Energy Management Strategy For A Parallel Hybrid Electric .
Proceedings of the American Control ConferenceArlington, VA June 25-27, 2001Energy Management Strategy for a Parallel Hybrid Electric TruckChan-Chiao Lin , Jun-Mo Kang 2, J.W. Grizzle 2, and Huei P e n g xDept. of Mechanical Engineering, University of Michigan, MI 48109-2125chancl @umich.edu, hpeng@umich.edu2 Dept. of Electrical Engineering and Computer Science, University of Michigan, MI 48109-2122junmo @eecs.umich.edu, grizzle@umich.eduAbstractDue 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 detailed 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 (HEV) suddenly appear moreviable and necessary than ever before. These vehicles eitherreduce or eliminate the reliance on fossil fuels. Owing to their dualon-board power sources and regenerative braking, HEVs offerunprecedented possibilities to pursue higher fuel economy,particularly if a parallel HEV configuration is employed. Torealize fuel economy benefits, the power management function ofthese advanced vehicles must be carefully designed. By powermanagement, we mean the development 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 intelligentcontrol techniques such as rules/fuzzy logic/NN 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 sourcesunder 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 optimization problem [5]. The basic idea of the third typeof HEV control algorithm takes into account the dynamic nature ofthe system when performing the optimization ([6],[7]).Furthermore, the optimization is with respect to a time horizon,rather than for a fixed point in time. In general, a power splitalgorithm resulting from dynamic optimization will be moreaccurate under transient conditions.over a driving cycle is developed. The resulting feedback lawsfrom the dynamic programming algorithms are not implementabledue to their preview nature and heavy computational 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 programming solution carefully, and extract simple, implementablerules. These rules are then used to augment a simple, intuitionbased 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 (HE-VESIM)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 downsized from the V8 (7.3L) to a V6(5.5L) and 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) and twodriveshafts (DS), coupling the differential with the driven wheels.Basic vehicle specifications are given in the Appendix.' ,: stDrivetrainHDsMotor:::: '::::::: :" :':':::::"::: SINiHiNii!Hi--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 problem0-7803-6495-3/01/ 10.00 2001 AACCEngine i . . . ./Figure 1: Schematic diagram of the hybrid electric truck2878
Our Hybrid Vehicle-Engine SIMulation (HE-VESIM) model isbased on the high-fidelity conventional vehicle simulator VESIMpreviously developed at the University of Michigan [8]. VESIMhas been validated against measurements for a Class 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 size/power, and the integration of electric componentmodels into the system. The model is implemented in theMATLAB/SIMULINK software environment, as presented inFigure 2. Since the detailed vehicle/chassis models have beenpresented in ([8],[9]), they are not reviewed here.LoadInputDataexceeds what the engine can efficiently generate, P,,. the motoris activated to supply the additional power ( Preq - P,. )"4s 400 \ ! - , a,)war/x 250I200. S15o. .z'r':-100 ';' ?iR Ee:o:or L r!!;P::P -- .N.,,t- I50L.PI1000 1200 1400 1600 1800 2000 2200 2400EngineSpeed(rpm)Figure 3: Power Split Control strategy2.2Figure 2: Hybrid-electric vehicle simulation in SIMULINKRecharging Control: T h e engine is the prime mover in thismode. In addition to powering the vehicle, the engine has toprovide additional power for charging the battery. A pre-selectedrecharge power level, Pch, is added to the driver's power request,Rule Based Control Strategyand the motor power command is forced to become negative inorder to recharge the battery (P,,, -Pch ). One exception is thatwhen the total power request is less than the "engine on" powerlevel, De. . . . the motor alone will still propel the vehicle to preventThe final HEV controller that will be implemented will berule-based.The energy management strategy will only usecurrent and past vehicle states and driver commands to calculate aproper (hopefully, close to optimal) control signal. The rule-basedenergy management strategy used as a starting point here wasdeveloped on the basis of engineering intuition and simpleanalysis of component efficiency tables/charts [9,10]. The designprocess starts from interpreting the driver pedal signal as a powerrequest, P,.eq. According to the power request, the operation ofthe engine from operating in this inefficient region. The otherexception is that when total power request is greater than themaximum engine power, the motor power will become positive toassist the engine.Braking Control: T h e regenerative braking is activated toabsorb the braking power. However, when the braking powerrequest exceeds the regenerative braking capacity P,, mm, thethis controller is divided into three control modes: Braking Control,Power Split Control or Recharging Control. If the power request isnegative, Braking Control will be applied to decelerate the 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 assuresthat the battery state of charge (SOC) stays within preset lowerand upper bounds. A 55-60% 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 determines the power flow in the hybridpowertrain. Whenever the SOC drops below the lower limit(55%), the controller will switch to the 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.P o w e r Split Control: Based on the engine efficiency mapshown in Figure 3, a pre-selected "engine on" power line, P, . . . .hydraulic brakes will be activated to assist in vehicle deceleration( Pb Preq - Pm n n ).The 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 with that of the conventionaldiesel engine truck.Table 1: Fuel economy comparison: conventional, and rule-based(RB)MPGRB12.56Conventional10.633. Dynamic Optimization Problemand "motor assist" power line, P,,. . . . are chosen to avoid engineContrary 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 deliveroperation in inefficient areas. If the total power request is lessthan the "engine on" power level, the electric motor will supplythe requested power. Beyond Pe. . . . the engine replaces themotor to provide the total power request. Once the power request2879
the best fuel economy can be obtained by solving a dynamicoptimization problem. A numerical dynamic 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 (kg/cycle), desired output torque fromthe motor (Nm), and gear shill command to the transmission, andx(k) is the vector of state variables of the system. The samplingtime has been selected to be one second.The goal of the optimization scheme is to find the optimal controlinput, u(k), which minimizes the total fuel consumption over adriving cycle. This defines the cost function to be minimized asfollows:N-1J fuel " L(x(k),u(k))(2)states. A simplified vehicle model is thus developed foroptimization purposes. The engine, torque converter, differential,and electric motor are reduced to static models with look-up tablesfor I/O mapping and efficiencies. Since the gear shilling durationis about one second, the automatic 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 valueso f - l , 0, and 1 for downshill, no shill and upshift, respectively.The other state left is the battery SOC that is dynamically 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 DP algorithm is presented as follows [ 11]:Step N - 1 :J*N-,(x(N - 1)) min [ L ( x ( N - 1),u(N - 1)) G(x(N))]u(N-1)Step k , f o r(5)0 k N-1k 0where N is the time length of the driving cycle, and L is theinstantaneous fuel consumption rate.During the optimization procedure, it is necessary to imposecertain inequality constraints on the states and control to ensurethey remain within their corresponding bounds:toe ram COe COe--rainSOCmm SOC SOCm T mi.(co ,SOC) -T T .x(CO ,SOC)(3)where coe is the engine angular speed and Tm 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:N-1J L(x(k),u(k)) G(x(N))(4)k 0where G ( x ( N ) ) a ( S O C ( N ) - S O C I ) zrepresents the penaltyassociated with the error in the terminal SOC; SOC Iis thedesired SOC at the final time; and c is a weighting factor.3.2 Model SimplificationThe detailed HE-VESIM model is not suitable for the purpose ofdynamic optimization because its complexity leads to lowcomputation efficiency. Dynamic Programming is well-known torequire computations that grow exponentially with the number ofJ*k(x(k)) minEL(x(k),u(k)) J*k l(x(k 1))u(k)(6)The recursive equation is solved backwards from step N - 1 to 0in order to find the optimal control policy. Each of theminimizations is performed 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],[12]).The state and control values are first quantized into finite grids. Ateach step of the DP algorithm, the function Jk(x(k)) is evaluatedonly at the grid points. If the next state, x(k 1), does not fallexactly on to a quantized value, then function interpolation is usedto determine the values of J*k l(x(k l)) in (6) as well asG(x(N)) in (5).Despite the use of a simplified model, the long horizon of theUDDSHDV driving cycle makes the direct application of theabove algorithm computationally infeasible for today's technology.Several approaches have been adopted to accelerate thecomputational speed [12]. From the velocity profile of 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. Once these tables are built,they can be used to update (6) in a very efficient manner [ 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 dynamic programming createsa family of optimal paths for 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( SOC ) while achieving the minimal fuel consumption.2880
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 consumption can be chosen based onthe steady-state engine fuel consumption 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 is improved to 13.02 MPG as shown in Table 4.3.4 Simulation ResultsSince the control policy determined by the dynamic programmingalgorithm is generated on the basis of 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 ofcalculating 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 shown in Table 1.120100---Actual0.# /'l0.56oo 0.54.1002003004008001002000100.200.300460. . . . . . . /. ,600700900,1000500 -'J-- .,/---'- " '- . j ,600 700 800 9601000800 2nd gear [!3rdgearI . . . . . . .4th gear 1:, '' .,--- --M ;:2 u \ . . . . . . .G)- )C o40 . . . . . . . . .%:. : 20.-- .c: G ', n -.%,: .i. C @10.: ! O' i ' : c ' Te --:L , , - , '- 71 2 , M0-o(5oo.[ []"5 60 .o500o 0 [] 2 " : . , .o. -- ,Eca40L! , T.3040'Wheel S p e e d (rad/s) i o , ,' %i 5060Figure 5: Gear operating points of DP optimization4013."60300 400.500 600.700.800----fl900 10' 0' d4.2 Power Split Control'-200100200300400500 600.time (sec)7008009001000Figure 4: Simulation result of UDDSHDV cycle. The engineand motor power are given in kW4. Improved Rule-Based Control StrategyAlthough the dynamic programming approach provides an optimalsolution for minimizing fuel consumption, 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.In 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: motor 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 power demand plane (see Figure 6).[] 0hybridengine only OD /[] [] /Oo[] [ []recharghgmotoronlyRegionA d/ 2t ;,, Rc ,unB80I toa 604.1 Gear Shift ControlDetermining the gear shift strategy is crucial to the fuel economyof hybrid electric vehicles [13]. In the dynamic programmingscheme, gear shift is one of the control
Energy Management Strategy for a Parallel Hybrid Electric Truck Chan-Chiao Lin , Jun-Mo Kang 2, J.W. Grizzle 2, and Huei Peng x Dept. of Mechanical Engineering, University of Michigan, MI 48109-2125 chancl @umich.edu, hpeng@umich.edu
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