF,=Fro+frNominalNonlinearModel (N2M)N=[Qg(No,Nrco-FRo)Ko-N]/loNTco=Qre(Neo,NTco,Fro)/ ITcUncertain Perturbation Model (UPM)[(qe1 -2KcoN。)/1qe2/1qre.//rcqrc2/11o9r.0/11.[/, [18]1013HierarchicalshippropulsioncontrolNik. Xiros147
7 POWER-PLANT MODEL DECOMPOSITION Signal decomposition scheme 0 0 0 , , N N n N N n F F f = + = + = + TC TC TC R R R Nominal Nonlinear Model (N2M) Uncertain Perturbation Model (UPM) 2 0 0 0 0 0 0 0 0 0 0 0 [ ( , , ) ] / ( , , ) / E E TC R Q TC TC E TC R TC N Q N N F K N I N Q N N F I = − ⋅ = ( ,1 0 0 ,2 ) ,1 ,2 ,0 1 ,0 2 0 E Q E TC TC TC TC TC TC E R TC TC n n q K N I q I n n q I q I q I d f q I − = ⋅ + ⋅ + 13 Hierarchical ship propulsion control Nik. Xiros 14
MARINEPROPULSIONCONTROLTHEPROBLEM:100Near-MCRengine-propeller matchingunderactual,transient operatingconditions区ioaurtmLow-iod running10050Engine revolutions (%)1HIERARCHICALSHIPPROPULSIONCONTROLSupervisorySetpointControlRegulatoryFeedbackControlMarinePropuisionPOWERLEVELPowerplant(%MCR)FRoNn-N.NreoPsETKTrSUPERVISORYCEERALCONTROLLERCONTROLLERTurbommifeeobacShatrpmfeedbaca168
8 MARINE PROPULSION CONTROL THE PROBLEM: Near-MCR enginepropeller matching under actual, transient operating conditions 15 HIERARCHICAL SHIP PROPULSION CONTROL - Supervisory Setpoint Control - Regulatory Feedback Control 16
HIERARCHCALSHPPROPULSIONCONTROLSupervisoryControllerStructureFROFuel indexoffset valueOPERATING以01sSETPOINTQEN.NTC.FR)NO(%MCR)Shafting system Engine-propellerEngine rpmPset%shaftsetpointnominal inertiaEngine Torque2KQOVectorXPropellerNominal propellerLawtorque coefficientLov+pass3Ie1sNTCOQTC(N,NTC,FR)TurbochargerTurboshaftTurbochargerrpmsetpointTurbochargerinertiaTorque17NONLINEARSTATE-SPACEMODEL一N2Mequations:Og(N,NTco, Fro)-Ko-N)N. =1oNrco = Src(No, Nrco, Fao)Irc-UPMequations:qeI-2KoN.E.0qE.2N?-ko +N。-4I111n+1Arc!qrc2qrc.o[nrc]e0IcIrcIrc189
9 HIERARCHICAL SHIP PROPULSION CONTROL Supervisory Controller Structure 17 NONLINEAR STATE-SPACE MODEL Ν2Μ equations: 2 0 0 0 0 0 0 0 0 0 0 0 ( , , ) ( , , ) E TC R Q TC TC R TC TC Q N N F K N N I Q N N F N I − ⋅ = = UPΜ equations: ,1 0 0 ,2 ,0 2 0 0 ,1 ,2 ,0 2 0 E Q E E Q R TC TC TC TC TC TC TC TC q K N q q N k N I n n I I I f I n n q q q I I I ∆ − ⋅ + ⋅ − = ⋅ + ⋅ + 18
Supervisory setpoint control of marine enginesNik.Xiros19HIERARCHICALSHIPPROPULSIONCONTROLSupervisoryControllerStructureFROFuel indexoffset valueOPERATING节真1/sQE(NNTCFR)NOSETPOINT(%MCR)Shating system Engine-propellererapermshaftPset%nominal ine rtiaEngine Torque中KQOVectorxPropellerNominal propellerIs+1Lawtorque coefficientLow-passsetpointfiterusQTC(N,NTC,FR)1VITC+NTCOTurboshaftTurbochargerTurbochargerrpmsetpointTurbo chargerinertiaTorque2010
10 Supervisory setpoint control of marine engines Nik. Xiros 19 HIERARCHICAL SHIP PROPULSION CONTROL Supervisory Controller Structure 20