Hybrid Electric Vehicle Model Predictive Control Torque ... - IEEE Xplore

2458

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 6, JULY 2012

Hybrid Electric Vehicle Model Predictive Control Torque-Split Strategy Incorporating Engine Transient Characteristics Fengjun Yan, Junmin Wang, Member, IEEE, and Kaisheng Huang

Abstract—This paper presents a model predictive control (MPC) torque-split strategy that incorporates diesel engine transient characteristics for parallel hybrid electric vehicle (HEV) powertrains. To improve HEV fuel efficiency, torque split between the diesel engine and the electric motor and the decision as to whether the engine should be on or off are important. For HEV applications where the engines experience frequent transient operations, including start–stop, the effect of the engine transient characteristics on the overall HEV powertrain fuel economy becomes more pronounced. In this paper, by incorporating an experimentally validated real-time-capable transient diesel-engine model into the MPC torque-split method, the engine transient characteristics can be well reflected on the HEV powertrain supervisory control decisions. Simulation studies based on an HEV model with actual system parameters and an experimentally validated diesel-engine model indicate that the proposed MPC supervisory strategy considering diesel engine transient characteristics possesses superior equivalent fuel efficiency while maintaining HEV driving performance. Index Terms—Hybrid electric vehicle (HEV), model predictive control (MPC), torque split.

Nice,ini Npt Nmax _speed_start Powem,in Qc RTor SOClow_ lim SOCup_ lim SOCact SOCini tst t tk td Tpt,req

N OMENCLATURE ΔNfilt Filtered first derivative of engine speed. ηem (Tem,act , wem ) Electric motor (EM) power efficiency. Maximum fuel air ratio (FAR). FARlim Actual FAR. FARact key_on Engine key status. K_start Speed-dependent multiplicative correction factor. Engine transient air mass flow rate (in m ˙ air kilograms per second). Engine mass flow rate (in kilograms per m ˙f second). Engine fuel mass flow rate output after the m ˙ f _corr_1 start-up correction. Desired engine start-up speed (in revoluNice,st tions per minute). Manuscript received August 3, 2011; revised December 29, 2011 and February 19, 2012; accepted April 26, 2012. Date of publication May 4, 2012; date of current version July 10, 2012. The review of this paper was coordinated by Dr. D. Cao. F. Yan and J. Wang are with the Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH 43210 USA (e-mail: [email protected]; [email protected]). K. Huang is with the Department of Automotive Engineering, Tsinghua University, Beijing 100084, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2012.2197767

TICE,req Tem,req Tem,act Vt Vo Rd

Engine initial speed (in revolutions per minute). Powertrain speed (in revolutions per minute). Engine idle speed (in revolutions per minute). Power into the EM (in watts). Battery energy capacity (in joules). Torque-split ratio. Lower bound of SOC. Upper bound of SOC. Actual battery SOC. Initial value of battery SOC. Desired engine start-up time (in seconds). Time (in seconds). Time instant of the start of the kth prediction horizon. Time duration of the prediction horizon. Required driving torque (in Newtonmeter). Required engine output torque (in Newton-meter). Required EM output torque (in Newtonmeter). Actual EM output torque (in Newtonmeter). Battery output voltage (in volts). Battery open-loop voltage. Equivalent battery internal resistance. I. I NTRODUCTION

T

HE HYBRID electric vehicle (HEV) is one of the promising solutions for improving ground vehicle energy efficiencies and emissions [1], [2], [15]. Typically, an HEV includes dual power sources, which are the internal combustion engine (ICE) and the electric capacity device, respectively [10], [14]. The advantages of an HEV are mainly due to its capability of regenerative braking and the potential of optimizing the operations of its power sources [4], [5]. To fully utilize the second attribute, the power management strategy becomes a critical issue in HEV control. In the upper level controller, including the interpretation of the driver’s intention and gearshifting mechanism, the required total torque for the powertrain system can be determined based on the desired and actual vehicle operating conditions, such as the vehicle speed and road

0018-9545/$31.00 © 2012 IEEE

YAN et al.: HEV MPC TORQUE-SPLIT STRATEGY INCORPORATING ENGINE TRANSIENT CHARACTERISTIC

slope [6]. With information on the required total driving torque, how to split it between the different power sources, such that the efficiency of the overall HEV powertrain system can be optimally achieved, is the main concern in power management strategies. Along this line, several HEV power management studies have been conducted from different viewpoints. For steady-state HEV energy optimization, there are rule- or logicbased techniques and efficiency-map-based optimization methods [11], [16], [17]. These methods are based on the energy optimization at an instant time point. Considering the transient features of the powertrain system during a specified time horizon, several dynamic optimization methods were employed to tackle this challenge in a more accurate but computationally intensive way [7], [9], [12], [18], [19]. One of the effective optimization algorithms is dynamic programming (DP) [7], which shows the effectiveness in global optimal energy management control for HEVs, whereas the complexity of the algorithm may raise some concerns for real-time online implementations. In most of the aforementioned HEV powertrain torquesplit control strategies, the engine steady-state fuel efficiency maps or equivalent functions have been employed to represent the fuel consumption characteristics of the ICEs. While such steady-state engine fuel efficiency maps are capable of approximating the engine characteristics at steady state, they may conceal opportunities of exploiting the ICE transient characteristics for further improving the fuel economy of HEVs, particularly those that experience frequent transient operations involving engine start–stop events. In this paper, a model predictive control (MPC)-based torque-split power management strategy is developed for parallel HEVs. The method explicitly considers the diesel-engine crank-to-idle mechanism and the startup transient routine and incorporates a diesel-engine, transient, fuel-consumption, and torque predictive model [3] that has been newly developed for HEV control applications. The main contribution of this work lies in the systematic incorporation of an experimentally validated, real-time-capable, transient, diesel-engine, fuel-consumption, and torque predictive model into the MPC-based HEV torque-split control strategy to enable controlling the torque-split ratio and determining the engine on/off in a more fuel-efficient fashion. The arrangement of this paper is given as follows. In Section II, the preliminaries and problem formulation, including the HEV configuration, engine start-up transient routine investigation, and HEV overall control scheme, are described. The control-oriented subsystem models, including a diesel-engine transient model and a battery/motor model, are presented in Section III. The MPC methodology for torque-split strategy under the proposed HEV configuration is designed in Section IV. Simulation results and comparisons of the performances among three different types of HEV torque-split strategies are conducted in Section V, followed by conclusive remarks. II. P RELIMINARIES AND P ROBLEM F ORMULATION In this section, aside from the descriptions of the HEV configuration and the control scheme, the diesel-engine smooth transient start-up routine design through a polynomial fitting method is also presented.

2459

Fig. 1. Parallel HEV powertrain configuration.

Fig. 2. HEV supervisory control structure schematic diagram.

A. HEV Configuration The parallel HEV configuration considered in this paper is shown in Fig. 1. As can be seen, this HEV configuration consists of two power sources (i.e., motor/battery and a diesel engine). The energy flow(s) can be either from the battery, the inverter, and the electric motor (EM) to the drive shaft and/or from the diesel engine and clutch to the drive shaft. The HEV powertrain may operate under one of the following three modes: 1) EM-only mode; 2) engine-only mode; and 3) hybrid mode. The functions of a HEV supervisory controller include the following: 1) determine the engine on/off and the desired engine torque; 2) control the state of the clutch (engage or disengage); 3) send the desired motor torque signal to the EM control unit; and 4) select the gear-shifting mechanism. B. HEV Control Scheme The high-level HEV power flows and control structure are illustrated by the schematic diagram in Fig. 2. The HEV controller consists of the driver’s intention interpretation and the torque-split supervisory controller. The driver’s intention interpretation part aims to simulate the driver’s decision on the accelerator and braking pedal positions based on the desired and actual vehicle speeds and road slope. Here, a typical proportional–integral controller was employed with kp = 0. 2 (h/km) and ki = 0. 01 (3600/km) as its P and I control parameters, respectively, to emulate the driver’s reaction with respect to the vehicle speed tracking. The reference vehicle speed is assumed to be known by the driver’s intention or the specified driving cycle. The input is the error between the reference and actual vehicle speeds, and the output is the pedal signal with a saturated scale from −1 to 1, which is interpreted as the accelerator pedal position when it is positive and the brake pedal position when it is negative.

2460


In the torque-split controller structure in Fig. 2, the desired vehicle torque (positive or negative) can be determined based on the accelerator or the brake pedal position. The gear shifting was decided through a state-flow block, and it depends on the current powertrain speed and the current gear. The gear ratios from position 1 to position 6 are 7.05, 4.13, 2.52, 1.59, and 0.78, respectively. The upper shift (1-2, 2-3, 3-4, 4-5, and 5-6, respectively) engine speeds are 200, 250, 300, 425, and 520 rad/s. The down-shift speeds (2-1, 3-2, 4-3, 5-4, and 6-5, respectively) are 120, 120, 120, 120, and 360 rad/s. The gear-shifting process also has a certain potential in the overall HEV energy optimization. However, because this study mainly focuses on the powertrain (diesel engine and EM) torque-split strategy, the state-flow-based gear-shifting method was utilized without loss of generality. With the gear ratio, the required driving torque can be derived. The torque-split control strategy starts from the availability of the required driving torque information. How to efficiently distribute the overall required driving torque to the diesel engine and EM on the basis of the vehicle operating conditions, the state of energy storage device (battery), and the powertrain operating conditions is the main concern in this study and will be addressed in the MPC-based torque-split strategy part of Section IV. Since the diesel-engine start–stop mechanism is considered in this method, the outputs of the torque-split controller are the engine key-on status and the torque-split ratio.

Fig. 3.

Comparison of three different engine accelerating cases.

2) Nice,st (tst ) = Npt (tst ), where Npt refers to the known powertrain speed, i.e., the desired engine speed at the end of the start-up process. 3) N˙ ice,st (tst ) = N˙ pt (tst ). Thus, according to preceding boundary conditions, coefficients of the cubic function in (1) satisfy the following equations: a4 = Nice,ini a1 t3st + a2 t2st + a3 tst + a4 = Npt (tst ) 3a1 t2st + 2a2 tst + a3 = N˙ pt (tst ).

C. Engine Start-Up Mechanism Investigation With the start–stop mechanism in a HEV configuration, the engine may start and stop at a much higher frequency than that for conventional vehicles, and consequently, the fuel consumption during each engine start-up may become nontrivial due to the accumulative effect. During an engine start-up process in the parallel HEV powertrain, the engine needs to be accelerated from idle speed to smoothly match with the motor/clutch-out shaft speed and couple with the powertrain output shaft via a clutch within the desired engine start-up time duration. While the fuel consumption from cranking to idle is quite constant under engine warmed-up conditions, which is attributed to the engine dynamics and fuel efficiency characteristics, different engine speed accelerating trajectories (from idle to the desired speed) may result in different fuel consumptions for the startup process. To achieve smooth engine start-up and engagement with the clutch-out shaft, a cubic polynomial function in the following form can be generated for the desired engine speed during the start-up process: Nice,st (t) = a1 t3 + a2 t2 + a3 t + a4 ,

for t ≤ tst

(1)

where t refers to time; tst is the engine start-up time duration; ai , i = 1, . . . , 4 are the polynomial coefficients to be determined; and Nice,st is the desired start-up engine speed. To meet the speed smoothness requirement of the engine start-up process (from idle to the desired speed), three boundary conditions need to be satisfied. 1) Nice,st (0) = Nice,ini , where Nice,ini refers to the engine initial speed (i.e., idle speed).

(2) (3) (4)

To be noted, according to (2)–(4), there is one more degree of freedom in terms of selecting the polynomial coefficients, which is the initial engine acceleration N˙ ice,st (0) = N˙ ice,ini

(5)

as an indication of the initial engine torque at the beginning of the accelerating process. With the boundary conditions 1–3 being satisfied, by properly selecting this initial engine speed acceleration, the engine start-up fuel consumption can be optimized. For instance, Fig. 3 shows the comparisons among different selections of the engine initial accelerations and the corresponding fuel consumptions. Assume that the required boundary conditions are the following: tst = 3 (s), Nice,ini = 520 (r/min) (idle speed), Npt (tst ) = 1500 (r/min), and N˙ pt (tst ) = 100 (rad/s2 ). In Fig. 3, N˙ ice,ini were selected as 50 rad/s2 (Trace 1), 100 rad/s2 (Trace 2), and 150 rad/s2 (Trace 3), respectively. As can be seen, among these three, the optimal accelerating trajectory in terms of fuel consumption for the engine idle-to-desired speed process is Trace 1. To be noted, the simulation results plotted in Fig. 3 were obtained by simulations based on an experimentally validated real-time-capable transient diesel-engine model recently developed in [3].

FOR

III. C ONTROL -O RIENTED M ODELS H YBRID E LECTRIC V EHICLE S UBSYSTEMS

The control-oriented models for the HEV system include a transient diesel-engine model, an EM model, and a battery


model. Such models are computationally efficient and real-time capable for integration into the MPC algorithm. A. Transient Diesel-Engine, Fuel-Consumption, and Torque Predictive Model In most of the HEV control designs, engine fuel mass flow rates were estimated through steady-state engine maps, whose inputs are engine speed and the required torque and output is the fuel mass flow rate. While such steady-state engine maps can represent engine characteristics to a large extent, they may conceal opportunities of further improving the HEV fuel economy by explicitly considering the effect of engine transient operating characteristics, which is more pronounced for some HEV applications where the engines experience frequent transient operations including start–stop. However, due to the complexity and nonlinearities of diesel engine air-path and fuel-path dynamics and interactions, accurately describing the diesel engine transient instantaneous fuel consumption and torque, which are the two most important quantities for HEV powertrain control, can be quite challenging. Due to the closedloop control efforts by the engine control unit (ECU), the input–output dynamics of the overall engine system, which consists of a diesel engine and its ECU, become simpler and more predictable. By utilizing this feature of the overall engine system, in the authors’ recent work [3], a real-time-capable, diesel-engine, instantaneous-fuel-consumption, and torque predictive model was developed and experimentally calibrated for a medium-duty diesel engine, which fits with the HEV powertrain application considered in this paper. By integrating the overall engine system steady-state maps and first-order dynamics, the model can accurately predict the diesel engine fuel consumption and torque at both steady-state and transient operations including the start-up and shutdown processes. The simplicity of the overall engine system dynamics also makes the model computationally efficient for real-time implementations. While the details regarding the aforementioned diesel-engine model and its transient driving-cycle experimental validation are available in [3], several transient features of the model are highlighted here. Owing to the complexity of the real diesel engine crank-to-idle process, involving the fuel injection, ignition, and combustion at relatively low engine speeds, the accurate fuel consumption cannot be effectively indicated in the steady-state fueling maps, which are typically obtained based on extrapolated values for normal engine operating conditions. The techniques in [3] gave an effective and computationally efficient solution through a transient engine start-up model by multiplying a set of factors at different engine speeds. Here, the transient model correction factors were obtained through several real engine crank-to-idle tests. The transient fueling correction can be described by the following formulas: if (cond = TRUE), K_start(N )· m ˙ f _ss (6) m ˙ f _corr_1 = else, m ˙ f _ss . Here, m ˙ f _ss is the steady-state fuel flow rate on the basis of steady-state engine operation map, K_start is an engine-speeddependent multiplicative correction factor identified from the

2461

experimental tests in crank-to-idle conditions, and cond is the condition described in f (ΔNfilt > 0 & N < Nmax _speed_start ), TRUE cond = else, FALSE. (7) Here, ΔNfilt is obtained by low-pass filtering the first derivative of the engine speed, and Nmax _speed_start is a constant value of 520 r/min as the idle speed for the diesel engine. The calibration of the crank-to-idle correction factor was performed through an optimization process for minimizing the difference between the measured instantaneous fueling mass flow rate trace and the transient mass flow rate output of the model in several crankto-idle traces. Aside from the crank-to-idle correction, the smoke limits in diesel engine transient operations were also specifically addressed in the model, as indicated in [3]. The following expression was developed for describing the diesel engine smoke limits during transient operations: ⎧ ⎨ if (FARact > FARlim (N, Treq )) , FARlim (N, Treq ) · m ˙ air m ˙f= ⎩ else, m ˙ f _corr_1 . (8) Here, m ˙ f _corr_1 is the modeled fuel mass flow rate output after the crank-to-idle correction, m ˙ air is the transient air mass flow rate, FARlim is a map of the maximum FAR obtained by the experimental data of the diesel engine, and FARact = m ˙ f _corr_1 /m ˙ air . Details on the derivation of the diesel engine air-path fresh air mass flow rate m ˙ air are neglected here; see [3]. In this paper, a simplified first-order dynamic model in [3] was utilized for torque prediction, where the transient torque Torquetr can be estimated as follows: τtorque (Treq )·

d(Torquetr ) +Torquetr = Torquess (N, m ˙ f ). (9) dt

Here, the steady-state torque Torquess can be illustrated as a function of engine speed N and fuel flow rate m ˙ f as ˙ bf5 Torquess = (b1 + b2 N + b3 N 2 ) 1 − b4 · m 120 − Tfr (N ) (10) ·m ˙ f · LHVf · N · Vd where b1 to b5 were calibrated by experimental data, LHVf is the lower heating value of the fuel, Vd is the engine displacement, and Tfr is the friction torque (illustrated as a polynomial function of engine speed). The time constant τtorque (Treq ) in (9) was modeled in the following logic: if(ΔTreq > 0), τ3 τtorque (Treq ) = (11) else, τ4 where τ3 and τ4 depend on the diesel engine experimental data. The engine-out torque cannot exactly match the required torque by the upper level torque-split strategy, with the considerations of engine-out torque steady-state limitations and transient dynamics. As shown in Fig. 7, the engine-out torques, which were derived by the aforementioned engine

2462


IV. M ODEL P REDICTIVE C ONTROL M ETHODOLOGY FOR H YBRID E LECTRIC V EHICLE T ORQUE -S PLIT C ONTROL The HEV supervisory torque-split controller aims to generate three output signals to the engine controller and the EM controller, i.e., the engine key-on signal, the required engine torque (interpreted as the pedal position with respect to the engine speed), and the required EM torque, respectively. The required diesel engine torque and the required EM torque are calculated as follows:

Fig. 4. EM and battery model scheme.

TICE,req = max(0, Tpt,req × RTor ) Tem,req = Tpt,req − TICE,req

Fig. 5. Resistive Thevenin equivalent circuit model.

torque estimation methods, do not exactly match the required engine torque. This is also true in real practice, where the precise engine torque prediction and control for diesel engine are still not feasible. Here, the remaining torque differences can be compensated through the EM and driver’s accelerator/brake control (proportional–integral–derivative (PID) upper level control in this paper).

(16) (17)

where Tpt,req is the required total torque, TICE,req is the required engine output torque, Tem,req is the required EM output torque, and RTor is the torque-split ratio. To be noted, the driving cycle is assumed to be known in advance in this paper, and the required powertrain torque can be therefore calculated through the vehicle acceleration. Accurately predicting the future powertrain torque demands may require a substantial amount of information/signals such as the traffic/road conditions and dedicated prediction methods in real time and is not specifically considered in this paper, whose focus is on utilizing the MPC scheme to systematically incorporate engine transient characteristics in the HEV powertrain supervisory control.

B. EM and Battery Models The EM and battery model layout is illustrated in Fig. 4. The actual EM output torque Tem,act was derived by applying the maximal and minimal EM torque limitations after the required EM torque Tem,req . These limitations are functions of the current EM speed (powertrain-out shaft speed) based on the EM design. The power into the EM Powem,in can be calculated as Powem,in =

Tem,act · wem . ηem (Tem,act , wem )

(12)

Here, ηem (Tem,act , wem ) is the EM power efficiency, which is a function of the EM torque and speed. The battery is modeled as a resistive Thevenin equivalent circuit model [8], as in Fig. 5 (13) Vt = Powem,in · Rd Id =

Vo − Vt Rd

(14)

where Vt is the battery output voltage; and Rd is the equivalent battery internal resistant, which is a function of the battery SOC. Vo is the battery open-circuit voltage. Then, the actual battery SOC SOCact can be calculated as

t Id (τ )dτ SOCact (t) = SOCini − 100 · 0 (15) Qc where SOCini is the initial value of battery SOC, and Qc refers to the overall battery energy capacity.

A. MPC Algorithm Brief Review In this section, the MPC algorithm is briefly reviewed. The MPC method has the capabilities in dealing with the optimization problems subject to constraints [13]. The scheme of the MPC algorithm is designed based on the system controloriented model and the cost functions that are constructed from the insight into system characteristics and the optimization requirements. The MPC algorithm consists of three main steps: 1) Calculate the optimal inputs in a prediction horizon to minimize the cost function subject to the constraints; 2) implement the first portion of the derived optimal inputs to the physical plant; and 3) move the entire prediction horizon forward and repeat step 1. Whether the MPC algorithm can find the optimal solutions heavily relies on two aspects, i.e., the accuracies of the control-oriented models and the proper selections of the input initial conditions. The former is because the accuracies of the control-oriented models indicate the prediction accuracy of the calculations in the prediction horizon. The latter is because the optimization problems in the prediction horizon are commonly nonlinear, particularly for the cases where the cost functions are nonconvex, such that only local minima may be achieved. In the following HEV MPC designs, these two issues will be considered. B. MPC Algorithm for HEV Torque-Split Control For the HEV torque-split control problem, the main objective here is to minimize the overall equivalent fuel consumption.


Thus, the cost function derived in the kth prediction horizon is expressed as follows: tk +tp

J(k) = α1

2463

Here, RTor (t) indicates the torque-split ratio. With this torquesplit ratio, the torque values for the diesel engine and the EM can be calculated by (16) and (17). The outputs in the control-oriented model (22) are

m ˙ f (t)dt y = [m ˙ f (t),

tk

+ α2 [SOC(tk ) − SOC(tk + tp )] + α3 [1 − key_on(tk + tp )]

(18)

subject to SOClow_ lim < SOC < SOCup_ lim

(19)

where SOClow_ lim and SOCup_ lim are the lower and upper bounds of SOC, respectively. key_on ∈ {0, 1} refers to the diesel engine key position, i.e., “1” represents the engine “on” and “0” represents the engine “off”; tk is the time instant of the start of the kth prediction horizon; and tp is the time duration of the prediction horizon. As can be seen from the preceding definition, the cost function consists of three terms: 1) the diesel engine fuel consumption; 2) the equivalent energy cost of battery; and 3) the penalty of the engine key-off status at the end of the prediction horizon. αi , i = 1, 2, 3 are the weighting parameters. The first two terms indicate the overall equivalent fuel cost of the powertrain. Therefore, the following relation holds: α2 = Csoc_fuel α1

α3 = mfuel_start α1

(21)

where mfuel_start is the nominal fuel consumption for the diesel engine start-up process, which includes the engine start from stop to idle and from idle to launch. The former was illustrated by a transient compensation model in Section III-A, and the latter was described by a polynomial speed approximation in Section III-C. To be noted, the penalty of the diesel engine initial keyoff status in the prediction horizon, i.e., key_on(tk ) = 0, was indirectly taken into account through the transient start-up fuel cost and thus is not contained in the cost function (18). For this cost function (18), the control-oriented model can be represented as follows: y = f (u(t), t) .

(22)

The inputs in (22) are u(t) = [key_on(t),

RTor (t)] .

(23)

(24)

With the outputs of the control-oriented model, the cost function (18) can be calculated in each prediction horizon. For computational simplicity, the control-oriented model was discretized with the sample time of 1 s. The prediction horizon is selected as 10 s, and the implementation horizon is selected as 1 s. Thus, the input vector in (23) for the kth prediction horizon was discretized as uk = [u(tk ), u(tk + 1), . . . , u(tk + tp )]

(25)

where u(tk +i) = [key_on(tk +i), RTor (tk +i)], i = 1, . . . , tp . As a local optimization method, the selections of the initial input values at each step are crucial for the MPC algorithm. The initial input value selections follow four criteria. 1) In the first prediction horizon, the initial input values are key_on = 1 and RTor = 1. 2) Supposing that the optimal inputs for the kth prediction horizon was calculated as

= uopt (tk ), uopt (tk + 1), . . . , uopt (tk + tp ) (26) uopt k

(20)

where Csoc_fuel is a multiplication factor, indicating the equivalent ratio between SOC and fuel consumptions. The third term in the cost function α3 [1 − key_on(tk + tp )] accounts for the fuel penalty at the end of the prediction horizon, i.e., if key_on(tk + tp ) = 0, then the engine needs to start up in the future and thus pay the fuel cost associated with it. α3 can be selected through the following equation:

SOC(t), key_on(t)] .

uini k+1

then the initial input value for the (k + 1)th prediction horizon is selected as = uopt (tk + 1), uopt (tk + 2), . . .

uopt (tk + tp ), uopt (tk + tp ) . (27)

3) If the initial diesel engine speed in the (k + 1)th prediction horizon is zero, which indicates that the diesel engine is off, then another set of initial input values was selected, ini = 0. where the initial values of key_onini = 0 and RTor 4) Following criterion 3, with the optimal solutions by criteria 2 and 3, compare the corresponding cost functions, and choose the better one (with a smaller cost function value) as the control input. Here, u_k is calculated based on a “Trust-Region Reflective” optimization method by using the command fmincon in Matlab/SIMULINK. V. T ORQUE -S PLIT C ONTROL A LGORITHM E VALUATIONS In this section, the effectiveness of the proposed MPC method is evaluated through a calibrated HEV simulator with system parameters from an actual HEV city bus and an experimentally calibrated medium-duty diesel-engine model [3]. A. Torque-Split Control Algorithms To show the effectiveness of the proposed diesel-engine transient-model-based MPC methodology in torque-split control, three torque-split control methods were proposed for the comparison purpose. Method 1 is the proposed MPCbased method with a transient diesel-engine model, and the simulation results were noted with “-TR” in Figs. 6 and 7.

2464

Fig. 6.


Fig. 7.

Engine torque predictions in the three methods.

Fig. 8.

Engine speed and torque by Method 1.

Fig. 9.

Engine key status and torque-split ratio by Method 1.

Vehicle speed tracking performance by the three torque-split strategies.

Method 2 employs the same MPC design method as the first one but neglects the diesel engine transient corrections in the control-oriented model. Here, it is referred to as the steady-state MPC method and noted with “-SS” in the following figures. In Method 3, a typical PID-based SOC regulation strategy was utilized, which aims at maintaining the SOC at a desired value. The simulation results were noted as “-PID” in the following figures. On the basis of the error between the desired and actual SOC, the required EM torque was calculated by a PID controller. Then, the required engine torque was derived as the difference between the required total driving torque and the EM torque. Method 1 and Method 2 both include the diesel engine start–stop mechanism, and in Method 3, the engine key position was always kept “on.” B. Torque-Split Control Algorithms A city-driving-like predescribed driving cycle, which includes several stops, was used for comparing the three different HEV control strategies. Fig. 6 shows the vehicle speed tracking performances by the three different HEV control methods. As the results indicate, all the three control methods can fulfill the vehicle speed tracking performance requirement well. In this context, the equivalent fuel consumptions among these three methods can be further evaluated and compared. Fig. 7 shows the required engine torque values that were derived by the torque-split strategies and the actual torque outputs from the engine model for each of the three methods, i.e., the transient MPC, the steady-state MPC, and the SOC PID control methods, respectively. To be noted, due to the simplified engine torque estimation and the engine torque dynamics, the engine output torque values cannot be exactly the same as the required ones. By the EM torque output and the driver model (a PID control law on the basis of vehicle speed error), the torque differences between the required one (by the torquesplit strategy) and the actual engine torque output (by the simplified engine torque estimation method in Section III-A) can be compensated. Fig. 8 shows the diesel engine operating performances, including the engine speed and engine output torque. As can

be seen, with the start–stop mechanism, the diesel engine was on only when the required engine torque was assigned by the torque-split controller. This way, the equivalent fuel consumption can be effectively minimized subject to the battery SOC constraints. Fig. 9 shows the engine key status and the torquesplit ratio calculated by Method 1.


2465

Fig. 12. Cost function comparison for Method 1 and Method 2.

Fig. 10. Engine speed and torque by Method 2.

Fig. 13. Engine speed and torque by Method 3.

Fig. 11. Engine key status and torque-split ratio by Method 2.

Fig. 10 shows the engine operating conditions when control Method 2 was employed. (Fig. 11 shows the engine key status and torque-split ratio correspondingly.) In this torque-split method, the engine start-up was based on a steady-state map. The discrepancies between the steady-state fueling-map-based fuel mass flow rate prediction and the actual fuel consumption caused inefficient usage of the engine. Compared with control Method 1, the engine start–stop frequencies are much higher in some circumstances where the usage of the engine is not necessary. This is due to the underestimations of fuel costs in the diesel engine crank-to-idle and start-up processes by the steadystate map-based prediction method. The other type of inefficient operation can be observed around the 273th second (as indicated by the ellipse region in Fig. 10). Due to the mismatched diesel engine start-up fuel consumption prediction, the engine speed did not catch up with the desired speed (powertrain-out speed) to couple with the powertrain for contributing the torque output and stopped again under the consequent control law. In this case, the inefficiency is apparent as the engine started up (fuel was consumed) but did not contribute useful torque output to the vehicle.

Fig. 11 shows the key status and the torque-split ratio. The benefit of transient fuel correction can also be quantitatively indicated through the cost function calculation in the implementation horizon, which can be calculated by substituting tp by tk+1 in (18). The implementation cost function comparisons are shown in Fig. 12. Fig. 13 shows the diesel engine operation under the PIDbased SOC regulation method (Method 3). Under this strategy, the engine was kept “on,” even though it was not required to generate any power. This caused the low fuel efficiency when the engine was idling and did not provide torque for quite a long period. The low limit on the engine speed curve is the engine idle speed. In Fig. 14, the fuel consumptions and the battery SOCs for the three torque-split methods are compared. The battery SOCs of all the three control methods were within the upper and lower bounds and ended up close to each other. For the fuel cost, Method 3 shows the worst performance. The steadystate MPC method (Method 2) shows better fuel efficiency improvement than Method 3. However, due to the transient fuel consumption mismatch during engine transient operations and the transient fuel estimation error, the equivalent fuel efficiency is still not optimal. Method 1 shows the best fuel efficiency among the three. Compared with Method 1, the increase in fuel consumption by Method 2 is mainly due to two facets: The first one is the higher engine start–stop frequency, which elevated the crank-to-idle and start-up fuel cost, and the second comes from improper calculation of optimal solution due to the inaccuracy of the engine control-oriented model used in the

2466


R EFERENCES

Fig. 14. Fuel costs and battery SOCs in the three torque-split control strategies.

prediction. These two aspects can be clearly observed in Fig. 14 and the corresponding parts in Figs. 8 and 10. The first aspect can be realized in the zoomed-in subplot in Fig. 10. As can be seen, the fuel consumption in Method 2 was larger than that in Method 1. Meanwhile, the corresponding zoomed-in part in Fig. 10 shows that there are higher frequency engine start–stop events in Method 2 than those in Method 1. The second aspect is shown in Fig. 12. By comparing the implementation cost functions, the benefit of Method 1 in terms of lower cost in transient can be qualitatively revealed. Comparing the discrepancies between these two regions in Fig. 14, it can be concluded that the transient fuel corrections dominated the fuel efficiency difference, particularly when the engine was working on the load transition region and the engine start–stop mechanism was involved. It should be noted that the quantitative benefits of the algorithm will be dependent on the vehicle driving cycles. As indicated in the preceding simulation studies, it is expected that the benefit will be more pronounced when the vehicle experiences more transient operations. VI. C ONCLUSION In this paper, an MPC-based HEV torque-split control strategy, which incorporates an experimentally validated dieselengine transient fuel-consumption and torque predictive model, has been proposed for HEV powertrain supervisory control applications. Comparative simulation studies based on a citydriving-like cycle have been conducted for three different HEV supervisory control strategies. Results have indicated that, while all three methods can satisfy the vehicle velocity tracking requirement, the MPC-based method can improve the HEV fuel economy. Moreover, the incorporation of the transient dieselengine model in the MPC algorithm can further benefit the HEV fuel economy by taking into account the effect of diesel engine transient characteristics, which is more pronounced in HEV applications where vehicle/engine experiences frequent transient operations including start–stop events. The control method assumes that the vehicle future powertrain torque demands are available from the given driving cycles.

[1] B. M. Baumann, G. N. Washington, B. C. Glenn, and G. Rizzoni, “Mechatronic design and control of hybrid electric vehicles,” IEEE/ASME Trans. Mechatron., vol. 5, no. 1, pp. 58–72, Mar. 2000. [2] K. Berkel, T. Hofman, B. Vroemen, and M. Steinbuch, “Optimal control of a mechanical hybrid powertrain,” IEEE Trans. Veh. Technol., vol. 61, no. 2, pp. 485–497, Feb. 2012. [3] F. Chiara, J. Wang, C. B. Patil, M. Hsieh, and F. Yan, “Development and experimental validation of a control-oriented diesel engine model for fuel consumption and brake torque predictions,” Math. Comput. Modell. Dyn. Syst., vol. 17, no. 3, pp. 261–277, Jun. 2011. [4] L. Fang and S. Qin, “Optimal control of parallel hybrid electric vehicles based on theory of switched system,” Asian J. Control, vol. 8, no. 3, pp. 274–280, Sep. 2006. [5] Y. Gurkaynak, A. Khaligh, and A. Emadi, “State of the art power management algorithms for hybrid electric vehicles,” in Proc. Veh. Power Prop. Conf., 2009, pp. 388–394. [6] T. K. Lee, B. Adornato, and Z. S. Filipi, “Synthesis of real-world driving cycles and their use for estimating PHEV energy consumption and charging opportunities: Case study for Midwest/US,” IEEE Trans. Veh. Technol., vol. 60, no. 9, pp. 4153–4163, Nov. 2011. [7] C. Lin, H. Peng, J. W. Grizzle, and J. Kang, “Power management strategy for a parallel hybrid electric truck,” IEEE Trans. Control Syst. Technol., vol. 11, no. 6, pp. 839–849, Nov. 2003. [8] D. Linden, Handbook of Batteries. New York: McGraw-Hill, 1995. [9] J. Liu and H. Peng, “Modeling and control of a power-split hybrid vehicle,” IEEE Trans. Control Syst. Technol., vol. 16, no. 6, pp. 1242–1251, Nov. 2008. [10] J. S. Martinez, D. Hissel, M.-C. Pera, and M. Amiet, “Practical control structure and energy management of a testbed hybrid electric vehicle,” IEEE Trans. Veh. Technol., vol. 60, no. 9, pp. 4139–4152, Nov. 2011. [11] G. Paganelli, G. Ercole, A. Brahma, Y. Guezenne, and G. Rizzoni, “General supervisory control policy for the energy optimization of charge-sustaining hybrid electric vehicles,” JSAE Rev., vol. 22, no. 4, pp. 511–518, 2001. [12] P. Pisu and G. Rizzoni, “A comparative study of supervisory control strategies for hybrid electric vehicles,” IEEE Trans. Control Syst. Technol., vol. 15, no. 3, pp. 506–518, May 2007. [13] S. J. Qin and T. A. Badgwell, “A survey of industrial model predictive control technology,” Control Eng. Pract., vol. 11, no. 2003, pp. 733–764, 2003. [14] G. Rizzoni, L. Guzzella, and B. M. Baumann, “Unified modeling of hybrid electric vehicle drivetrains,” IEEE/ASME Trans. Mechatron., vol. 4, no. 3, pp. 246–257, Sep. 1999. [15] F. R. Salmasi, “Control strategies for hybrid electric vehicles: Evolution, classification, comparison, and future trends,” IEEE Trans. Veh. Technol., vol. 56, no. 5, pp. 2393–2404, Sep. 2007. [16] N. Schouten, M. Salman, and N. Kheir, “Fuzzy logic control for parallel hybrid vehicles,” IEEE Trans. Control Syst. Technol., vol. 10, no. 3, pp. 460–468, May 2002. [17] N. Schouten, M. Salman, and N. Kheir, “Energy management strategies for parallel hybrid vehicles using fuzzy logic,” Control Eng. Pract., vol. 11, no. 2, pp. 171–177, 2003. [18] A. Sciarretta, M. Back, and L. Guzzella, “Optimal control of parallel hybrid electric vehicles,” IEEE Trans. Control Syst. Technol., vol. 12, no. 3, pp. 352–363, May 2004. [19] H. Zhang, Y. Zhu, G. Tian, Q. Chen, and Y. Chen, “Optimal energy management strategy for hybrid electric vehicles,” presented at the SAE World Congr. Exhib., Detroit, MI, 2004, Paper 2004-01-0576.

Fengjun Yan received the B.E. degree in control science and engineering from Harbin Institute of Technology, Harbin, China, in 2004 and the M.S. degree in power engineering and engineering thermophysics from Tsinghua University, Beijing, China, in 2006. He is currently working toward the Ph.D. degree with the Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus. His research interests include dynamic system modeling, nonlinear system control and estimation, and diesel engine advanced combustion mode controls.


Junmin Wang (M’06) received the B.E. degree in automotive engineering and the M.S. degree in power machinery and engineering from Tsinghua University, Beijing, China, in 1997 and 2000, respectively, the second and third M.S. degrees in electrical engineering and mechanical engineering from the University of Minnesota, Twin Cities, in 2003, and the Ph.D. degree in mechanical engineering from the University of Texas at Austin in 2007. He has five years of full-time industrial research experience (May 2003–August 2008) with Southwest Research Institute, San Antonio, TX. Since September 2008, he has been an Assistant Professor with the Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus. He is an author/coauthor of more than 110 peer-reviewed papers in journals and conference proceedings. He is the holder of ten U.S. patents. His research interests include control, modeling, estimation, and diagnosis of dynamical systems, specifically for engine, powertrain, after treatment, hybrid, flexible fuel, alternative/renewable energy, (electric) ground vehicle, transportation, energy storage, sustainable mobility, and mechatronic systems. Dr. Wang is a member (as the Liaison for IEEE Control Systems Society) of the IEEE Transportation Electrification (Electric Vehicle) Steering Committee (since 2012). He has been the Chair (2010–2012) of the Society of Automotive Engineers (SAE) International Control and Calibration Committee and the Secretary (2010–2012) of the American Society of Mechanical Engineers (ASME) Automotive and Transportation Systems Technical Committee. He serves as an Associate Editor for the IEEE T RANSACTIONS ON V EHIC ULAR T ECHNOLOGY and on the Conference Editorial Board of the ASME Dynamic Systems and Control Division, the American Control Conference, and the ASME Dynamic Systems and Control Conference. He received the SAE Ralph R. Teetor Educational Award, the National Science Foundation CAREER Award, The Ohio State University Lumley Research Award in 2012, the SAE International Vincent Bendix Automotive Electronics Engineering Award in 2011, the Office of Naval Research Young Investigator Program Award in 2009, and the Oak Ridge Associated Universities Ralph E. Powe Junior Faculty Enhancement Award in 2009.

2467

Kaisheng Huang received the B.E. degree in automotive engineering, the M.S. degree in power machinery and engineering, and the Ph.D. degree in power engineering and engineering thermophysics from Tsinghua University, Beijing, China, in 1993, 1996, and 2007, respectively. He was an Assistant Professor and Lecturer with the Department of Automotive Engineering, Tsinghua University, in 1996 and 1998, respectively, and has been an Associate Professor since 2003. He is an author or coauthor of more than 40 peer-reviewed papers in journals and conference proceedings. His research interests include control, modeling, estimation, and diagnosis of dynamical systems, specifically for engine, powertrain, after treatment, hybrid, and electric ground and underground mining vehicles, as well as intelligent unmanned vehicles and transportation. Dr. Huang received the Scientific and Technological Progress Award from the Chinese Automotive Industry (second prize) in 2006 and 2011.