Energy Management Strategy for a Parallel Hybrid Electric Truck

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Proceedings of the American Control ConferenceArlington, VA J u n e 25-27 2001Energy Management Strategy for a Parallel Hybrid Electric Truck

Chan-ChiaoLin , Jun-Mo Kang , J.W. Grizzle2,and H u e i Peng'Dept. of Mechanical Engineering, University of Michigan, MI [email protected] ,[email protected]

'Dept. of Electrical Engineering and Compu ter Science, Universityof Michigan, MI [email protected] ,[email protected]

AbstractDue to the complex nature of hybrid electric vehicles, controlstrategies based on engineering intuition frequently fail to achievesatisfactory overall system efficiency. This paper presents aprocedure for improving the energy management strategy for aparallel hybrid electric truck on the basis of dynamic optimizationover a given drive cycle. Dynamic Programming techniques areutilized to determine the optimal control actions for a hybridpowertrain in order to minimize fuel consumption. By carefullyanalyzing the resulting optimal policy, new rules can beascertained to improve the basic control strategy. The resultingnew control strategy is shown to achieve better fuel economythrough simulations on a d etailed vehicle model.

1. IntroductionWith the growing demand from the world community to reducethe emission of carbon dioxide, and after a decade of intenseresearch, hybrid electric vehicles HEW) suddenly appear moreviable and necessary than ever before. These vehicles eitherreduce or eliminate the reliance on fossil fuels. Owing to their dualon-board power sou rces and regen erative braking, HEVs offerunprecedented possibilities to pursue higher fuel economy,particularly if a parallel HEV con figuratio n is employed. Torealize fuel economy benefits, the power management function ofthese advanced vehicles must be carefully designed. By powermanagement, we mean the dev elopment of a higher-level controlalgorithm that determines the total amount of energy to begenerated, and its split between the two power sources.Most of the control strategies developed for parallel HEVs can beclassified into three categories. The first type employs intelligentcontro l techniques such as ruledfuzzy log&iNN for estimation andcontrol algorithm development ([1],[2]). The second approach isbased on static optimization methods. Generally speaking, electricenergy is translated into an equivalent amount of fuel to calculatethe energy cost [3],[4]). The optimization scheme then figures outproper energy and or power split between the two energy so urcesunder steady-state operation. Because of its relatively simplepoint-wise optimization nature, it is possible to extend suchoptimization schemes to solve the simultaneous fuel economy andemission optim ization problem [ 5 ] . Th e basic idea of the third typeof HEV control algorithm takes into a ccou nt the dynamic nature ofthe system when performing the optimization ([6],[7]).Furthermore, the optimiz ation is with respect to a time horizo n,rather than for a fixed point in time. In general, a power splitalgorithm resulting from dynamic optimization will be moreaccurate under transient conditions.In this paper, we apply dynamic programming to solve theminimum fuel optimal control problem for a hybrid electric truck.A dynamic optimal solution to the energy management problem

over a driving cycle is developed. The resulting feedback lawsfrom the dynamic programming algorithms are not implementabledue to their preview nature and heavy comp utational requirement.They are, on the other hand, a good design tool and a benchmarkagainst which a basic control strategy can be compared andimproved. We then study the behavior of the dynamic pro-gramming solution carefully, and extract simple, implementablerules. These rules are then used to augment a simple, intuition-based control algorithm . It was found that the performance of theintuition (rule) based algorithm can be enhanced significantlythrough this design procedure.The paper is organized as follows: In Section 2, the configurationof the hybrid electric truck is briefly described, followed by thedescription of the preliminary rule-based control strategy. Next,dynamic programming is introduced and the optimization resultfor minimum fuel consumption is given in Section 3. Section 4discusses how to design a better rule-based strategy using theresults of the dynamic programming algorithm. Conclusions arepresented in Section 5.

2. Hybrid-Electric Vehicle System (HEVESIM)2.1 System ConfigurationThe baseline vehicle studied here is the International 4700 seriestruck, a 4x2 Class VI diesel truck produced by Navistar. Theoriginal diesel engine was do wnsized Erom the V8 (7.3L) to a V6(5.5L) nd a 49 KW electric motor has been selected as the secondpower source. The vehicle system in this study is configured as aparallel hybrid with the electric motor positioned after thetransmission. A schematic of the vehicle and the propulsionsystem is given in Figure 1 The engine is connected to thetorque converter (TC), whose output shaft is then coupled to thetransmission (Trns). The transmission and the electric motor canbe linked to the propeller shaft PS), differential D) nd twodriveshafts DS), coupling the differential with the driven wheels.Basic vehicle specifications are given in the A ppendix.

Engine

Figure 1: Schematic diagram of th e hybrid electric truck

0-7803-6495-3/011$10.000 2001 AACC
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Our Hybrid Vehicle-Engine SIMulation (HE-VESIM) model isbased on the high-fidelity c onve ntiona l vehicle simula tor VESIMpreviously developed at the University of Michigan [8]. VESIMhas been validated against measurements for a Clas s VI truck, andproven to be a very versatile tool for mobility, fuel economy anddrivability studies. To construct a hybrid-vehicle simulator, someof the main modules required modifications, e.g. reduction of theengine sizdpower, and the integration of electric componentmodels into the system. The model is implemented in theMATLAEVSIMULINK software environment, as presented inFigure 2. Since the detailed vehicldchassis models have beenpresented in ([8],[9]), they are not reviewed here.

Figure 2: Hybrid-electric vehicle Simulation in SIMUL INK2.2 Rule Based Control StrategyThe final HEV con troller that will be implemented will berule-based. The energy management strategy will only usecurrent and past vehicle state s and driver commands to calc ulate aproper (hopefully, close to optimal) con trol signal. The rule-basedenergy management strategy used as a starting point here wasdeveloped on the basis of engin eering intuition and simp leanalysis of componen t efficiency tabledcharts [9,10]. The designprocess starts from interpretin g the driver pedal signal as a powerrequest, . According to the power request, the operation ofthis controller is divide d into three control modes: Braking Contro l,Power Split Control or Recharging Con trol. If the power request isnegative, Braking Contro l will be applie d to deceler ate he vehicle.If the power request is positive, either Power Split Control orRecharging Control will be applied according to acharge-sustaining policy. The charge-sustaining strategy assure sthat the battery state of charge SOC) stays within preset lowerand upper bounds. A 5 6 0 % SOC range is chosen for efficientbattery operation as well as to prevent battery depletion or damagein an extreme situation. In a normal propulsive driving condition,the Power Split Control determ ines the power flow in the hy bridpowertrain. Whenever the SOC drops below the lower limit( 5 5 ) , the contro ller will switch to th e Recharging Control modeuntil the SOC reaches the upper limit (60 ), and then Power SplitControl will resume. The basic logic of each control mode isbriefly described in the following.

Power Split Control: Based on the engine efficiency mapshown in Figure 3, a pre-selected engine on power line,e-ofland motor assist power line, Pm- are chosen to avoid engineoperation in inefficient areas. If the total power request is lessthan the engine on power level, the electric motor will supplythe requested power. Beyond e-,, the engine replaces themotor to provide the total power request. Once the power request

exceeds what the engine can efficiently generate, e,,-u he motoris activated to supply the additional power ( Pr ).

Figure 3: Power Split Control strategyRecharging Control: The engine is the prime mover in thismode. In addition to powering the vehicle, the engine has toprov ide additio nal power for charg ing the battery. A pre-selectedrecharge power level,eh,s added to the drivers power request,

and the motor power command is forced to become negative inorder to recharge the battery E ,=-eh). ne exception is thatwhen the total power request is less than the engine on powerlevel,e-onhe motor alone will still propel the vehicle to preventthe engine from operating in this inefficient region. The otherexception is that when total power request i s greater than themaximum engine power, the motor pow er will becom e positive toassist the engine.

Braking Control: The regenerative braking is activated toabsorb the braking power. However, when the braking powerrequest exceeds the regenerative braking capacity e,--, thehydraulic brakes will be activated to assist in vehicle deceleration(4 = e q - n _rrdn 1The hybrid electric truck with this preliminary rule-basedcontroller was tested through simulation over the EPA UrbanDynamometer Driving Schedule for Heavy-Duty Vehicles(UDDSHDV) in order to evaluate the fuel economy. Table 1compares the resulting fuel economy w ith that of the conventionaldiesel eng ine truck.Table 1: Fuel e conomy comuarison: con ventional, and rule-based

I Fa? [ ConventionalMPG

3. Dynamic Optimization ProblemContrary to the rule-based algorithm, the dynamic optimizationapproach usually relies on a model to compute the best controlstrategy. The model can be either analytical or numerical; in otherwords, it can work with numerical black boxes like HE-VESIM.For a given driving cycle, the optimal operating strategy to deliver

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the best fuel economy can be obtained by solving a dynamicoptimization problem. A numerical dyn amic programmingapproach will be applied to solve this finite horizon optimizationproblem.3.1 Problem FormulationIn the discrete-time format, a model of the hybrid electric vehiclecan be expressed as:

x(k 1) = f ( x ( k ) , u ( k ) ) (1)where u k) is the vector of control variables such as fuelinjection rate to the engine (kglcycle), d esired output torque fromthe motor ( and gear shift command to the transm ission, andx ( k ) is the vector of state variables of the system. The samplingtime has been selected to be one second .The g oal of the optimization scheme is to find the optimal controlinput,u(k) , which minimizes the total fuel consumption over adriving cycle. This defmes the cost function to be minimized asfollows:

I

where N is the time length of the driving cycle, and L is theinstantaneous uel consump tion rate.During the op timization procedure, it is necessary to imposecertain inequality constraints on the states and control to ensurethey remain within their corresponding bo yd s:

@.-mi. 50 cu -soc 5soc 5 soc-T m - m ( @ m , s o c )T, 5 T,--(~ C)

(3)

where we s the engine angular speed and T, is the motor torque.In addition, equality constraints are imposed so that the vehiclealways meets the speed and load demands of the specific drivingcycle.Since the above problem formulation does not impose a chargesustaining policy, the optimization algorithm tends to deplete thebattery in order to attain minimal fuel consumption. Hence, a finalstate constraint on SOC should be imposed to account formaintaining the energy of the battery and to achieve a faircomparison of fuel economy. A soft terminal constraint on SOC(quadratic penalty function) is added to the cost function asfollows:

J = g L ( x ( k ) , u ( k ) ) + G ( x ( N ) )-0 4)where G ( x ( N ) )= a(S O C (N )- SOC,)' represents the penaltyassociated with the error in the terminal SOC; SOC, is thedesired SOC at the final time; and is a weighting factor.3.2Model SimplificationThe detailed HE-VESIMmodel is not suitable for the purpose ofdynamic optimization because its complexity leads to lowcomputation efficiency. Dynamic Programming is well-known torequire computations hat grow exponentially with the number of

states. A simplified vehicle model is thus developed foroptimization purposes. The engine, torque converter, differential,and electric motor are reduc ed to static m odels with look-up tablesfor U 0 mapping and efficiencies. Since the gear shifting durationis about one second , the autom atic transmission was approximatedto be a gearbox with gear number as the state. For this reason, thecontrol to the transmission is constrained to take on the valuesof -1, 0, and 1 for downshift, no shift and upshift, respectively.The other state left is the battery SOC that is dynam ically updatedby the battery current. The simplified model was found toapproximate well the complex model except under rapidtransients.3.3 Dynamic Programming (DP) SolutionA powerful algorithm to solve the above optimization problem isto use Dynamic Programming (DP). Based on Bellman's principleof optimality, the D P algorithm is presented as follows [111:S tep N-1 :

S tep k , f o r O < k < N - lJ*k(x(k))= ~ $ [ L ( ~ ( k ) , u ( k ) ) + J * k + I ( x ( k + l ) ) (6)

The recursive equation is solved backwards from step - to 0in order to find the optimal control policy. Each of theminimizations is perform ed subject to the constraints imposed by(3) and the driving cycle.The standard method to solve a Dynamic Programming problemnumerically is to use quantization and interpolation ([11],[ 121).The state and control values are first quantized into finite grids. Ateach step of the DP algorithm, the function J , (x(k)) is evaluatedonly at the grid points. If the next state,x(k +1) oes not fallexactly on to a quantized value, then function interpolation is usedto determine the values of f w ( x ( k + l ) ) in (6) as well asG(x( in 5).Despite the use of a simplified model, the long horizon of theUDDSHDV driving cycle makes the direct application of theabove algorithm com putationally infeasible for today's technology.Several approaches have been adopted to accelerate thecomputational speed [12]. From the velocity profile o f the drivingcycle, the vehicle model can be replaced by a finite set ofoperating points parameterized by wheel torque and speed.Pre-computed look-up tables are constructed for recording nextstates and instantaneous cost as a function of quantized states,control inputs, and operating points. O nce these tables are built,they can be used to update (6) in a very eff icient manne r [12].The dynamic programming procedure produces an optimal,time-varying, state-feedback control policy that is stored in a tablefor each of the quantized states and time stages, i.e., u' (x(k) ,k );this function is then used as a state feedback controller in thesimulations. It should be noted that d ynamic programm ing createsa family of optimal paths f or all possible initial conditions. In ourcase, once the initial SOC is given, the optimal policy will find anoptimal way to bring the final SOC back to the terminal value( S O C , ) while achieving the minimal fie1 consumption.

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3.4 Simulation ResultsSince the control policy determined by the dynamic programmingalgorithm is generated on the basis o f the simplified model, thecontrol policy should be verified on the original complex model.Therefore, the optimal control policy found by DP was applied tothe original HE-VESIM model. The same driving cycle(UDDSHDV) is used to evaluate the fuel economy. The terminalSOC constraint was selected as 0.57 and the initial SOC in thesimulation is chosen to be 0.57 as well for the purpose ofcalcula ting fuel economy. Dynamic trajectories of the vehicleunder the optimal control policy for the UDDSHDV cycle areshown in Figure 4. The difference between the desired vehiclespeed (UDDSHDV) and the actual vehicle speed is within 2 mph.The SOC trajectory starts at 0.57 and ends around 0.57 with asmall quantization error. Consequently, we have confidence thatthe optimal solutions based on the simplified model are reliable.The fuel economy of the DP-optimized hybrid truck is 13.63(MPG). Significant improvement has been achieved by the DPalgorithm as compared with values show n in T able 1.

0.640 i W 2W 3W 400 500 600 700 8W Sa, I OWi w

nra s o

0 i W 2M 300 4 500 6W 7W 800 W 1OWI5. a t I i

Figure 4: Simulation result of UDDSHD V cycle. The engineand motor power are given in kW

4. Improved Rule-Based Con trol StrategyAlthough the dynamic programming approac h provides an optimalsolution for minimizing fuel consum ption, the resulting controlpolicy is not implementable in real driving conditions because theoptimal policy requires knowledge of the future speed and loadprofile of the vehicle. Nonetheless, analyzing optimal policiesdetermined through dynamic programming can provide insightinto how the fuel economy improvement is achieved. An improvedrule-based control algorithm is proposed in this section based onthe investigation of the dynamic programming results.4 Gear hift ControlDeterm ining the gear shift strategy is crucial to th e fuel economyof hybrid electric vehicles [13]. In the dynamic programmingscheme, gear shift is one of the control inputs to the system. It isinteresting to find out how the D P solution chooses the gearposition to improve fuel economy. From the optimization results,the gear operation points are expressed on the engine powerdemand vs. wheel speed plot (Figure 5). It can be seen that fourgear positions are separated into four regions and the boundarybetween two adjacent regions seem to represent better gearshifting thresholds. After addin g a hysteresis function to the

shifting thresholds, a new gear shift map determining when anupshift or downshift event occurs was developed. It should bementioned that the optimal gear shift map for minimum fuelconsumption can also be constructed through static optimization[10],[14]). Given an engine power and wheel speed, the best gearposition for minimum fuel consump tion can be chosen based onthe steady-state engine fuel consum ption map. It is found that thesteady-state gear map nearly coincides with Figure 5. This is notsurprising since the electric motor is positioned after thetransmission, which means that the engine efficiency willdominate the gear shifting policy. Finally, we apply the new gearshift logic (Figure 5 ) to the original rule-based control strategy.Fuel economy s improved to 13.02 MPG as shown in Table 4.

DMeelSpeed (rad/s)Figure 5 : Gear operating points of DP optimization

4.2 Power Split ControlIn this section, we explore how Power Split Control of thepreliminary rule-based strategy can be improved on the basis ofdynamic programming. In Power Split Control, there are fourpossible operating modes of splitting the power demand betweenthe engine and motor: m otor only mode, engine only mode, hybridmode (both the engine and motor), and recharge mode (the engineoffers additional power to charge the battery). Rules for switchingbetween the different modes will be established by examining theoptimization results obtained from Section 3. The operating pointsdisplaying different operating modes are presented in thetransmission input speed and pow er demand plane (see Figure 6).

Tram h p u t S p e d taus)Figure 6:Operating points of DP o ptimization overUDDSHDV cycle

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Some observations can be made as ollows:0

00

Use the motor alone when power demand is less than 15kW.In region A, DP chooses to operate in the hybrid mode.The recharge mode rarely happens.The low number of recharging events may imply that under thecurrent vehicle configuration t isnot e fficient to use engine powerto charge the battery, even if increasing the engines power wouldmove its operation to a more efficient region. As a result, we willassume there is no recharging during Power Split Control, andrecharge will only occur under Recharging Control when S OC istoo low. The power distribu tion between the two prime movers inthe hybrid mode is determined next. We wish to extract from theDP solution an optimal motor power m odel in the hybrid mode,and then determine the engine power demand by subtracting themotor power from the driver power demand. Clearly, optimalmotor power may depend on many variables such as wheel speed,engine speed, power demand, SOC, gear ratio, etc. For this reason,a regression-based program was first used to assess which of thesevariables were the dom inant factors in determ ining motor power.It tumed out that power demand, engine speed, and transmissioninput speed were the critical factors. Motor power, as determinedby the DP algorithm, was then fit to these three factors with aNeural Network (NN), using two hidden layers with 3 and 1neurons, respectively. The basic logic of this improved PowerSplit Control is summarized in Table 2. M e r implementing thenew Power Split Control rules, the fuel economy was furtherimproved to 13.17 MPG as shown in Table 4.

Table 2: Basic logic rules of new Power Split ControlI f P , 5 1 5 k W , P m = P m q P , = OElse IfRegionA, P, = Nnet,(P,,, 0 - omg , = Pa,, - P,

If Region B, P, =0 4 = PmqIf p.>e_,, p .=E-, P, = P,, p .4.3 Recharging Co ntrol

In the modified rule-bked control algorithm, the thermostat-like charge sustaining strategy is retained, owing to robustness andsafely concerns. The recharging mode will turn on if the batterySOC falls below the lower limit as described in the preliminaryrule-based control. However, requiring the engine to provide aconstant recharging power level is n ot necessarily the mostefficient way to recharge the battery. For this reason, when torecharge and at what rate to recharge should be investigated toimprove the recharging control policy. Since the engine is rarelyused to recharge the battery from th e previous optimization result,the dynamic programming procedure was modified in an attemptto o bserve an optimal recharging policy. First, we turned off theregenerative braking h nct ion in the dynamic programming routine.In other words, all the braking power was supplied by thehydraulic braking and hence there was no free energy securedfrom the regenerative braking to rech arge the battery. F urthermore,after comp uting the optimal con trol policy via DP, the initial SOCwas specified o be 0.52 for the purpose of sim ulating the situationthat SOC was too low and the battery needed to be recharged.The simulation result is shown in Figure 7.Note that the aboverepresents the optimal policy for minimum fuel consumptionunder the condition that the battery SOC has to be recharged back

to 0.57 from 0.52. Note also that negative motor power nowrepresents the recharging power su pplied by the engine since thereis no regenerativebraking.

2 -100 iM 200 300 400 O 6W 700 Bw 9W IWOlima Sec)

Figure 7: Simulation results of UDD SHDV cycle withoutregenerative braking

Several rules were extracted from the optimization result asfollow s @ossible reasons are in parentheses):Recharging happens only when wheel sp eed is greaterthan 10 rad/s (better moto r efficiency).Battery recharging power is normally smaller than 15kW(better battery charging efficiency).The electric motor is the only power source to drive thevehicle when power demand is less than 8 kW (avoid lowengin e efficiency).

Further rules c n be constructed as shown in Figure 8. A thresholdline is drawn to divide the plot into two regions. In region C,there are few recharging even ts and m ost of the recharging eventshappen in region D. W e extracted all the recharging data in regionD in an attempt to determine a h c t i o n for optimal rechargingpower, using th e method of Section 4.2. A regression program w asfirst used to find w hich factors should be used to build the modeland then a Neural Network was used to fit the function. The basiclogic of this improved Rec harging Control is summ arized in Table3. As hown in Table 4, fuel economy has been improved to 13.24

0

0

Trans h p u t S p c e d ( r a d k )

Figure 8: Operating points ofDP optimization overUDDSHDV cycle without regenerative braking

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MPG under this new Recharging Control policy. The gradualimprovements in fuel economy can be seen in Table 4 as the newstrategies were added one after another to the preliminaryrule-based algorithm.

ConventionalPreliminary Rule-BasedNew Sh ift ControlNew Power S plit Control

Table 3: Basic logic rules of new Recharging Contr ol(If P,,S8kW, Pm= p C = O

10.6312.5613.0213.17

Table 4: Fuel economy comparison over UDDSHDV cy cleI Fuel Economy (MPG )

DC MotorLead-acid BatteryAutomatic Transmission49kWCapacity: 18Ah, Number: 254 speed, G R 2.59/1.68/1.06/0.75

New Recharging Control 13.24Dynamic Programming 13.63

5. ConclusionsDesign of the energy management strategy for a hybrid electricvehicle with the aid of dynamic programming has the adv antage ofoptimizing the overall system efficiency. Dynamic Programmingprovides engineers with fast quantitative analysis and hrth runderstanding of the complex hybrid system. In this paper, theproblem of predicting he best fuel economy of a hybrid truck overa driving cycle was investigated. A D ynamic Programm ing (DP)algorithm based on a simplified vehicle model was developed todetermine the optimal policy for hybrid operation. It was foundthat improvements in fuel economy were derived mainly fromoptimizing the gear-shifting policy and dischargingkhargingschedule, and relieving the engine load through more efficientmotorlbattery operation. By carefu lly analy zing the op timiza tionresults an improved rule-based control strategy was develo ped forreal driving application.

AcknowledgmentsThis research i s supported by the U.S. h y ARDEC under thecontract DAAE07-98-C-R-LOOS. Th e work of J.W. Grizzle wassupported in part by NSF contract 11s-9988695.

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[3]Kim, C., NamGoong, E., and Lee, S., Fuel EconomyOptimization for Parallel Hybrid Vehicles with CVT, SAEPaper No. 1999-01-1148.[4]Paganelli, G, Ercole, G, Brahma, A., Guezennec, Y. andRizzoni, G, A General Formulation for the InstantaneousControl of the Power Split in Charge-Sustaining Hybrid

Electric Vehicles. Proceedings of 5th Intl Symposium onAdvanced Vehicle Contr ol, Ann Arbor, MI, 2000.[5]John son, V.H., Wipke, K.B. and Rausen, D.J., HEV Co ntrolStrategy for Real-Time Optimization of Fuel Economy andEmissions, Proceedings of the F uture Car Congress, April2000, SAE Paper No. 2000-01-1543.[6]Brahma, A., Guezennec, Y. and Rizzoni, G, DynamicOptimization of MechanicallElectricaI Power Flow in ParallelHybrid Electric Vehicles Proceedings of 5th Intl Symposiumon Advanced V ehicle Control, Ann Arbor, MI, 2000.[7]Zoelch, U ., and S croeder, D., Dynam ic Optim ization Methodfor Design and Rating o f the Comp onents of a HybridVehicle, Interna tional Journal of Vehicle Design, v19, nl , .pl-13, 1998[8]Assanis, D.N., Filipi, Z.S., Gravante, S., Grohnke, D., Gui, X.,Louc a, L.S., Rideo ut, GD., Stein, J.L., Wang, Y., Validationand Use of SIMULINK Integrated, High Fidelity,Engine-In-Vehicle Simulation of the International Class VITruck, SAEPaper No. 2000-01-0288[9]Lin, C.C., Filipi,Z.S., Wang, Y., Louca, L.S., Peng, H., Assanis,D.N., and Stein, J.L., Integrated, Feed-Forward HybridElectric Vehicle Simulation in SIMULMK and its Use forPower Management Studies, SAEPaper No. 2001-01-133410]Bowles, P. D., M odeling and Energy Managem ent for aParallel Hybrid Electric Vehicle (PHEY) with ContinuouslyVariable Transmission (CVT), MS thesis, U niversity ofMichigan, Ann Arbor, MI, 19991IIBerts ekas, D.P., Dyn amic Program ming and Optimal Control,Athena Scientific, 1995121Jun-MO Kang, Ilya Kolmanovsky and J.W. GrizzleApproximate Dynamic Programming Solutions for LeanBurn Engine Aftertreatment, Proceedings of t h e E E ECon ference on Decision and C ontrol, Phoenix,AZ, ecember

[13]Le e, H.D., SUI, S.K., Cho, H.S., and Lee, J.M., A dvanc edGear Shifting and Clutching Strategy for Parallel HybridVehicle with Automated Manual Transmission, IEEEIndustry Applications Conference, v3, 1998[14]So ltic, P., and Guzzella , L., Optim um SI Engine BasedPowertrain Systems for Lightweight Passenger Cars, SAEPaper No. 2000-01-0827

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AppendixTable 5 : Basic vehicle specificationID1 Diesel Engin e IV6,5.475L, 157HP/2400rpm

Vehicle ITotal mass: 258 kg

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Energy Management Strategy for a Parallel Hybrid Electric Truck

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