Real-Time Control Strategy for CVT-Based Hybrid Electric Vehicles Considering Drivability Constraints

applied sciences

Article Real-Time Control Strategy for CVT-Based Hybrid Electric Vehicles Considering Drivability Constraints

Hangyang Li 1,* , Yunshan Zhou 1, Huanjian Xiong 1, Bing Fu 2 and Zhiliang Huang 1,3

1 State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China; [email protected] (Y.Z.); [email protected] (H.X.); [email protected] (Z.H.) 2 School of Mechanical Engineering, Xiangtan University, Xiangtan 411105, China; [email protected] 3 School of Mechanical and Electrical Engineering, Hunan City University, Yiyang 413002, China * Correspondence: [email protected]

Received: 17 April 2019; Accepted: 17 May 2019; Published: 20 May 2019

Abstract: The energy management strategy has a great influence on the fuel economy of hybrid electric vehicles, and the equivalent consumption minimization strategy (ECMS) has proved to be a useful tool for the real-time optimal control of Hybrid Electric Vehicles (HEVs). However, the adaptation of the equivalent factor poses a major challenge in order to obtain optimal fuel consumption as well as robustness to varying driving cycles. In this paper, an adaptive-ECMS based on driving pattern recognition (DPR) is established for hybrid electric vehicles with continuously variable transmission. The learning vector quantization (LVQ) neural network model was adopted for the on-line DPR algorithm. The influence of the battery state of charge (SOC) on the optimal equivalent factor was studied under different driving patterns. On this basis, a method of adaptation of the equivalent factor was proposed by considering the type of driving pattern and the battery SOC. Besides that, in order to enhance drivability, penalty terms were introduced to constrain frequent engine on/off events and large variations of the continuously variable transmission (CVT) speed ratio. Simulation results showed that the proposed method efficiently improved the equivalent fuel consumption with charge-sustaining operations and also took into account driving comfort.

Keywords: hybrid electric vehicle; continuously variable transmission; driving pattern recognition; adaptive-ECMS; learning vector quantization

1. Introduction Hybrid electric vehicles adopt multiple power sources to drive vehicles to improve fuel economy and reduce pollutant emissions. The energy management strategy (EMS) greatly impacts the fuel economy by controlling the power distribution among the power sources [1,2]. Global optimization methods such as dynamic programming (DP), genetic algorithm (GA), and simulated annealing (SA) are widely used to solve the optimal energy management problem over a finite horizon [3–5]. Major disadvantages of these numerical methods are the computational burden and the need to know the driving cycle in advance in order to calculate the required power at the wheels. Therefore, it is not applicable in an actual controller. To tackle this problem, based on Pontryagin’s minimum principle, Paganelli et al. [6] first proposed the equivalent consumption minimization strategy (ECMS). The equivalent factor has a great influence on the results of ECMS and the constraint on the battery state of charge (SOC), and it varies with different driving cycles. In order to enhance robustness to varying driving cycles, Musardo et al. [7] proposed a method by adding an on-the-fly algorithm for the estimation of the equivalent factor to the original ECMS framework, so that the SOC is maintained within the boundaries and the fuel consumption is minimized. Ambuhl et al. [8]

Appl. Sci. 2019, 9, 2074; doi:10.3390/app9102074 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 2074 2 of 15 employed a penalty function, and the equivalent factor was continuously estimated as a function of SOC deviations. In some studies, total fuel consumption was regarded as a function of the equivalent factor, and the control parameters under optimal fuel economy could be calculated by using systematic methods for given driving cycles [9,10]. In [11], the piecewise correction coefficient was used to penalize SOC variations, which was updated by a period of historical driving data. The abovementioned methods usually adopted fixed initial conditions while neglecting the influence of complex driving conditions on the performance of the EMS, thus often leading to suboptimal results. In order to improve the flexibility of the controller, it is necessary to periodically recognize the driving pattern and update the control parameters accordingly [12]. Typically, a learning vector quantization (LVQ) neural network model can be well suited for realizing the on-line driving pattern recognition (DPR) through calculating the Euclidean distances [13]. In [14], based on the sample database of several standard driving cycles, the representative feature parameters were obtained by principal component analysis (PCA), and a real-time DPR algorithm was established by using an LVQ neural network model. The optimized control parameters were then periodically updated according to the driving pattern. A comprehensive review of DPR-based control algorithms can be found in [15]. In addition, the DPR algorithm can be incorporated into an adaptive-ECMS (A-ECMS) controller for on-line estimation of the equivalent factor. In [16], an A-ECMS based on DPR was proposed, and a reasonable time window of historical driving data for the DPR algorithm was determined. In [17], the standard driving cycles were classified by K-means clustering, and the nominal equivalent factor was periodically updated by a mean equivalent factor of the selected driving class. A similar method can be found in [18], in which fuzzy rules were adopted for driving cycle classification, and each driving pattern was represented by the optimal equivalent factor of a typical standard cycle in the driving class. These methods have shown promising results for on-line implementation of the ECMS; however, they ignore the influence of the SOC on the estimation of the equivalent factor. In fact, the initial SOC and the subtle change of the equivalent factor are very sensitive to the SOC balance [19]. In this paper, a novel adaptation method of the equivalent factor is proposed by considering the type of driving pattern and the battery SOC to improve fuel economy. In real-time application of the optimization method, if the fuel economy is the only criterion, results will lead to poor drivability [20,21]. Previous research on the multiobjective optimization of fuel economy and drivability mainly focused on the frequent engine on and off events, gear shifting, and improving the engine torque reserve [22–24]. Since the speed ratio changes continuously in a continuously variable transmission (CVT), driving problems caused by an automatic transmission can be avoided to a large extent. However, a large variation of the speed ratio will cause an abrupt change of the speed at the CVT output shaft, resulting in negative dynamics [25]. Usually, an optimal speed ratio trajectory can be obtained by using global optimization methods; then, the speed ratio is controlled by a feedforward controller or static look-up tables [26]. In this paper, penalty terms are incorporated into the cost function to enhance drivability. The remainder of this paper is constructed as follows: in Section2, a forward-facing model of a typical CVT-based hybrid electric vehicle is established. In Section3, toward the real-time application of the A-ECMS, first, drivability problems caused by the single-criterion cost function for the CVT-based hybrid electric vehicle (HEV) are analyzed, and penalty terms are incorporated into the cost function to enhance drivability. Second, based on the real-time DPR algorithm, a novel adaptation method of the equivalent factor is proposed. In Section4, a random test cycle is used to validate the e ffectiveness of the proposed method. Finally, conclusions are given in Section5.

2. HEV Powertrain Modeling

2.1. Vehicle Conﬁguration The structure of the CVT-based parallel hybrid electric vehicle studied in this paper is shown in Figure1. In this system, an integrated starter /generator (ISG) is powered by a Li-ion battery pack Appl. Sci. 2019, 9, 2074 3 of 15

Appl. Sci. 2019, 9, x FOR PEER REVIEW 3 of 14 and connected to the engine crankshaft through a disc clutch. The torque converter in a conventional connected to the engine crankshaft through a disc clutch. The torque converter in a conventional CVT CVT is removed, and the clutch is installed inside the rotor of the ISG. An electric oil pump (EOP) is is removed, and the clutch is installed inside the rotor of the ISG. An electric oil pump (EOP) is employed in order to meet the pressure and ﬂow demand of the CVT hydraulic system under electric employed in order to meet the pressure and flow demand of the CVT hydraulic system under electric driving mode. Driving mode transition is realized by controlling the working state of the engine, ISG, driving mode. Driving mode transition is realized by controlling the working state of the engine, ISG, and clutch. The vehicle parameters are shown in Table1. and clutch. The vehicle parameters are shown in Table 1.

1 2 3 4 5 6

7 8 9 1.Engine 2.Disc Clutch 3.ISG 4.Electric Oil Pump 5.EOP drive motor 6.Variator 7.Battery Pack 8.Final Drive 9.Differential Gear

Figure 1. VehicleVehicle Configuration. Conﬁguration.

Table 1. Vehicle Parameters. Table 1. Vehicle Parameters. Parameter Value Parameter Value VehicleVehicle mass mass (kg) (kg) 1500 EngineEngine placement placement (L) (L) 1.5 EngineEngine max. max. power power (kW) (kW) 78 IntegratedIntegrated starter starter/generator/generator (ISG) (ISG) max. max. power power (kW) (kW) 26 Battery energy capacity (Ah) 6 Battery energy capacity (Ah) 6 Electric oil pump (EOP) motor max. power (kW) 2.5 Electric oil pump (EOP) motor max. power (kW) 2.5 Speed ratio range of the continuously variable transmission (-) 0.44–2.43 Speed ratio range of the continuously variable transmission(-) 0.44–2.43

2.2. Vehicle Model According to physical causality principles, two two different diﬀerent modeling approaches approaches can can be be used: forward- or backward-facing modeling. In In the the back backward-facingward-facing model, model, the the required torque at the wheel is calculated backwards through the drivelinedriveline until the outputs of the components in the system are obtained. This method is usually adoptedadopted to design high-level control strategies. In the forward-facing model, based on the feedback of th thee actual vehicle speed, a driver model is adopted to generate the the control control signals signals of of the the acceleration acceleration and and the the brake brake pedals. pedals. These These signals signals are are received received by theby thevehicle vehicle control control units units (VCUs), (VCUs), and and the the optima optimall torque torque split split is is computed. Then, Then, the the energy consumption ofof thethe power power sources sources can can be be calculated. calculated. This This method method serves serves as theas the platform platform of design of design and andcalibration calibration of real-time of real-time control control strategies. strategies. In this study, In this a forward-facing study, a forward-facing simulator was simulator developed was in developedthe Matlab /inSimulink the Matlab/Simulink environment. environment. For the single-shaft parallel parallel hybrid hybrid system system desc describedribed above, above, the the power power demand demand of ofthe the vehicle vehicle is satisfiedis satisﬁed by by the the sum sum of of the the output output power power of of the the engine engine and and the the ISG, ISG, and and the the demanded power to propel the vehicle can be calculated as

1 2 PCAvmgf=+++⋅((sincos))ραα1 2 mvv . reqPreq = DρCDAv + mg(sin r α + fr cos α) + mv v (1) (1) 2 2 · ρ C where is the air density, D is the drag coefficient of wind, A is the frontal area, m is the total where ρ is the air density, CD is the drag coeﬃcient of wind, A is the frontal area, m is the total mass of α f massthe vehicle, of the αvehicle,is the road slope, is the vroadis the slope, vehicle v is speed, the vehicle and fr speed,is the rolling and resistancer is the rolling coeﬃcient. resistance coefficient.

2.2.1. Engine Appl. Sci. 2019, 9, 2074 4 of 15

2.2.1. Engine The engine was modeled as static look-up tables, and data were obtained through bench tests. . Fuel ﬂow rate is a function of the engine speed and output torque: m f (t) = f (TEng(t), ωEng(t)). The engine output power can be calculated by

. PEng = LHV m ηEng (2) · f · where LHV is the lower heating value of the fuel, and ηEng is the mechanical eﬃciency of the engine.

2.2.2. ISG A permanent magnet synchronous motor (PMSM) was adopted in this research, and the lumped eﬃciency of the system was obtained through bench tests. The speed of the ISG is proportional to the wheel speed and can be calculated as

ω = ω iFD i (3) ISG wh · · CVT where iCVT and iFD represent the speed ratio of the CVT and the ﬁnal drive, respectively. The output torque of the ISG is conﬁned by the maximum torque available and the output power of the battery, and the ISG output power can be calculated as

P = T ω ηk (T , ω ). (4) ISG ISG · ISG · ISG ISG ISG when k = 1/ 1, the ISG works as a generator/motor. − 2.2.3. CVT The CVT employs an electric oil pump to decouple the ﬂow of the oil pump from the engine speed, which can reduce the energy consumption of the oil pump better than a mechanical oil pump. CVT mechanical eﬃciency is a function of the speed ratio, input speed, and torque:

ηCVT = f (ωin, Tin, iCVT). (5)

The required power by the EOP drive motor can be calculated as

P = Ppump,req/(ηpump η ) (6) EOP,mot · EOP,mot where ηpump and ηEOP,mot represent the eﬃciencies of the oil pump and the drive motor, respectively. PEOP,req is the power demand of the oil pump, which can be calculated as

Ppump = P Q /60 (7) hyd · hyd where Phyd is the required pressure of the hydraulic system, Qhyd is the ﬂow of the hydraulic system, determined by the ﬂow demand for speed ratio control, cooling, lubrication, and leakage.

2.2.4. Battery The battery is modeled as a static equivalent circuit as described in [19], which is considered as a series structure of an ideal voltage source and internal resistance. The current can be calculated as q 2 Uoc U 4R P − oc − int bat Ibat = (8) 2Rint Appl. Sci. 2019, 9, 2074 5 of 15

where Uoc and Rint represent the open circuit voltage and the internal resistance of the battery, respectively, Pbat is the power of the battery and is determined by the sum of the power demand of the ISG and the EOP drive motor. The value of Ibat is positive during discharging and negative during charging. The battery SOC can be derived using ampere-hour integration: Z 1 t SOC(t) = SOCinit Ibat(τ)dτ (9) − Cnom 0 where SOCinit is the initial SOC, and Cnom is the nominated capacity of the battery pack.

3. A-ECMS Based on Driving Pattern Recognition

3.1. ECMS and SOC Management The optimal control problem in terms of fuel economy can be stated as follows: for a given driving cycle, find the optimal control sequence u U in the admissible control set to minimize the total fuel ∗ ∈ consumption: Z t f . J = φ f (x(t f )) + m f (x, u, t)dt (10) t0  .  x(t) = f (x, u, t)    x(t0) = x0 s.t. (11)  x(t) X, t > 0  ∈ ∀  u(t) U, t > 0 ∈ ∀ . where m f is the fuel flow rate, and φ f (x(t f )) represents a constraint on the final state. For a CVT-based HEV, the battery SOC is chosen as the only state variable, xt = SOC(t). The control variables are the CVT speed ratio and the torque split factor between the engine and ISG motor: ( ) i (t) u(t) = CVT . (12) SF(t)

With respect to the real-time optimal control problem with state and control variable constraints, according to Pontryagin’s minimum principle, for each time instant, the minimization of the cost function (10) is equivalent to minimizing the following Hamiltonian function:

. . H(x, u, λ, t) = m (u(t), t) + λ(t) SOC(t) (13) f · . where SOC(t) can be derived by Equation (9), and λ(t) is the adjoint state, deﬁned by the Euler–Lagrange equation: . ∂H(x, u, λ, t) λ(t) = . (14) − ∂x The instantaneous cost function is to minimize the sum of the fuel consumption of the engine and . . the equivalent fuel consumption of the ISG, H = m f (t) + m f ,bat,eq(t). Deﬁne the equivalent factor s(t) for balancing fuel and battery power consumption as

LHV s(t) = λ(t) . (15) − Cnom Uoc · The equivalent fuel consumption can be calculated as

. P m (t) = s(t) bat . (16) f ,bat,eq LHV Appl. Sci. 2019, 9, 2074 6 of 15

Conmmonly, a pair of equivalent factors (schg, sdis) can be defined according to charge and discharge of the battery, and a more accurate result of the fuel consumption can be expected. However, this also leads to a bidimensional problem, which burdens the computational cost. In fact, research shows that the performances are practically the same for ECMS with a pair and a unique equivalent factor [7]. In order to reduce the computational cost, a unique equivalent factor is used for the charging and discharging of the battery [19,21]. In hybrid electric vehicles, battery SOC is controlled to change in a certain range, so the influence of the SOC deviations on the battery parameters, such as open-circuit voltage, internal resistance, and the charge/discharge efficiencies, is rather small; in other words, . the dependence of H on the state variable x can be neglected. Thus, in Equation (14), λ(t) = 0, and the equivalent factor s is a constant. For a given driving cycle, a shooting algorithm can be used to determine the optimal equivalent factor sopt, so that the constraint on the final state can be fulfilled, SOC(t f ) = SOC(t0). However, the optimal equivalent factor varies with different driving cycles. In on-line applications, the equivalent factor needs to be continuously adjusted. By incorporating a reference SOC, the equivalent factor can be calculated as

s(t) = snom fp(SOC(t) SOC ) (17) · − re f where snom is the nominal equivalent factor, and fp is the penalty function to prevent the SOC from large variations. Typically, a proportional-integral (PI) controller can be adopted to maintain the SOC around the reference value. In this study, the following functions, as described in [27], were used for SOC correction:

 !2n+1  SOC(t) SOCre f  fp(SOC(t)) = 1 −  (1 + tanh(m I )) (18)  − SOC SOC  · · SOC re f − min I kT) =0.01(SOC SOC(t)) + 0.99I (t kT) (19) SOC re f − SOC − where kT is the sampling time, and n and m are the tuning parameters for the P,I multipliers, respectively. In this study, n = 4 and m = 5 were used in the penalty function. The P control was used to keep the SOC in the conﬁned boundary [SOCmin, SOCmax], and the I control was adopted to eliminate the accumulated deviation of the SOC from the reference value.

3.2. Drivability Problems In real-time applications, if the fuel economy is the only criterion, drivability problems may arise. Typically, in a CVT-based HEV, the unconstrained control signals in Equation (13) will lead to frequent engine on/off events and drastic fluctuations of the CVT speed ratio. An engine on/off event often involves a driving mode transition; thus, excessive engine events will result in bad drivability. Additionally, when an abrupt change in the speed ratio occurs, the dynamic characteristics of the driveline will have a negative impact on the drivability. In engineering applications, CVT is usually controlled to adjust engine operating points along the optimal operating line to ensure fuel economy. The target speed ratio is a function of vehicle speed and engine output torque. Considering the dynamic response of the hydraulic system, the rate of change of the speed ratio is usually confined to a certain range [28]. As long as there is no sudden change in driving conditions, the speed ratio will not fluctuate significantly. However, in an optimization method, the algorithm is designed to select the best control policies that minimize fuel consumption, without considering the drivability performance. So, it is possible to cause erratic control signals. Therefore, control policies that are more representative of real-world driving behaviors and ensure good drivability are needed. In this paper, penalty terms have been incorporated into the cost function to constrain the frequent engine Appl. Sci. 2019, 9, 2074 7 of 15 on/off events and large variations in the rate of change of the CVT speed ratio. The Hamiltonian in Equation (13) can be reformulated as

. 2 . H = m (t) + α IEE + β (∆i ) + s(t) m (t) (20) f · · CVT · f ,bat,eq where α and β are the weighting factors, and IEE is an indicator function that equals 1 when an engine on or oﬀ event take places. The speed ratio diﬀerences are quadratic in order to keep the penalty term always positive and penalize large variations of the speed ratio. The Hamiltonian described above not only minimizes instantaneous fuel consumption but also takes the drivability into account. Note that the tuning of the weighting factors needs some trial and error depending on the desired outcomes. Based on previous research [29], the weighting factors α = 0.3 and β = 1 were selected in this study.

3.3. The Adaptation of the Equivalent Factor In the A-ECMS, the selection of the nominal equivalent factor has a great influence on the estimation of the equivalent factor, which affects the minimization of fuel consumption and the final state of the SOC. In Figure2, SOC evaluations for di fferent nominal equivalent factors for an initial SOC of 65% under the Urban Dynamometer Driving Schedule (UDDS) are depicted. We can see that, as the snom increases, the final SOC value increases and does not converge to the initial value. Since the strategy is more inclined to constrain the use of battery power, this also leads to more fuel consumption, as shown in Table2. Therefore, in on-line implementations, the nominal equivalent factor needs to be regularly updated according to different driving cycles. Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 14

Snom=3 0.85 Snom=3.2 0.8 Snom=3.4 Snom=3.5 0.75 0.7

SOC [-] 0.65 0.6 0.55 0.5 0 200 400 600 800 1000 1200 Time [s]

s Figure 2. StateState of of Charge Charge (SOC) (SOC) evaluations evaluations for for different diﬀerent snomnom under the Urban Dynamometer Driving Schedule (UDDS) cycle.

Table 2. Fuel Consumption and Final SOC for Different s under UDDS. snom Table 2. Fuel consumption and final SOC for different nom under UDDS. Snom Fuel Consumption (g) Final SOC S Fuel consumption (g) Final SOC 3nom 362.2 0.58 3.23 384.4362.2 0.58 0.64 3.43.2 428.5384.4 0.64 0.74 3.53.4 428.5 436 0.74 0.754 3.5 436 0.754 3.3.1. Classification of the Driving Cycles 3.3.1. Classification of the Driving Cycles The extraction of feature parameters and clustering method of driving cycles was systematically The extraction of feature parameters and clustering method of driving cycles was systematically introduced in [30]. On this basis, 11 typical driving cycles were selected as the basic sample database. introduced in [30]. On this basis, 11 typical driving cycles were selected as the basic sample database. The database was divided into four classes, namely, urban, suburban, and highway cycles, in which The database was divided into four classes, namely, urban, suburban, and highway cycles, in which the suburban driving was divided into suburban A and suburban B according to the distribution of the suburban driving was divided into suburban A and suburban B according to the distribution of the optimal equivalent factors. The classification of driving cycles are shown in Table3. Note that a the optimal equivalent factors. The classification of driving cycles are shown in Table 3. Note that a sufficient number of samples was required to ensure the training effect of the LVQ neural network. Moreover, in order to better reflect the characteristics of the standard cycles, a microtrip extraction method [31] was used to collect the velocity information for statistical analysis. Later, the feature vectors of each microtrip were imported as training sample data. Finally, the 11 standard cycles were divided into 81 microtrips, which could ensure the recognition accuracy.

Table 3. Classification of the standard driving cycles.

CYC1 Urban CYC2 Suburban A CYC3 Suburban B CYC4 Highway UDDS US06 WVUINTER Manhattan FTP CSHVR HWFET NYCC LA92 WVUBUS US06WHY

Table 3. Classiﬁcation of the standard driving cycles.

CYC1 Urban CYC2 Suburban A CYC3 Suburban B CYC4 Highway UDDS US06 WVUINTER Manhattan FTP CSHVR HWFET NYCC LA92 WVUBUS US06WHY

3.3.2. Driving Pattern Recognition Based on LVQ An LVQ neural network model was constructed in the Matlab/Simulink environment, which consisted of an input layer, a competition layer, and an output layer. The neural network was trained under supervision and the competition layer weights were adjusted according to the learning results. In this study, the LVQ1 algorithm was used, and the training process was as follows: Step 1: Initialize the competition layer weights wij and the learning rate η (η > 0). T Step 2: Send the input vector X = (x , x xR) into the input layer and calculate the Euclidean 1 2 ··· Appl.distance Sci. 2019 of, the 9, x inputFOR PEER vector REVIEW and the competition layer neurons. 8 of 14 Step 3: Select the closest compitition layer neuron (e.g., dm), then mark the correspnding linear Step 4: If the category of the output layer neuron is consistent with that of the input layer, the output layer neuron connected as Cm. competition layer weights are updated according to Equation (21); otherwise, they are updated Step 4: If the category of the output layer neuron is consistent with that of the input layer, according to Equation (22): the competition layer weights are updated according to Equation (21); otherwise, they are updated ww=+−η () xw (21) according to Equation (22): ij,, new ij old ij , old www=−=-(ηw xw+ η( )x. w ) (22)(21) ij,, newij,new ij oldij,old ij , old − ij,old wij,new = wij old η(x wij old).v (22) Eleven feature parameters were used as input, − neurons,− , including (1) average speed m , (2) v a a maximumEleven speed feature max parameters, (3) maximum were acceleration used as input max neurons,, (4) average including acceleration (1) averagem , (5) maximum speed vm, (2) maximumd speed vmax, (3) maximum accelerationd amax, (4) averager acceleration am, (5) maximum deceleration max , (6) average deceleration m , (7) idle time ratio idle , (8) acceleration time ratio deceleration dmax, (6) average deceleration dm, (7) idle time ratio ridle, (8) acceleration time ratio racc, racc rb rc f idle (9) deceleration, (9) deceleration time time ratio ratiorb, (10) constant, (10) constant speed time speed ratio timerc, ratio and (11) idle, and times (11) idlefidle. times The competition . The competitionlayer was deﬁned layer was as 20 defined neurons, as and20 neurons, 4 output and neurons 4 output represented neurons 4represented driving patterns. 4 driving The patterns. training Theresult training is shown result in Figure is shown3. The in learningFigure 3. rateThe waslear 0.001.ning rate After was 42 0.001. iterations, After the 42 meaniterations, squared the mean error wassquared reduced error to was less reduced than 0.05. to less than 0.05. Mean squared error [-] error squared Mean

FigureFigure 3. 3. TrainingTraining process process of the learning vect vectoror quantization (LVQ) neural network.

In order to verify the on-line DPR algorithm, a random combination of standard driving cycles was used, as shown in Figure 4. Since the driving cycle is not known a priori, in this paper, we assumed that the driving cycle did not change frequently. Thus, feature vectors extracted from 120 s of historical data were used to predict the driving pattern for the next 10 s. It is worth noting that the length of the recognition cycle has a great influence on the recognition accuracy. A long cycle will lead to poor accuracy, while a short cycle will increase the computational burden and may also result in frequent switching of the driving mode [16]. Due to the lack of historical data in the first 120 s at the beginning of the driving cycle, a default pattern of urban driving was used. As shown in Figure 5, the algorithm successfully recognized most of the driving patterns. However, at some points when transtioning from one driving pattern to another and the vehicle speed dramatically changed, the recognition accuracy decreased, mainly because the feature vectors were relatively close and the algorithm was sensitive to changes in speed and acceleration.

100

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Time [s] Appl. Sci. 2019, 9, x FOR PEER REVIEW 8 of 14

Step 4: If the category of the output layer neuron is consistent with that of the input layer, the competition layer weights are updated according to Equation (21); otherwise, they are updated according to Equation (22): =+−η wwij,, new ij old() xw ij , old (21)

=−η wwij,, new ij old-( xw ij , old ). (22)

v Eleven feature parameters were used as input neurons, including (1) average speed m , (2) v a a maximum speed max , (3) maximum acceleration max , (4) average acceleration m , (5) maximum d d r deceleration max , (6) average deceleration m , (7) idle time ratio idle , (8) acceleration time ratio r r r f acc , (9) deceleration time ratio b , (10) constant speed time ratio c , and (11) idle times idle . The competition layer was defined as 20 neurons, and 4 output neurons represented 4 driving patterns. The training result is shown in Figure 3. The learning rate was 0.001. After 42 iterations, the mean squared error was reduced to less than 0.05. Mean squared error [-] error squared Mean

Appl. Sci. 2019, 9, 2074 9 of 15 Figure 3. Training process of the learning vector quantization (LVQ) neural network.

InIn order order to to verify verify the the on-line on-line DPR DPR algorithm, algorithm, a a random random combination combination of of standard standard driving driving cycles cycles waswas used, asas shownshown in in Figure Figure4. Since4. Since the the driving driving cycle cycle is not is known not known a priori, a inpriori, this paper,in this we paper, assumed we assumedthat the drivingthat the cycle driving did cycle not change did not frequently. change frequently. Thus, feature Thus, vectors feature extracted vectors from extracted 120 s offrom historical 120 s ofdata historical were used data towere predict used the to predict driving the pattern driving for pa thettern next for 10 the s. next It is worth10 s. It notingis worth that noting thelength that the of lengththe recognition of the recognition cycle has cycle a great has inﬂuence a great oninfluence the recognition on the recognition accuracy. A accuracy. long cycle Awill long lead cycle to poorwill leadaccuracy, to poor while accuracy, a short while cycle a willshort increase cycle will the incr computationalease the computational burden and burden may also and result may inalso frequent result inswitching frequentof switching the driving of the mode driving [16]. Duemode to [16]. the lack Due of to historical the lack dataof historical in the ﬁrst data 120 in s the at thefirst beginning 120 s at theof thebeginning driving of cycle, the driving a default cycle, pattern a default of urban pattern driving of wasurban used. driving As shown was used. in Figure As shown5, the algorithmin Figure 5,successfully the algorithm recognized successfully most recogn of theized driving most patterns. of the driving However, patterns. at some However, points when at some transtioning points when from transtioningone driving patternfrom one to driving another pattern and the to vehicle another speed and dramatically the vehicle changed,speed dramatically the recognition changed, accuracy the recognitiondecreased, mainlyaccuracy because decreased, the feature mainly vectors because were th relativelye feature closevectors and were the algorithmrelatively was close sensitive and the to algorithmchanges in was speed sensitive and acceleration. to changes in speed and acceleration.

100

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Appl. Sci. 2019, 9, x FOR PEER REVIEW 9 of 14 Time [s]

Figure 4. VelocityVelocity proﬁleprofile of the test cycle.

5 DPR result 4 Target result

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Time [s] Figure 5. Real-time driving pattern recognition (DPR) veriﬁcation.verification.

3.3.3. Selection of the Nominal Equivalent Factor In previous research, a fixed fixed equivalent factor was used to to represent represent each each driving driving pattern pattern [17,18], [17,18], which, however, ignoredignored thethe influenceinfluence ofof thethe SOCSOC on the estimation of the equivalent factor. Because of the complexity of driving conditions, when the type of driving pattern changes, the SOC does not necessarily equal thethe correspondingcorresponding initialinitial SOCSOC of of the the optimal optimal equivalent equivalent factor, factor, as as shown shown in in Figure Figure6. At6. At this this point, point, the the fixed fixed equivalent equivalent factor factor will will lead lead to to inaccurate inaccurate estimationestimation ofof thethe equivalentequivalent factor during the driving cycle. SOC [-] SOC Driving Pattern [-]

Figure 6. SOC state during driving pattern transition.

Figure 7 presents the optimal equivalent factors for initial SOCs ranging from 0.55 to 0.8 for different driving patterns when the target final SOC was set to 0.7. It can be seen that for a certain initial SOC, the optimal equivalent factors corresponding to different standard cycles were very concentrated, except for SOCs ranging from 0.72 to 0.8 in urban driving. Further, the relationship between the optimal equivalent factor and the initial SOC was almost linear for each driving pattern. From a statistical sense, the average curve can well reflect the general tendncy of a class of driving cycles. In this study, the average curve (shown by the red line) was used to represent the relationship between the initial SOC and the optimal equivalent factor for each driving pattern. Thus, the nominal equivalent factor in Equation (16) was periodically updated as a function of the driving pattern and the SOC. = snom fCYCt((),()) SOCt (23)

Appl. Sci. 2019, 9, x FOR PEER REVIEW 9 of 14

Figure 4. Velocity profile of the test cycle.

Figure 5. Real-time driving pattern recognition (DPR) verification.

3.3.3. Selection of the Nominal Equivalent Factor In previous research, a fixed equivalent factor was used to represent each driving pattern [17,18], which, however, ignored the influence of the SOC on the estimation of the equivalent factor. Because of the complexity of driving conditions, when the type of driving pattern changes, the SOC does not necessarily equal the corresponding initial SOC of the optimal equivalent factor, as shown in Figure 6.Appl. At Sci.this2019 point,, 9, 2074 the fixed equivalent factor will lead to inaccurate estimation of the equivalent 10factor of 15 during the driving cycle.

FigureFigure 6. SOCSOC state state during during driving driving pattern pattern transition transition..

FFigureigure 77 presentspresents thethe optimaloptimal equivalentequivalent factorsfactors forfor initialinitial SOCsSOCs rangingranging fromfrom 0.550.55 toto 0.80.8 forfor differentdifferent drivingdriving patternspatterns when when the the target target final final SOC SOC was was set set to 0.7. to 0.7. It can It becan seen be seen that forthat a certainfor a certain initial initialSOC, the SOC, optimal the optimal equivalent equivalent factors corresponding factors corresponding to different to standard different cycles standard were very cycles concentrated, were very concentrated,except for SOCs except ranging for fromSOC 0.72s ranging to 0.8 infrom urban 0.72 driving. to 0.8 Further,in urban the driving. relationship Further between, the relationship the optimal betweenequivalent the factor optimal and equivalent the initial factor SOC and was the almost initial linear SOC for was each almost driving linear pattern. for each From driving a statistical pattern. Fromsense, a the statistic averageal sense, curve the can average well reflect curve the can general well tendncyreflect the of ageneral class of tendncy driving of cycles. a class In of this driving study, cycles.the average In this curve study (shown, the average by the curve red line) (shown was by used the tored represent line) was the used relationship to represent between the relationship the initial betweenSOC and the the initial optimal SOC equivalent and the optimal factor for equivalent each driving factor pattern. for each Thus, driving the nominal pattern. equivalentThus, the nominal factor in equivalentEquation (16) factor was in periodically Equation (16 updated) was periodically as a function updated of the drivingas a function pattern of and the thedriving SOC. pattern and the SOC. = ( ( ) ( )) snom s fnom( CYC (f t ),CYC SOCt ( t )), SOC t (23(23)) Appl. Sci. 2019, 9, x FOR PEER REVIEW 10 of 14

3.6 NYCC 3.6 UDDS MANHANTTAN 3.4 3.4 LA92 Mean value FTP 3.2 3.2 Mean value 3 3 2.8 2.8 Optimal EF Optimal Optimal EF 2.6 2.6 CYC1 CYC2 2.4 2.4 0.55 0.6 0.65 0.7 0.75 0.8 0.55 0.6 0.65 0.7 0.75 0.8 Initial SOC Initial SOC (a) (b) 3.6 3.6 3.4 3.4 3.2 3.2 3 3 US06 HWFET 2.8 CSHVR 2.8 Optimal EF Optimal US06WHY Optimal EF Optimal 2.6 WVUSUB 2.6 WVUINTER CYC3 CYC4 2.4 Mean value 2.4 Mean value 0.55 0.6 0.65 0.7 0.75 0.8 0.55 0.6 0.65 0.7 0.75 0.8 Initial SOC Initial SOC (c) (d)

FigureFigure 7. 7. InitialInitial SOC SOC versus versus optimal optimal equivalent equivalent factor factor under under different diﬀerent driving driving patterns. patterns. (a) CYC1, (a) CYC1, (b) CYC2,(b) CYC2, (c) CYC3, (c) CYC3, (d) CYC4. (d) CYC4.

3.4. Implementation of the A-ECMS The schematic diagram of the adaptive-ECMS strategy based on driving pattern recognition is shown in Figure 8. Vehicle speed is fed back to the controller, and the DPR algorithm regularly recognizes the driving pattern according to the feature vectors. Then, the adapter in the A-ECMS controller updates the nominal equivalent factor according to the driving pattern and the current battery SOC. Finally, the ECMS algorithm computes the optimal controls based on the real-time equivalent factor and the torque request.

SOC(t)

Feature On-line v(t) DPR Driving Vehicle Model parameters estimation of S(t) Algorithm Pattern Extraction S(t)

Torque Request ECMS

Optimal Control

Figure 8. Schematic diagram of the adaptive equivalent consumption minimization strategy (A- ECMS).

4. Simulation Results In order to verify the effectiveness of the proposed method, simulation tests were conducted under a test driving cycle, which was a random combination of six standard driving cycles: NurembergR36, HL05, SC03, REP05, HWFET, and FTP. The velocity profile of the cycle and the result of the on-line DPR are shown in Figure 9. The sampling time for the simulation was 0.1 s. Both the initial and the reference SOCs were set to 0.7. For simplicity, the proposed adaptive-ECMS based on DPR is hereinafter referred to as the “proposed method”. Appl. Sci. 2019, 9, x FOR PEER REVIEW 10 of 14

Appl. Sci.Figure2019 7., 9 ,Initial 2074 SOC versus optimal equivalent factor under different driving patterns. (a) CYC1, (b11) of 15 CYC2, (c) CYC3, (d) CYC4.

3.4. Implementation Implementation of of the the A-ECMS The schematic schematic diagram diagram of of the the adaptive-ECMS adaptive-ECMS stra strategytegy based based on on driving driving pattern pattern recognition recognition is shownis shown in inFigure Figure 8.8 .Vehicle Vehicle speed speed is is fed fed back back to to the the controller, and thethe DPRDPR algorithmalgorithm regularlyregularly recognizes the driving pattern according to the featurefeature vectors.vectors. Then, the adapter in the A-ECMS controller updates the nominal equivalent factor according to the driving pattern and the current battery SOC. Finally, the ECMS algorithm computes the optimal controls based on the real-time equivalent factor and the torque request.

SOC(t)

Feature On-line v(t) DPR Driving Vehicle Model parameters estimation of S(t) Algorithm Pattern Extraction S(t)

Torque Request ECMS

Optimal Control

Figure 8.8. SchematicSchematic diagram diagram of of the the adaptive adaptive equivalent equiva consumptionlent consumption minimization minimization strategy strategy (A-ECMS). (A- ECMS). 4. Simulation Results 4. SimulationIn order to Results verify the effectiveness of the proposed method, simulation tests were conducted under a test driving cycle, which was a random combination of six standard driving cycles: NurembergR36, In order to verify the effectiveness of the proposed method, simulation tests were conducted HL05, SC03, REP05, HWFET, and FTP. The velocity profile of the cycle and the result of the on-line DPR under a test driving cycle, which was a random combination of six standard driving cycles: are shown in Figure9. The sampling time for the simulation was 0.1 s. Both the initial and the reference NurembergR36, HL05, SC03, REP05, HWFET, and FTP. The velocity profile of the cycle and the result SOCs were set to 0.7. For simplicity, the proposed adaptive-ECMS based on DPR is hereinafter referred of the on-line DPR are shown in Figure 9. The sampling time for the simulation was 0.1 s. Both the to as the “proposed method”. Appl.initial Sci. and 2019 the, 9, x reference FOR PEER REVIEWSOCs were set to 0.7. For simplicity, the proposed adaptive-ECMS based11 of on14 DPR is hereinafter referred to as the “proposed method”. 150 Velocity DPR result 100 4 3 50 2 1 0 0 0 1000 2000 3000 4000 5000 6000 7000 8000 Time [s] FigureFigure 9. 9. VelocityVelocity profile profile and the DPR result.

InIn this this part, part, simulation simulation results results are are demonstrated demonstrated to to verify verify the the drivability drivability improvements. improvements. α = = ComparisonComparison of of the the torque torque split split factor factor is isshown shown in inFigure Figure 10. 10When. When the weighting the weighting factor factor α0 , the0, enginethe engine on/off on /eventsoff events took took place place as asmuch much as as828 828 times times for for the the test test cycle. cycle. After After the the constraint constraint was imposed,imposed, the the frequency frequency of changing changing of of the the torque torque sp splitlit factor factor decreased decreased to to a a large large extent, extent, which which means means thatthat less less driving driving mode mode switching switching occurred, occurred, better better drivability drivability could could be be expe expected,cted, and and engine engine on/off on/off eventsevents dropped byby 62.6%.62.6%. ImprovementImprovement of of the the CVT CVT speed speed ratio ratio signal signal is shownis shown in Figurein Figure 11. 11. When When the weighting factor β = β0, the= 0 fluctuation of the speed ratio was rather frequent and drastic. After the theconstraint weighting was factor imposed, the, speedthe fluctuation ratio signal of the was speed smoothed ratio andwas morerather representative frequent and drastic. of real-world After thedriving constraint behavior. was Although imposed, the the introduction speed ratio of signal penalty was terms smoothed inherently and leads more to extrarepresentative fuel consumption, of real- worldfor the driving test cycle, behavior. the equivalent Although fuel the consumption introduction only of increasedpenalty terms by 1.1%, inherent whichly isleads fairly to acceptable. extra fuel consumption, for the test cycle, the equivalent fuel consumption only increased by 1.1%, which is fairly acceptable.

Figure 10. Comparison of the torque split factor.

Figure 11. Comparison of the CVT speed ratio.

To examine the fuel economy improvement of the proposed method, an adaptive-ECMS with a PI controller and a DPR-algorithm-based A-ECMS as reported in [17] were calculated under test cycles for comparison. For simplicity, the former is referred to as the “A-ECMS”, and the mean equivalent factor of four driving patterns for an initial SOC of 0.7 was selected as the nominal equivalent factor. The latter is referred to as the “DPR A-ECMS”, in which the nominal equivalent Appl.Appl. Sci.Sci. 20192019,, 99,, xx FORFOR PEERPEER REVIEWREVIEW 1111 ofof 1414

150150 VelocityVelocity DPRDPR resultresult 100100 44 33 5050 22 11 00 00 00 1000 1000 2000 2000 3000 3000 4000 4000 5000 5000 6000 6000 7000 7000 8000 8000 Time [s] Time [s] FigureFigure 9.9. VelocityVelocity profileprofile andand thethe DPRDPR result.result.

InIn thisthis part,part, simulationsimulation resultsresults areare demonstrateddemonstrated toto verifyverify thethe drivabilitydrivability improvements.improvements. αα ==0 ComparisonComparison ofof thethe torquetorque splitsplit factorfactor isis shownshown inin FigureFigure 10.10. WhenWhen thethe weightingweighting factorfactor 0,, thethe engineengine on/offon/off eventsevents tooktook placeplace asas muchmuch asas 828828 timestimes forfor thethe testtest cycle.cycle. AfterAfter thethe constraintconstraint waswas imposed,imposed, thethe frequencyfrequency ofof changingchanging ofof thethe torquetorque spsplitlit factorfactor decreaseddecreased toto aa largelarge extent,extent, whichwhich meansmeans thatthat lessless drivingdriving modemode switchingswitching occurred,occurred, betterbetter drivabilitydrivability couldcould bebe expeexpected,cted, andand engineengine on/offon/off eventsevents droppeddropped byby 62.6%.62.6%. ImprovementImprovement ofof thethe CVTCVT speedspeed ratioratio signalsignal isis shownshown inin FigureFigure 11.11. WhenWhen ββ == 00 thethe weightingweighting factorfactor ,, thethe fluctuationfluctuation ofof thethe speedspeed ratioratio wawass ratherrather frequentfrequent andand drastic.drastic. AfterAfter thethe constraintconstraint waswas imposed,imposed, thethe speedspeed ratioratio signalsignal waswas smoothedsmoothed andand moremore rerepresentativepresentative ofof real-real- worldworld drivingdriving behavior.behavior. AlthoughAlthough thethe introductionintroduction ofof penaltypenalty termsterms inherentinherentlyly leadsleads toto extraextra fuelfuel consumption,Appl.consumption, Sci. 2019, 9, 2074forfor thethe testtest cycle,cycle, thethe equivalentequivalent fuelfuel consumptionconsumption onlyonly increasedincreased byby 1.1%,1.1%, whichwhich12 of 15isis fairlyfairly acceptable.acceptable.

FigureFigure 10. 10. ComparisonComparison of of the the torque torque split split factor. factor.

Figure 11. Comparison of the CVT speed ratio. FigureFigure 11.11. Comparison of the CVT speed ratio.

ToTo examineexamine the thethe fuel fuelfuel economy economyeconomy improvement improvementimprovement of ofof the thethe proposed proposedproposed method, method,method, an anan adaptive-ECMS adaptive-ECMSadaptive-ECMS with withwith a PI aa PIcontrollerPI controllercontroller and andand a DPR-algorithm-based aa DPR-algorithm-DPR-algorithm-basedbased A-ECMS A-ECMSA-ECMS as reported asas reportedreported in [17 inin] were [[17]17] calculatedwerewere calculatedcalculated under underunder test cycles testtest cyclesforcycles comparison. forfor comparison.comparison. For simplicity, ForFor simplicity,simplicity, the former thethe is formerformer referred isis toreferredreferred as the “A-ECMS”,toto asas thethe “A-ECMS”,“A-ECMS”, and the mean andand equivalent thethe meanmean equivalentfactorequivalent of four factorfactor driving ofof fourfour patterns drivingdriving for anpatternspatterns initial SOCforfor anan of 0.7initialinitial was SOCSOC selected ofof 0.70.7 as thewaswas nominal selectedselected equivalent asas thethe nominalnominal factor. equivalentTheequivalent latter is factor.factor. referred TheThe to aslatterlatter the is “DPRis referredreferred A-ECMS”, toto asas thethe in which “DPR“DPR the A-ECMS”,A-ECMS”, nominal in equivalentin whichwhich thethe factor nominalnominal was periodically equivalentequivalent updated only by the selected driving pattern. The off-line ECMS with an optimal equivalent factor served as the benchmark for the on-line strategies. In Figure 12, the optimal equivalent factor for the corresponding test cycle was 2.987, and the equivalent factors for on-line strategies varied continuously with time and fluctuated around the optimal equivalent factor. As can be seen from Figure 13, for the proposed method, the battery SOC decreased at the beginning of the driving cycle, since the nominal equivalent factor was relatively smaller, and the penalty for the use of battery power was smaller as a result. At about 1200 s, when the HEV was in engine recharge mode, the vehicle speed suddenly decreased, and the battery SOC increased to 0.9 due to the braking energy regeneration. At this time, the equivalent factor decreased rapidly to penalize the output of the engine power, and the SOC was quickly controlled within the target range. At the end of the test cycle, compared with the off-line ECMS, the SOC for on-line strategies did not perfectly converge with the initial SOC; however, the proposed method showed better robustness. Note that for A-ECMS, better fuel economy and SOC management can be expected for a smaller nominal equivalent factor. Appl. Sci. 2019, 9, x FOR PEER REVIEW 12 of 14 Appl. Sci. 2019, 9, x FOR PEER REVIEW 12 of 14 factor was periodically updated only by the selected driving pattern. TheThe off-line off-line ECMS ECMS with with an optimal equivalentequivalent factor servedserved as ththee benchmark for the on-lineon-line strategies. In Figure 12, the optimal equivalent factor for the corresponding test cycle was 2.987, and the equivalent factors for on-lineon-line stra strategiestegies variedvaried continuouslycontinuously with time and fluctuated fluctuated around the the optimal equivalent factor. As can be seen from Figure 13, for the proposed method,method, the battery SOC decreaseddecreased at the beginning of the driving cycle, sisincence the nominal equivalent factor was relatively smaller, and the penalty for the use of battery power was smaller as a result.result. At about 1200 s, when the HEV was in engine recharge mode, the vehiclvehiclee speed suddenly decreased,decreased, and the battery SOC increased to 0.9 due to the braking energy regeneratiregenerationon.. At this time, the equivalent factor decreaseddecreased rapidly to penalize the output of the engine power, and the SOC was quickly controlled within the target range. At the end of the test cycle, co comparedmpared with the off-line off-line ECMS, the SOC for on-line on-line strategies did not perfectly converge with the ininitialitial SOC;SOC; however, the proposed method showedshowed betterAppl. Sci. robustness.2019, 9, 2074 Note that for A-ECMS,A-ECMS, better fufuelel economy and SOC management can be expected13 of 15 for a smaller nominal equivalent factor.

4.5 4 3.5 3 2.5 2 ECMS 1.5 A-ECMS 1 DPR A-ECMS 0.5 Proposed method 0 0 1000 2000 3000 4000 5000 6000 7000 Time [s]

Figure 12. Comparison of the equivalent factors. Figure 12. Comparison of the equivalent factor factors.s.

1 ECMS A-ECMS 0.9 DPR A-ECMS Proposed method 0.8

0.7

0.6

0.5 0 1000 2000 3000 4000 5000 6000 7000 Time [s]

Figure 13. Comparison of the SOC states. Figure 13. Comparison of the SOC state states.s.

The comparison ofofthe the cumulated cumulatedcumulated fuel fuel consumption consumption and and the the final final SOC SOC is shown is shown in Table in Table4. The 4. fuelThe fuelconsumption consumption for the for DPR the DPR A-ECMS A-ECMSA-ECMS was verywas closevery toclosclose thate to of that the of proposed the proposed method method and off and-line off-lineoff ECMS;-line ECMS;ECMShowever,; however,however the constraint, the constraint effect oneffect the on final the statefinal ststate wasate relativelywaswas relatively poor. poor. Considering Considering the the correction correction of ofthe the total total fuel fuel consumption consumptionconsumption at at the the end end of of the the driving drivindrivingg cycle, cycle, the the actual actual fuelfuel consumptionconsumption willwill be even higher. The The propopsed propopsed method method showedshow showeded the the most most prpromisingomising promising results results comparedcompare comparedd with with the theother other two twoon-on- lineon-line strategies,strate strategies,gies, and and the the performance performance was was very very close close to tothat that of of the the off-lineoff off-line-line ECMS ECMS with with the the optimal equivalentequivalent factor.

TableTable 4. ComparisonComparison of the fuel consumption and final ﬁnal SOC. SOC. Strategy Fuel consumption (g) Final SOC value StrategyStrategy FuelFuel Consumptionconsumption (g)(g) Final Final SOC SOC value Value ECMS 4144 0.707 ECMSECMS 41444144 0.707 0.707 A-ECMS 4191 0.782 A-ECMSA-ECMS 41914191 0.782 0.782 DPR A-ECMS 4160 0.636 DPRDPR A-ECMS A-ECMS 41604160 0.636 0.636 Proposed Method 4157 0.71

5. Conclusions In this paper, a real-time optimal control strategy for a CVT-based hybrid electric vehicle was developed. In order to enhance drivability performance, penalty terms were incorporated into the Hamiltonian to constrain frequent engine on/off events and large variations of the CVT speed ratio. For the on-line estimation of the equivalent factor, an LVQ neural network model was adopted for on-line recognition of the driving pattern. The influence of initial SOC on the optimal equivalent factor was analyzed under different driving patterns. On that basis, a method of adaptation of the equivalent factor was proposed by considering the driving pattern and the battery SOC. Simulation results indicate that the use of the penalty function can effectively enhance drivability with very little fuel overconsumption. Besides that, compared with traditional A-ECMS strategies, the proposed Appl. Sci. 2019, 9, 2074 14 of 15 method has better fuel economy and robustness to varying driving cycles, and the result is close to that of the off-line ECMS with an optimal equivalent factor.

Author Contributions: Conceptualization, H.L.; methodology, H.L.; software, H.X.; validation, B.F. and H.X.; formal analysis, H.L.; investigation, B.F.; data curation, H.L.; writing—original draft preparation, H.L.; writing—review and editing, Z.H.; Funding acquisition, Y.Z. and Z.H.; supervision, Y.Z.; project administration, Y.Z. Funding: This research was supported by the National Natural Science Foundation of China (2012AA111710); The Research Foundation of Education Bureau of Hunan Province, China (Grant No. 18A403); and the Laboratory Program of Hunan City University (2019056). Conﬂicts of Interest: The authors declare no conﬂict of interests.

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