Derivation and Experimental Validation of a Power-Split ... - CiteSeerX

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 55, NO. 6, NOVEMBER 2006

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Derivation and Experimental Validation of a Power-Split Hybrid Electric Vehicle Model Fazal U. Syed, Ming L. Kuang, John Czubay, Member, IEEE, and Hao Ying, Senior Member, IEEE

Abstract—Hybrid electric vehicles (HEVs) have attracted a lot of attention due to environmental and efficiency reasons. Typically, an HEV combines two power trains, a conventional power source such as a gasoline engine, a diesel engine, or a fuel cell stack, and an electric drive system (involving a motor and a generator) to produce driving power with a potential of higher fuel economy than conventional vehicles. Furthermore, such vehicles do not require external charging and thus work within the existing fueling infrastructures. The power-split power train configuration of an HEV has the individual advantages of the series and parallel types of HEV power train configurations. A sophisticated control system, however, is required to manage the power-split HEV power trains. Designing such a control system requires a reasonably accurate HEV system plant model. Much research has been done for developing dynamic plant models for the series and parallel types, but a complete and validated dynamic model for the power-split HEV power train is still in its infancy. This paper presents a power-split power train HEV dynamic model capable of realistically replicating all the major steady-state and transient phenomena appearing under different driving conditions. A mathematical derivation and modeling representation of this plant model and its components is shown first. Next, the analysis, verification, and validation through computer simulation and comparison with the data actually measured in the test vehicle at the Ford Motor Company’s test track is performed. The excellent agreements between the model and the experimental results demonstrate the fidelity and validity of the derived plant model. Since this plant model was built by integrating the subsystem models using a system-oriented approach with a hierarchical methodology, it is easy to change subsystem functionalities. The developed plant model is useful for analyzing and understanding the dominant dynamics of the power train system, the interaction between subsystems and components, and system transients due to the change of operational state and the influence of disturbances. This plant model can also be employed for the development of vehicle system controllers, evaluation of energy management strategies, issue resolution, and verification of coded algorithms, among many other purposes. Index Terms—Electronic-continuously variable transmission (e-CVT), derivation, hybrid electric vehicle (HEV), modeling, power-split, simulation, validation.

Manuscript received March 31, 2005; revised August 29, 2005. The review of this paper was coordinated by Prof. A. Emadi. F. U. Syed is with the Department of Electrical and Computer Engineering, Wayne State University, Detroit, MI 48202 USA, and also with the Hybrid Vehicle Program, Sustainable Mobility Technologies Laboratory II, Ford Motor Company, Dearborn, MI 48120 USA. M. L. Kuang and J. Czubay are with the Hybrid Vehicle Program, Sustainable Mobility Technologies Laboratory II, Ford Motor Company, Dearborn, MI 48120 USA (e-mail: [email protected]). H. Ying is with the Department of Electrical and Computer Engineering, Wayne State University, Detroit, MI 48202 USA (e-mail: hao.ying@ wayne.edu). Color versions of Figs. 1 and 12–18 are available online at http:// ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2006.878563

I. I NTRODUCTION

T

HE AUTOMOTIVE industry’s focus has been shifting toward an emphasis on environmentally clean, more efficient, and safe products [1], [2]. This shift in the focus has caused major automotive companies to set the environment and efficiency as two of their most important goals and are working toward achieving them. They are actively developing various new technologies such as electric vehicles (EVs), hybrid EVs (HEVs), and fuel cell hybrid vehicles (FCHVs). FCHVs will not likely be ready for mass production in the next five to ten years because of the unavailability of the desired infrastructure and relative immaturity of the technology. Similarly, EVs are not in demand because of their shortfall in terms of performance, relatively short driving range, long battery charging times, and the lack of a battery charging infrastructure. HEVs have attracted a great deal of attention in the last few years since they do not necessarily require external battery charging or new infrastructure. HEVs also provide great potential for better fuel economy and lower emissions without compromising performance. Generally, there are two types of HEVs, namely 1) the series hybrid system [3], [4] and 2) the parallel hybrid system [3], [4]. The more recent type of complex HEV [5], i.e., the power-split hybrid system [5]–[8], combines the benefits of both the parallel- and series-type hybrid systems without sacrificing the cost effectiveness of this hybrid system. This system consists of two kinds of power sources, a gasoline engine, a motor, a generator, and a high-voltage battery. This system also has the capability of driving the vehicle on electric power as well (a full HEV) [5]–[8]. Fig. 1 describes the power-split HEV configuration and its control system. This power train system consists of four subsystems/components, namely 1) the engine subsystem, 2) the transaxle subsystem, 3) the brake subsystem, and 4) the battery subsystem. They are connected to the driveline through a combination of engine and generator subsystems using a planetary gear set to connect each other and the electric drive system (motor, generator, and battery subsystems) to construct two power sources to propel the vehicle. Each subsystem requires its own controller. It can be noted that the transaxle subsystem controller module (TCM) is integrated with this transaxle subsystem where both electric machines, i.e., the motor and the generator, are housed to provide electrical functionality and are used for different purposes, depending on the driving conditions. It can also be noted that the brake subsystem is an electrohydraulic brake system, which provides the seamless integration of the friction brakes and regenerative braking functionality. In order to ensure that all these controllers work

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 55, NO. 6, NOVEMBER 2006

Fig. 1. Power-split-type HEV configuration.

together to meet the driver’s demand and provide the desired energy management and functionality, a supervisory vehicle system controller (VSC) is essential. For a given driver demand and vehicle operation conditions, this VSC maintains the vehicle at its most efficient operating point by managing the power among the various components of the vehicle and coordinating the operating state of the engine, generator, motor, and battery. In addition, the VSC will ensure the required vehicle’s performance and drivability. Clearly, a very complicated and sophisticated VSC [7]–[10] is required to achieve better fuel economy, emissions, and energy management without compromising vehicle performance. The plant modeling of the power train is very critical and crucial to the VSC effective design [11], [12]. Efforts have been made to develop experimentally validated HEV plant models for the series- or parallel-type hybrid systems [12]–[20]. Furthermore, there are various ADVISOR-based [21]–[25] validated vehicle models that use mostly backward facing approaches [21]. While such models are good predictors of vehicle performance and energy usage, and their simulations times are up to eight times faster than forward facing approaches [21], the drawback of the backward facing approach is that it imposes a specific speed cycle. Imposing a speed cycle in the backward facing approach results in the forces acting on the wheel, and then the simulation goes backward through the drivetrain up to the primary energy source. Therefore, in the backward facing approach, the driver’s behavior does not get reflected, since cycles are followed precisely and, hence, cannot be used for detailed control system development [21], [40], [41]. In conclusion, this method is not suited for control system development that requires controlling and studying reasonably accurate behavior of drivetrain performances. Furthermore, since this approach uses steady-state test data along with imposing a speed cycle, dynamics affects cannot be studied either. Few results [26]–[28], however, exist in the literature regarding mathematical dynamics plant model of a power-

split transmission (transaxle) that can be used for studying and simulating dynamics related to speed, torque, and power behavior of this subsystem. The objective of this work was to develop a complete plant model of a power-split HEV, which is also validated against the experimental results. Indeed, as described later in this paper, the objective was achieved through the theoretical derivation and experimental vehicle validation. The results clearly demonstrate that the developed power-split HEV plant model is capable of producing dynamics of both steady-state phenomena and transient phenomena that are related to driveline/wheel torque, vehicle speed, engine torque, engine speed, generator torque, generator speed, motor torque, motor speed, and highvoltage battery power. This demonstration is accomplished by describing the power train system (Fig. 1) and detailing the derivation of key subsystem mathematical representations and the model architecture. Finally, the plant model behaviors corresponding to the experimental conditions for different driving conditions, including transient phenomena, are compared with the experimental vehicle data. II. M ODELING OF A P OWER -S PLIT HEV D YNAMICS The modeling of the power-split HEV dynamics can be broken down into the power plant dynamics model, the brake system dynamics model, the driveline dynamics model, and the vehicle dynamics model. In order to proceed further into the development of the HEV dynamics plant model, a brief introduction to the power-split power train operation is first provided. A. Introduction to Power-Split Power Train Operation As shown in Fig. 1, the power-split HEV power train consists of two power sources, namely 1) combination of engine, generator, and planetary gear set and 2) a combination of motor and battery [6]–[8], [26]–[28]. The planetary gear set provides interconnection between the engine, generator, and motor. This

SYED et al.: DERIVATION AND EXPERIMENTAL VALIDATION OF A POWER-SPLIT HEV MODEL

Fig. 2.

Power-split HEV system power flow diagram.

planetary gear configuration provides decoupling of the engine speed from the vehicle speed, which provides a great potential to achieve better engine efficiency. Fig. 2 shows the power flow diagram of the power-split HEV system. In an electric-only drive mode (EV mode), where the engine is turned off, the electric motor draws the power from the battery and provides propulsion to the vehicle for forward and reverse motions. In the EV mode, the generator can also be used as a motor to draw power from the battery to assist the vehicle’s forward launch due to the one-way clutch at the carrier (engine) shaft. Note that during an EV mode for reverse launch, the generator cannot provide assistance since there is no reaction torque available to transmit the generator torque. In a hybrid–electric drive mode, as is evident in Fig. 2, the engine output power can be split into two paths by controlling the generator [6]–[8], [26]–[28], namely 1) mechanical path τr ωr (from the engine to the carrier to the ring gear to counter shaft) and 2) electrical path τg ωg to τm ωm (from the engine to the generator to the motor to the counter shaft). Due to the kinematics property of planetary gear set, this split in engine power is accomplished by controlling the engine speed to a desired value, independent of the vehicle speed, thereby providing an opportunity for decoupling the engine speed from the vehicle speed by varying the generator speed accordingly. It is noted that the generator can rotate in either directions (i.e., clockwise or counterclockwise). The changing generator or engine speed varies the engine power split between its electrical path and mechanical path. The generator provides reaction torque to the engine output torque for control of the engine speed and transmits the engine output torque to the ring gear of the planetary gear set and, finally, to the wheels. For a given driver demand and vehicle operating conditions, if the generator speed that results from the desired engine speed is in the opposite direction of its torque, the generator behaves as an electric generation unit, and this power train operation is called the positive split mode. This mode of operation usually occurs when the driver demands more power (e.g., a driver pedal tip in maneuver) or when battery requires charging. Due to the kinematics property of the planetary gear set, the generator can possibly rotate in the same direction of its torque, which reacts to the engine output torque (e.g., a driver pedal tip out maneuver). In this operation, the generator inputs power (like the engine) to the planetary gear set to drive the vehicle. This operation mode is called the negative split mode. Similar to the positive split mode, the generator torque produced by the generator speed control in the negative split mode reacts to the

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engine output torque and conveys the engine output torque to the wheels. In these two operation modes, the motor operation is coordinated with the generator to transmit the engine output power to the driven wheels to meet the driver’s demand. This combination/coordination operation among generator, motor, and planetary gear set can be regarded as a continuous variable transmission (CVT) function. When the generator brake (as shown in Fig. 1) is actuated (called parallel mode), the sun gear is locked from rotating, and the generator braking torque provides the reaction torque to the engine output torque. In this operation, like a parallel HEV, all the engine output power is transmitted to the drivetrain only through the mechanical path with a fixed mechanical ratio. In summary, under all hybrid electric drive modes, the engine requires either the generator torque or the generator brake torque to transmit its output power through both its electrical and mechanical paths (split modes) or only through its mechanical path (parallel mode) to the drivetrain for propulsion. When the vehicle is decelerated, the system operation in this mode is similar to the positive split mode. In other words, the generator is controlled according to the decrease of vehicle speed to function as a generator to make sure that the engine is being operated in the desired and allowable region. In this mode, the electric motor not only provides regenerative braking torque to meet the driver’s demand but also absorbs the torque from the engine. In summary, this power-split power train system provides a CVT [27] like functionality through the planetary gear set and generator control to decouple the engine speed from the vehicle speed and through the motor transmitting the part of the engine power from the engine electrical path (generator) to the wheel. This CVT functionality provides great potential to achieve better engine efficiency and lower emissions. In addition, with the electric drive capability and regenerative braking, the power-split power train provides a great potential to achieve better overall fuel economy without compromising vehicle performance. In order to study the dynamics of this power train system and to design and develop control strategies for this type of HEV, it is essential to model the dynamics of the subsystems of this power-split HEV power train plant and then integrate these subsystems to obtain the complete plant model of the power-split HEV power train. The main subsystems of this power-split HEV power train are power plant, brake system, driveline, and vehicle. B. Power Plant Dynamics Model There are two different sources of power, namely 1) engine and 2) electric machines (motor and generator). Furthermore, the high-voltage battery is the energy storage device for this type of vehicle. Therefore, the power plant dynamics model can be broken down into the engine dynamics model, the electric machine dynamics model, the one-way clutch and generator brake dynamics model, the planetary gear sets system dynamics model, and the battery dynamics model. 1) Engine Dynamics Model: The engine modeling is essential to the power-split power train modeling and can be

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Fig. 4.

Fig. 3. Engine dynamics model block diagram.

very complicated since it is a complex system and has various subsystem levels that need to be modeled [18], [19]. However, since studying vehicle emissions is not the goal of this modeling tool, and the driveline dynamics and the interactions among subsystems are of primary interest, the engine model can be simplified such that a first- or second-order transfer function is used to characterize the following engine torque output response: Teng_act =

1 Teng_desired τs + 1

or Teng_act =

s2

ωn2 Teng_desired + 2ςωn s + ωn2

(1)

where τ is the time constant (in seconds) of a first-order system, ς and ωn are the damping ratio and undamped natural frequency (in radians per second) of the second-order system, respectively, 1/ςωn represents the time constant of the second-order system, Teng_act is the actual delivered engine torque (in newton meters), and Teng_desired is the desired engine torque (in newton meters). Note that the selection of appropriate time constant and damping ratio is very important since these parameters reflect the response of the engine to the desired engine torque. An iterative process is employed to determine the appropriate values for these parameters under specific driving conditions, where these parameters are also calibrated under a simulation environment to match the experimental data. In this process, an engine or the subsystem is used on a dynamometer to study the engine torque response to a desired torque at different engine speeds. These experimental data are then used to determine appropriate values of time constant and damping ratio. Later, simulations are done with this engine subsystem to see if the desired response is achieved, and these parameters are further tuned to match the desired response. This process is repeated until the desired response is achieved. The decision to choose the type of transfer function depends on the type of engine torque, speed response, or behavior desired. The engine model is shown in Fig. 3. In order to maintain the properties such as engine losses, engine torque, or power delivery for fuel economy studies, empirical data for the maximum–minimum engine torque curves along with the engine loss curves are used to characterize the engine under steady-state conditions. Similarly, the consumption (fuel or electrical) calculation is also based on empirical data.

Block diagram of the electric machine model.

2) Electric Machine Dynamics Model (Motor or Generator): The electric machine in a HEV provides the ability for boosting performance and energy (electricity) regeneration [29] as well as electric-only drive capability for reduced emissions and improved fuel economy. The development of advanced magnetic materials, power electronics, and digital control systems makes electric machines (motors/generator) today a viable solution for a wide range of applications. This increased interest in electric machines has led to its use in the automotive industry [30] for fuel cell vehicles, HEVs, and EVs. The type of electric machine used for the power-split HEV is a permanent magnet ac synchronous machine for its lower losses, higher torque density, and reliability. Hence, the focus of this work will be on permanent magnet ac synchronous machines used in HEVs. Fig. 4 shows the simplified model of a permanent magnet synchronous machine system. This figure shows the basic blocks involved in a permanent magnet synchronous machine system model. In this model, the desired electric machine torque is limited as a function of machine speed and highvoltage battery. A simple lookup controller determines the direct axis voltage Vd (in volts) and quadrature axis voltage Vq (in volts) parameters, which are used as inputs to the electric machine dynamics model. The electric machine dynamics equations, as derived from [18] and [19] and used in the model, are given as follows: dId − np ωm Lq Iq dt dIq + np ωm Ld Id Vq = Rs Iq + Lq dt + np ωm ψPM

Vd = Rs Id + Ld

3np (ψPM Iq + (Ld − Lq )Id Iq ) 2 dωm = Jm dt 3 = (Vd Id + Vq Iq ) 2 dθe = dt = np ωm

Tm = Tm − Tload − Tfr Pe ωe ωe

(2)

(3) (4) (5) (6) (7) (8)

where Id and Iq are the direct and quadrature axis currents (in amperes), respectively, Ld and Lq are the direct and quadrature axis inductances (in henries) respectively, ωm is the rotor

SYED et al.: DERIVATION AND EXPERIMENTAL VALIDATION OF A POWER-SPLIT HEV MODEL

mechanical speed (in radians per second), ωe is the electrical rotor speed (in radians per second), Rs is the series resistance (in ohms), np is the number of pole pairs, ψPM is the permanent electric machine flux (in webers), Jm is the electric machine inertia (in kilogram square meters), Tm is the mechanical electric machine torque (in newton meters), Tfr is the electric machine friction torque (in newton meters), Tload is the load torque (in newton meters), Pe is the electrical power (in watts), and θe is the electrical rotor angle (in radians). Using these equations, the final delivered torque, total power, and system losses can be calculated. Note that the system losses here refer to combined losses in both the motor and the inverter and are function of electric machine speed, its delivered torque, and terminal voltage of the battery [19]. It is clear from the equations above that the electric machine dynamic model developed requires knowledge of various machine parameters such as Rs , Ld , Lq , and ψPM . These parameters need to be calibrated under a simulation environment such that they closely match the experimental data. Use of such a complicated simulation model requires a lot of computing power and slows down the simulation times; hence, a simpler model could be used for specific conditions and studies, where empirical data relating to an electric machine’s maximum torque, speed, and power loss are available, and the importance for very accurate transient behavior of system is overshadowed by the slow time constants of engine subsystem. Under such conditions, empirical data are used to represent the electric machine model [31] and, hence, a first- or secondorder system, depending on the desired response or behavior, is used to represent the electric machine model. This way, the modeling for the inverter can be ignored, and inverter losses can be combined with the electric machine losses. The following equations represent the approximate modeling of electric machine when empirical data are available: Tm =

1 Tm_desired τs + 1

or Tm =

s2

ωn2 Tm_desired + 2ςωn s + ωn2

Pe = Tm ωm + Ploss

(9)

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experimental data are then used to determine appropriate values of time constant and damping ratio. Later, simulations are done with this electric machine subsystem to see if the desired response is achieved, and these parameters are further tuned to match the desired response. This process is repeated until the desired response is achieved. Under rare conditions, such as studying driveline behavior at electric machine’s maximum capabilities, where motor transient phenomenon [32] plays a very important role, the aforementioned first- or second-order approximation may not be used. In that case, the use of the previously mentioned detailed electric machine dynamic model to study such phenomena is required. 3) One-Way Clutch and Generator Brake Model: The oneway clutch is modeled to provide reaction torque when engine speed is negative, and zero when engine speed is positive. This is mathematically represented as follows:
dωeng when ωeng < 0 (11) Towc = kωeng − Jeng dt , 0, when ωeng ≥ 0 where Towc is the one-way clutch reaction torque (in newton meters), ωe is the engine speed (in radians per second), Jeng is the engine inertia (in kilogram square meters), and k is a constant that is tuned in the simulation environment. We modeled the desired generator brake, which was used in parallel mode as mentioned in Section II-A, using a friction coefficient that is a function of the percentage of slip and a constant normal force or torque as follows: Tgenbrk_des = kf Tk

(12)

where kf is the friction coefficient, and Tk is the normal constant torque (in newton meters). Appropriate values for these parameters are selected under a simulation environment in a manner that they match the experimental vehicle data. Finally, we used a first-order system transfer function to represent the dynamic response of the generator brake as follows: Tgen_brake
1 T , = τ s+1 genbrk_des 0,

when in parallel mode operation when in nonparallel mode operation

(10)

(13)

where Tm is the mechanical electric machine delivered torque (in newton meters), Tm_desired is the desired electric machine torque (in newton meters), Pe is the total electric machine power (in watts), Ploss is the electric machine power losses (in watts), and ωm is the electric machine speed (in radians per second). Again, the selection of appropriate time constant and damping ratio is critical, as these parameters reflect the response of the electric machine to the desired electric machine torque. The value selection for these parameters employs an iterative process where these parameters are calibrated under a simulation environment to match the experimental data. Again, this process is similar to the one described in Section II-B1, where an electric machine or the subsystem is used on a dynamometer to study the electric machine torque response to a desired torque at different electric machine speeds. These

where Tgen_brake is the generator brake torque (in newton meters). The generator brake torque response is achieved by carefully selecting appropriate values for the time constant. The appropriate time constant selection is done through various simulations using different values of time constants and selecting the value that closely matches the experimental data. 4) Planetary Gear Sets System Dynamics Model: The following assumptions are made for the derivation of planetary gear set system dynamics equations: 1) All shafts within the power plant are assumed to be rigid. 2) The inertia of the pinion gears is neglected because it is relatively small, and there is no interest in the torque acting on the pinion gears. The carrier inertia is lumped with engine inertia. The sun gear inertia is lumped with the generator rotor inertia. The inertia of the ring gear and

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shaft to the counter shaft, which is the ratio between gears 5 and 4 represented by Rg = N5 /N4 , Rmot2ring is the gear ratio from the motor to the ring gear, which is the ratio between gears 1 and 3 represented by Rmot2ring = N1 /N3 , Reng2gen is the gear ratio from the engine to the generator represented by (1 + 1/ρ), ρ is the planetary gear ratio, which is the ratio between the sun and ring gears represented by ρ = Ns /Nr , Jeng&carrier is the lumped moment inertia of the engine and the carrier gear (in kilogram square meters), Jgen&sun is the lumped moment inertia of the generator rotor and the sun gear (in kilogram square meters), and Jmot_lumped is the lumped moment inertia of the motor rotor, the ring gear, and all the gears (in kilogram square meters). Note that these parameters are calibrated under a simulation environment to match the experimental data. Substituting (17) into (16) yields

Fig. 5. Planetary gear sets system components diagram.

other gears as shown in Fig. 1, i.e., N1 , N2 , N3 , N4 , and N5 , are lumped with the motor rotor inertia. 3) The engine brake torque and speed in clockwise direction are positive. The generator torque and speed in clockwise direction are positive. The motor torque and speed in clockwise direction are positive (note that clockwise motor speed implies that the vehicle travels in the forward direction). The engine loss torque in the counterclockwise direction is positive. The one-way clutch torque in the counterclockwise direction is positive. The generator brake torque in the counterclockwise direction is positive. Fig. 5 shows the diagram of the planetary gear sets system components and the sign conventions for respective variables (torque and speed). From these assumptions, the dynamic equations are represented as follows: dωeng = Teng − Towc + Reng2gen Tsungear (14) dt dωmot 1 R2 = Tmot − R1 R2 Tsungear − Jmot_lumped Tdrive_sh dt ρ Rg Jeng&carrier

dωeng dt 1 dωmot + Jgen&sun R1 R2 . (18) ρ dt

Tsungear = Tgen − Tgen_brake − Jgen&sun Reng2gen

After substituting (18) into (14) and (15) and some mathematical manipulations, the governing dynamic equations of the planetary gear sets system are obtained as follows: dωeng dωmot − Jgen_couple dt dt = Teng − Towc + Reng2gen Tgen − Reng2gen Tgen_brake

Jeng_eff

(19) dωeng dωmot + Jmot_eff dt dt 1 R2 = Tmot − R1 R2 (Tgen − Tgen_brk ) − Tdrive_sh ρ Rg

− Jgen_couple

(20)

(15) Tsungear = Tgen − Tgen_brake − Jgen&sun

ωgen =

1 (1 + ρ) ωeng − R1 R2 ωmot ρ ρ

dωgen dt (16) (17)

where ωeng is the engine speed (in radians per second), ωmot is the motor speed (in radians per second), ωgen is the generator speed (in radians per second), Teng is the engine brake torque (engine combustion torque minus engine loss—in newton meters), Towc is the one-way clutch torque (in newton meters), Tmot is the motor torque (in newton meters), Tsungear is the sun gear torque (in newton meters), Tgen is the generator torque (in newton meters), Tgen_brake is the generator brake torque (in newton meters), Tdrive_sh is the drive shaft torque (in newton meters), R1 is the gear ratio from the counter shaft to the ring gear shaft, which is the ratio between gears 2 and 3 represented by R1 = N2 /N3 , R2 is the gear ratio from the motor shaft to the counter shaft, which is the ratio between gears 1 and 2 represented by R2 = N1 /N2 , Rg is the gear ratio from the drive

where 2 Jgen&sun Jeng_eff = Jeng&carrier + Reng2gen

Jgen_couple =

Reng2gen R1 R2 Rgen&sun Jgen&sun ρ

Jmot_eff = Jmot_lumped +

R1 R2 Jgen&sun . ρ2

(21) (22) (23)

Equations (18) and (19) are the mathematical representation of the planetary gear sets system dynamics. It can be seen that two differential equations are required to represent the planetary gear sets system since there are only two independent state variables, namely 1) engine speed and 2) motor speed. With some mathematical manipulation, (19) and (20) can be represented as follows: ˙ = βu αX

(24)

SYED et al.: DERIVATION AND EXPERIMENTAL VALIDATION OF A POWER-SPLIT HEV MODEL

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and other accessories. Hence, the battery power is calculated as follows: Pbatt = Pmot + Pgen + Paccessories .

(27)

The battery current (in amperes) is calculated as follows: Ibatt =

Fig. 6.

Block diagram for the planetary gear sets system modeling.

where  X= 

ωeng ωmot



 Teng  Towc     Tgen  u=   Tgen_brake    Tmot Tdrive_sh   Jeng_eff −Jgen_couple α= −Jgen_couple −Jmot_eff

1 −1 Teng2gen −T  eng2gen  β= T1 T2 T1 T2 0 0 − ρ ρ

0

0

1

− TTg2

.

With this manipulation, the dynamics of the planetary gear sets system can be represented in state-space equation as follows: ˙ = AX + Bu X

(25)

Y = CX + Du

(26)

where B = α−1 β, and 

 ωeng ω  Y =  mot  ωdrive ωgen   0 0 A= 0 0  1  0 C= 0   D=

0 1

Teng2gen

R2 Rg − R1ρR2

0 0

0 0

0 0

0 0

0 0

    0 0

 0 . 0

With the state-space representation of the planetary gear sets system dynamics, the planetary gear sets system model can now be described by the block diagram shown in Fig. 6. 5) Battery Dynamics Model: The power to or from the battery is the result of the power required by the motor, generator,

Pbatt Vbatt

(28)

where Vbatt is the battery voltage (in volts). To calculate the battery voltage Vbatt as a result of power draw, the battery voltage needs to be modeled. To evaluate the battery voltage, various battery models exist, which involve assuming battery as individual packs [33] having open-circuit voltage, internal resistances, and capacitances [19]. Note that other models employing internal resistances, battery inductances, and two depressed semicircles in the complex domain [37] can also be used to model the battery voltage. However, since the focus of the model is system dynamics and not internal battery dynamics, we choose to use a model as presented in [19]. If the data for open-circuit voltage, internal resistances, and capacitances are not known, then a practical battery model in [34]–[36] can be used to model the battery voltage. To calculate the battery state-of-charge SOCbatt (%), Peukert’s equation [39] can be used, but it requires that a given combination of current and discharge rate be known (through experimental curves) to calculate a new discharge rate corresponding to the current at a given time. This is an iterative approach for computing SOCbatt for a specific battery condition. Since the battery model [19] used for calculating the battery voltage assumes that battery data related to open-circuit voltage and internal resistances (which are also functions of the stateof-charge and battery temperature defined through experimental curves for both discharge and charge conditions) are known, an iterative approach similar to the Peukert’s equation approach using experimental data curves of battery parameters [19] is used to calculate the battery state-of-charge SOCbatt (in percent) at any given time by using the following equation:  Pbatt 100 SOCbatt = SOC0 + dt (29) 3600 · Abatt Vbatt where Abatt is the battery capacity (in ampere hours), and SOC0 (in percent) is the battery state-of-charge at the previous time step. Battery temperature is modeled using ambient temperatures, SOC, battery current, and battery voltage as inputs to empirical data to obtain battery temperature. This method for calculating battery temperature is sufficient since modeling the battery temperature accurately is not the main objective. Now that we have developed the models for the power sources and the energy storage device, engine, electric machines (motor and generator), one-way clutch, generator brake, and battery, the block diagram shown in Fig. 7 can be used to represent the complete power plant dynamics model. C. Brake System Model In a HEV, braking functionality is obtained via friction brakes or regenerative braking through the electric motor. In

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Fig. 7. Power plant dynamics model block diagram.

a typical HEV, it is the responsibility of the VSC to coordinate with the brake system controller and transaxle control module to determine and provide the amount of regenerative braking and friction braking to meet the driver’s braking request. Notice that the regenerative braking functionality is obtained through the electric motor. The dynamic equations for the motor are already explained in Section II-B2. Depending on the desired response behavior, the friction braking functionality can be expressed by using a first- or a second-order system. The transfer function used to represent the dynamic response of the friction braking for each wheel is given as follows:

Tfric_brake_tire =

1 1 η· Tfric_brake_desired 2 τs + 1

or

Tfric_brake_tire =

ωn2 1 η· 2 Tfric_brake_desired 2 s + 2ςωn s + ωn2 (30)

where Tfric_brake_desired is the desired friction braking torque (in newton meters) and Tfric_brake_tire is the friction braking torque (in newton meters) at each wheel, and η is the braking factor representing the braking effort between the front and rear wheels and can take a value between 0 and 1. If the braking factor η is calibrated to a constant value k for the front wheels, then its value is always 1 − k for the rear wheels. The value of k is selected in such a manner that most of the braking effort is done by the front wheels. The use of appropriate time constant is very important since this parameter reflects the response of the brakes to the desired vehicle friction braking torque request. Simulating friction braking torque response for a range of different time constants and then the time constant that corresponds closely to the experimental vehicle friction braking torque response is selected.

D. Driveline and Vehicle Model Fig. 8 shows the components and sign conventions of the driveline and vehicle dynamics system. Considering the half shaft compliance and wheel/tire dynamics, the mathematical representation of the driveline and vehicle dynamics is expressed by the following equations:

dθ = (2ωdrive_sh − ωwheel_right − ωwheel_left ) dt (31) 1 dωwheel_right = (Thalf _sh −Tbrake_right −Ftire_right rw ) dt Jw (32) dωwheel_left 1 = (Thalf _sh − Tbrake_left − Ftire_left rw ) dt Jw (33) dV 1 = (Ftire_right − Ftire_left − Fresist ) dt M (34) Thalf _sh = Ks θ + Rsh (2ωdrive_sh − ωwheel_right − ωwheel_left )

(35)

Ftire_right = f (ωwheel_right , V, µroad , Nwheel_right ) (36) Ftire_left = f (ωwheel_left , V, µroad , Nwheel_left )

(37)

Fresist = Faerodyn_resist + Ftireroll_resist

Faerodyn_resist Ftireroll_resist

+ Froad_surface + Fother_road_load 1 = ρCd Af V 2 2 = 9.8µroll M (|V |kv + Cv )

(38) (39) (40)

Froad_surface = 9.8M sin(θroad_grade ) + 9.8M µroad cos(θroad_grade ) Fother_road_load = b0 + b1 V + b2 V

2

(41) (42)

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Fig. 9. Block diagram for the driveline and vehicle dynamics model.

Fig. 8.

Driveline and vehicle dynamics system.

where θ is effective displacement of half shaft (in radians), ωwheel_right and ωwheel_left are the right and left wheel speeds (in radians per second), respectively, V is the vehicle speed (in meters per second), Thalf _sh is half shaft torque (in newton meters), Ftire_right and Ftire_left are the right and left tire force (in newtons), respectively, which are functions of wheel slip (determined through wheel speeds ωwheel_right and ωwheel_left and vehicle velocity V ), Nwheel_right and Nwheel_left are normal forces (in newtons), µroad is the road coefficient of friction, rw is the effective radius (in meters), M is the vehicle mass (in kilograms), and Fresist is the resistance force (in newtons) including aerodynamic drag force, rolling resistance force, and road surface force [37], [38]. The aerodynamic drag force (in newtons) is represented by (39), where ρ is the air density (in kilograms per cubic meter), Cd is the road coefficient of drag, V is the vehicle velocity (in meters per second), and Af is the frontal area (in square meters) of the vehicle. The rolling resistance force is represented by (40), where µroll is tire rolling coefficient, M is the vehicle mass (in kilograms), V is the vehicle velocity (in meters per second), kv is velocity dependence coefficient, which is a function of vehicle velocity and is obtained through test data, and Cv is a constant, which is also obtained through test data. The road surface force (in newtons) is represented by (41). Fother_road_load , which is represented by (42), is the portion of the resistance force component (in newtons) to accommodate for the difference between the experimental results and the other components of resistance force; therefore, this term represents the correction between the aerodynamic drag force, rolling resistance force, driveline gear losses, planetary gear losses, chassis losses, and brake losses. Again, these parameters are calibrated under a simulation environment to match the experimental data. Equations (31)–(35) represent the driveline dynamics model and (36)–(42) represent the vehicle dynamics model. These equations clearly show that there are four state variables, which are the equivalent half shaft displacement, the right and left wheel speeds, and the vehicle speed. This mathematical representation can be described in the block diagram as shown in Fig. 9.

Fig. 10. HEV simulation model—top level.

E. Model Architecture/Construction MATLAB-SIMULINK tools were used for model architecture development and simulations. For the purpose of this power train system dynamics study and control system development, it is necessary to integrate the developed dynamics models with a driver and environmental inputs model and a VSC. The complete simulation environment for power-split HEV power train model will therefore consist of the driver and environmental model, the vehicle controller, and the plant model for the power-split HEV. The plant model for the powersplit HEV under simulation is developed by integrating the developed subsystems’ mathematical representations and models in a hierarchical architecture, as shown in Figs. 10 and 11. The subsystems in this architecture are modularized, which enables us, when needed, to easily change a subsystem model to one with different capability required for a different purpose. For example, if one is interested in very accurate transients of engine torque generation with different input conditions such as temperature and air mass, a more sophisticated engine model can be used. Such a sophisticated model can be plugged into the engine model block shown in Fig. 3 without requiring any other interface changes in order to perform a study. Similarly, if one is interested in using induction machines instead of permanent magnet synchronous machines for motor and generator, then such a model can be plugged into the electric machine model block shown in Fig. 4 without requiring interface changes. The “driver and environmental inputs” block in Fig. 10 contains the driver model that generates driver inputs (e.g., accelerator and brake pedal commands) and the environmental conditions such as road coefficient of friction, road grade, and ambient temperature. The “vehicle system controller” block contains the VSC, transmission control module (TCM), engine controller, battery control module (BCM), and brake system

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Fig. 11. Complete power-split power train HEV dynamics plant model. TABLE I VEHICLE AND SUBSYSTEMS SPECIFICATIONS

module (BSM). The power-split power train HEV dynamics plant model block contains power plant dynamics model, brake system dynamics model, driveline dynamics, and vehicle dynamics model, as shown in Fig. 11. Note that the detail of the power plant block is already shown in Fig. 7, whereas the driveline and vehicle dynamics blocks are shown in Fig. 9. III. M ODEL V ALIDATION R ESULTS A. Qualitative Validation Using Computer Simulation The goal of this step is to see if the developed powersplit HEV dynamics model under simulation behaves the same way as the actual vehicle with all the possible modes such as electric drive mode, positive split mode, parallel mode, and negative split mode. In order to collect experimental data, the vehicle was equipped with torque, speed, current, and voltage sensors to accurately measure the torques, speeds, currents, and voltages of specific subsystems. The vehicle and power train specifications are shown in Table I. For validation purposes, a

functional vehicle controller model (provided by Ford Motor Company for this study) along with the power-split HEV dynamics plant model developed in Section II-E was also used. Approximate values for parameters related to the engine, motor, generator, battery, brake system, driveline, and vehicle models were initially used for simulation purposes. Several simulations were performed to tune these parameters to actual vehicle values. Tuning these parameters is also an iterative process, where the HEV is mounted on a dynamometer to study the vehicle’s response to a desired driver inputs at different vehicle speeds and subsystem conditions. These experimental data are then used to confirm and fine-tune the appropriate subsystem parameter values. Later, complete vehicle simulations are done with these parameters to see if the desired response is achieved, and these parameters are further tuned to match the desired response. This process is repeated until the desired response is achieved. After various simulation iterations, these parameters were fine-tuned to match the desired behavior for this specific vehicle and driving conditions such as ambient temperature and pressure.

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Fig. 12. Acceleration from 0 to 26.82 m/s (0 to 60 mi/h) and deceleration to 0 m/s (0 mi/h)—simulation results.

Fig. 12 shows a simulation result using the following driving scenario: a 0- to 26.82-m/s (0 to 60 mi/h) full accelerator pedal takeoff, then a constant 26.82-m/s (60 mi/h) speed, and finally, deceleration down to 0 m/s (0 mi/h). The reason for using such a drive cycle over standard cycles is that this drive cycle ensures the operation of the vehicle under all its hybrid modes and, at the same time, is very effective to study speed, torque, and power responses of the hybrid vehicle. The top graph in the figure shows the engine speed and generator speed in revolutions per minute and vehicle speed in meters per second (multiplied by 223.7 for scaling) or miles per hour (multiplied by 100 for scaling). The bottom graph shows the engine torque (in newton meters), generator torque (in newton meters), and motor torque (in newton meters) responses. Based on the driving scenario, the model responded appropriately and demonstrated the expected operating modes: electric drive mode, positive split mode, parallel mode, and negative split mode. These modes are illustrated in the bottom graph of Fig. 12. It can be seen in Fig. 12 that in the EV mode, the vehicle is propelled by the an electric motor powered by the battery, which is evident from the motor, generator, and engine torques and speeds. After engine start, the generator provides negative or reaction torque to transmit the engine output to the drivetrain. For the given vehicle speed and engine speed, the generator is rotating in the positive direction, which is in accordance with the defined sign convention. The motor torque varies based on the driver demand and engine/generator response. This operation is the positive split mode. When the generator speed and torque are zero, which implies that the generator brake is actuated, the vehicle is in the parallel mode, and the motor torque depends on the engine torque output. In the negative split mode, the generator provides negative torque, as in the positive split mode, but the generator is rotating in the negative direction. Furthermore, the motor torque varies accordingly in

the negative split mode similar to the positive split mode. Notice also that at around 60 s, the motor torque is compensating for the desired driver demand to maintain the drive trace, resulting in a supplemental tractive force being provided through the battery, thereby providing an opportunity for fuel economy improvement by using the battery power instead of the engine torque to provide the transient driver demand. B. Quantitative Validation Using Test Track Experimental Data The developed power-split HEV dynamics plant model was further validated by comparing critical power train and vehicle variables of the model with those measured during the experimental vehicle testing on the Ford Motor Company’s test track. The first task was the selection of drive cycle for quantitative model validation. As a first test, the federal test procedure (FTP) city drive cycle was used for the validation of the developed power-split HEV dynamics plant model. This drive cycle was used mainly for fuel-economy-related validation. Using this drive cycle, our simulations using the developed plant model predicted the fuel economy of the vehicle to be 6.34 L/100 km (38.3 mpg) in the city test, which is very close to the experimental measured value of 6.32 L/100 km (38.4 mpg). Overall, analyzing various FTP results, the simulations using the developed plant model predicted the fuel economy with a 90% confidence interval to be within 0.066 L/100 km (0.16 mpg) accuracy. We also compared the engine-on time under FTP city drive cycle for both the model and experimental vehicle results. The engine-on time predicted was 54.9%, which is very close to the experimental result of 54.4%. Similarly, the battery power during this cycle predicted was 7.72 kW, which is, again, very close to the experimental result of 7.41 kW. It is clear from these tests that the behavior of the developed plant model was very close to the experimental vehicle under FTP city drive cycles.

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Fig. 13. Vehicle speed and wheel torque validation. Plot [A] shows the vehicle speed simulation and experiment results. Plot [B] shows the difference between experimental data and simulation data versus experimental data for vehicle speed. Plot [C] shows the wheel torque simulation and experiment results. Plot [D] shows the difference between experimental data and simulation data versus experimental data for wheel torque. See analysis data in Table II.

Since the objective was to develop the plant model capable of studying the subsystem’s speed, torque, and power responses, a specific short stop-and-go driving test on the test track was designed to validate the subsystem’s speed, torque, and power responses. By using such a short drive cycle, this specifically designed short stop-and-go driving test on the test track would help in emphasizing more on speed, torque, and power responses validation of the HEV. The desired power train and vehicle variables were recorded for validating the model developed earlier in this paper. In the model, validation simulation, signals of accelerator, and brake pedal commands from the test data were used as inputs to the model, and vehicle weight (1820 kg) and road load in the model were properly adjusted based on the actual testing conditions. In order to know if the experimental results obtained are very close or the same as the vehicle simulation results, the experimental and simulations results first need to be aligned such that there are no timing delays between the two data set results at the beginning of the event. The analysis method employed made use of the fact that if the experimental and simulation results are exactly the same, then a plot of simulation result versus the experimental result would be a straight line with a slope of 1. Therefore, in other words, a plot of the difference between the experimental and the simulation result versus the experimental result would ideally have a straight line with both slope and offset of zero. Figs. 13–18 illustrate these validation results. The following variables/parameters are compared between vehicle experimental data and simulation result in Figs. 13–18: 1) vehicle speed (in meters per second) and wheel torque (in newton meters); 2) engine speed (in revolutions per minute) and

engine torque (in newton meters); 3) generator speed (in revolutions per minute) and generator torque (in newton meters); 4) motor speed (in revolutions per minute) and motor torque (in newton meters); 5) battery power (in kilowatts) and battery voltage (in volts); and 6) battery state of charge (in percent) and battery temperature (in degrees Celsius). These are the variables that could completely define the behavior of power-split-type HEV operation of interest. Plots [A] and [C] of Figs. 13–18 show the comparison between the experimental and simulated results for various vehicle system parameters, whereas plots [B] and [D] reveal the analysis performed on plots [A] and [C], respectively. This analysis includes mean and standard deviation of the difference between the experimental and simulation results and the linear curve fitting to the difference. The slope and offset of the fitted linear equation is used to show the closeness between simulation and experimental results. Finally, the 90% confidence interval for this difference was computed to show the range with a 90% probability that the simulation results could represent the experimental results. The results of these analyses are summarized in Table II. The interpretations of the results in Table II are similar. For example, plot [A] of Fig. 13 shows the experimental and simulated vehicle speed comparison. The simulation and experimental vehicle speed results are very close, as the analysis on the vehicle speed parameter in Table II clearly shows that the mean and standard deviation of the difference between simulation and experimental vehicle speed results are negligible. The linear fit shows a very small slope, i.e., 0.058, and a very small offset, i.e., −0.214 m/s, indicating a very small difference between experimental and simulation results. The 90% confidence

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Fig. 14. Engine speed and engine torque validation. Plot [A] shows the engine speed simulation and experiment results. Plot [B] shows the difference between experimental data and simulation data versus experimental data for engine speed. Plot [C] shows the engine torque simulation and experiment results. Plot [D] shows the difference between experimental data and simulation data versus experimental data for engine torque. See analysis data in Table II.

Fig. 15. Generator speed and generator torque validation. Plot [A] shows the generator speed simulation and experiment results. Plot [B] shows the difference between experimental data and simulation data versus experimental data for generator speed. Plot [C] shows the generator torque simulation and experiment results. Plot [D] shows the difference between experimental data and simulation data versus experimental data for generator torque. See analysis data in Table II.

interval indicates that there is a 90% probability that the difference between the experimental and simulation results will be between −2.82 and 1.38 m/s. Similar interpretation can be made for the rest of the comparisons in Table II. The conclusion for the analysis of each of them is the same—the

experimental and simulation results are reasonably close. The only exception is that if one closely looks at plot [D] of Fig. 14, he or she could interpret that an engine torque difference of 20 Nm between experimental and simulation results is possible, but as this HEV operates engine at its most efficient point

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Fig. 16. Motor speed and motor torque validation. Plot [A] shows the motor speed simulation and experiment results. Plot [B] shows the difference between experimental data and simulation data versus experimental data for motor speed. Plot [C] shows the motor torque simulation and experiment results. Plot [D] shows the difference between experimental data and simulation data versus experimental data for motor torque. See analysis data in Table II.

Fig. 17. Battery power and battery voltage validation. Plot [A] shows the battery power simulation and experiment results. Plot [B] shows the difference between experimental data and simulation data versus experimental data for battery power. Plot [C] shows the battery voltage simulation and experiment results. Plot [D] shows the difference between experimental data and simulation data versus experimental data for battery voltage. See analysis data in Table II.

(> 120 Nm), the difference between the experimental and simulation results for engine torque is actually less than 17%, which is well suited, as modeling engine torque more accurately does not provide huge benefits for studying overall system

response and control system development. Altogether, these comparisons demonstrate that the simulated vehicle response is very close to the actual vehicle response, which implies that the vehicle system parameters or variables in the power

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Fig. 18. Battery state-of-charge and battery temperature validation. Plot [A] shows the state-of-charge simulation and experiment results. Plot [B] shows the difference between experimental data and simulation data versus experimental data for state-of-charge. Plot [C] shows the battery temperature simulation and experiment results. Plot [D] shows the difference between experimental data and simulation data versus experimental data for battery temperature. See analysis data in Table II. TABLE II ANALYSIS ON DIFFERENCE BETWEEN EXPERIMENTAL AND SIMULATION RESULTS ON VARIOUS VEHICLE SYSTEM PARAMETERS

train/vehicle model developed in this paper responded to the driver demand (accelerator pedal) in almost the same way as the actual vehicle and that the developed model represents the actual power train/vehicle system with reasonable accuracy.

IV. C ONCLUSION Developing control algorithms and studying steady-state and transient behaviors of a power-split HEV power train requires the availability of a dynamic model for the power train. This

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paper describes the mathematical modeling, analysis, model architecture, simulation, and validation of a power-split power train HEV. This paper also describes the operation of the power-split power train system along with the mathematical representations for modeling the major subsystems in this power train system and its incorporation into a complete powersplit power train HEV model. The complete power-split HEV model was built by integrating the subsystem models using a system-oriented approach with a hierarchical methodology that makes it very convenient for updating or replacing subsystem functionality. The simulation results demonstrate qualitatively that the developed model represents the power-split power train operation and the interaction among subsystems. Further simulation and experiment results presented illustrate quantitatively the fidelity of the model. The model was validated through the comparison of the critical variables in the model with those actually measured in a test vehicle on the Ford test track. The validation reveals that the developed model predicts the power train response with reasonable accuracy and has a relatively high degree of fidelity. In conclusion, the developed model is effective for simulation study and analysis of this power train operation and for demonstrating the interaction among the various subsystems. The model can be used as a very effective tool for advanced control system development for power-split HEVs. It can also be used for issue resolution, development of new control system strategies, and verification of coded algorithms, among many other purposes. R EFERENCES [1] C. C. Chan, “The state of the art of electric and hybrid vehicles,” Proc. IEEE, vol. 90, no. 2, pp. 247–275, Feb. 2002. [2] R. Dettmer, “Hybrid pioneers [hybrid electric vehicles],” IEE Rev., vol. 49, no. 1, pp. 42–45, Jan. 2003. [3] G. Maggetto and J. Van Mierlo, “Electric and electric hybrid vehicle technology: A survey,” in Proc. IEE Semin. Elect., Hybrid and Fuel Cell Veh. (Ref. No. 2000/050), Apr. 11, 2000, pp. 1–11. [4] F. A. Wyczalek, “Hybrid electric vehicles (EVS-13 Osaka),” in Proc. Northcon, Nov. 4–6, 1996, pp. 409–412. [5] C. C. Chan and Y. S. Wong, “Electric vehicles charge forward,” IEEE Power Energy Mag., vol. 2, no. 6, pp. 24–33, Nov./Dec. 2004. [6] R. Nesbitt, C. Muehlfeld, and S. Pandit, “Powersplit hybrid electric vehicle control with electronic throttle control (ETC),” presented at the SAE Int., Powertrain and Fluid Systems Conf. and Exhibition, Pittsburgh, PA, Oct. 2003, Paper 2003-01-3280. [7] F. Syed and J. Czubay, “Improving the efficiency of production level algorithm development for an SUV HEV powertrain,” presented at the SAE Powertrain and Fluid Systems Conf. and Exhibition, San Antonio, TX, Oct. 2004, Paper 2004-01-3039. [8] R. A. Mcgee, “Model-based control system design and verification for a hybrid electric vehicle,” presented at the SAE Tech. Paper Series, Future Transportation Technology Conf., Costa Mesa, CA, Jun. 2003, Paper 2003-01-2308. [9] P. Caratozzolo, M. Serra, and J. Riera, “Energy management strategies for hybrid electric vehicles,” in Proc. IEEE IEMDC, Jun. 1–4, 2003, vol. 1, pp. 241–248. [10] A. Piccolo, L. Ippolito, V. Galdi, and A. Vaccaro, “Optimisation of energy flow management in hybrid electric vehicles via genetic algorithms,” in Proc. IEEE/ASME Int. Conf. Adv. Intell. Mechatronics, Jul. 8–12, 2001, vol. 1, pp. 434–439. [11] G. Rizzoni, L. Guzzella, and B. M. Baumann, “Unified modeling of hybrid electric vehicle drivetrains,” IEEE/ASME Trans. Mechatronics, vol. 4, no. 3, pp. 246–257, Sep. 1999. [12] G. A. Hubbard and K. Youcef-Toumi, “Modeling and simulation of a hybrid–electric vehicle drivetrain,” in Proc. Amer. Control Conf., Jun. 4–6, 1997, vol. 1, pp. 636–640.

[13] S. R. Cikanek, K. E. Bailey, and B. K. Powell, “Parallel hybrid electric vehicle dynamic model and powertrain control,” in Proc. Amer. Control Conf., Jun. 4–6, 1997, vol. 1, pp. 684–688. [14] B. Powell, X. Zhang, R. Baraszu, and P. Bowles, “Computer model for a parallel hybrid electric vehicle (PHEV) with CVT,” in Proc. Amer. Control Conf., Jun. 28–30, 2000, vol. 2, pp. 1011–1015. [15] S. R. Cikanek, K. E. Bailey, R. C. Baraszu, and B. K. Powell, “Control system and dynamic model validation for a parallel hybrid electric vehicle,” in Proc. Amer. Control Conf., Jun. 2–4, 1999, vol. 2, pp. 1222–1227. [16] J. A. MacBain, J. J. Conover, and A. D. Brooker, “Full-vehicle simulation for series hybrid vehicles,” presented at the SAE Tech. Paper, Future Transportation Technology Conf., Costa Mesa, CA, Jun. 2003, Paper 2003-01-2301. [17] X. He and J. Hodgson, “Hybrid electric vehicle simulation and evaluation for UT-HEV,” presented at the SAE Tech. Paper Series, Future Transportation Technology Conf., Costa Mesa, CA, Aug. 2000, Paper 200001-3105. [18] K. E. Bailey and B. K. Powell, “A hybrid electric vehicle powertrain dynamic model,” in Proc. Amer. Control Conf., Jun. 21–23, 1995, vol. 3, pp. 1677–1682. [19] B. K. Powell, K. E. Bailey, and S. R. Cikanek, “Dynamic modeling and control of hybrid electric vehicle powertrain systems,” IEEE Control Syst. Mag., vol. 18, no. 5, pp. 17–33, Oct. 1998. [20] K. L. Butler, M. Ehsani, and P. Kamath, “A Matlab-based modeling and simulation package for electric and hybrid electric vehicle design,” IEEE Trans. Veh. Technol., vol. 48, no. 6, pp. 1770–1778, Nov. 1999. [21] K. B. Wipke, M. R. Cuddy, and S. D. Burch, “ADVISOR 2.1: A user-friendly advanced powertrain simulation using a combined backward/forward approach,” IEEE Trans. Veh. Technol., vol. 48, no. 6, pp. 1751–1761, Nov. 1999. [22] T. Markel and K. Wipke, “Modeling grid-connected hybrid electric vehicles using ADVISOR,” in Proc. 16th Annu. Battery Conf. Appl. and Adv., Jan. 9–12, 2001, pp. 23–29. [23] S. M. Lukic and A. Emadi, “Effects of drivetrain hybridization on fuel economy and dynamic performance of parallel hybrid electric vehicles,” IEEE Trans. Veh. Technol., vol. 53, no. 2, pp. 385–389, Mar. 2004. [24] A. Emadi and S. Onoda, “PSIM-based modeling of automotive power systems: Conventional, electric, and hybrid electric vehicles,” IEEE Trans. Veh. Technol., vol. 53, no. 2, pp. 390–400, Mar. 2004. [25] J. M. Tyrus, R. M. Long, M. Kramskaya, Y. Fertman, and A. Emadi, “Hybrid electric sport utility vehicles,” IEEE Trans. Veh. Technol., vol. 53, no. 5, pp. 1607–1622, Sep. 2004. [26] M. Schulz, “Circulating mechanical power in a power-split hybrid electric vehicle transmission,” Proc. Instrum. Mech. Eng.—Part D J. Automob. Eng., vol. 218, no. 12, pp. 1419–1425, Dec. 2004. [27] G. Y. Liao, T. R. Weber, and D. P. Pfaff, “Modelling and analysis of powertrain hybridization on all-wheel-drive sport utility vehicles,” Proc. Instrum. Mech. Eng.—Part D J. Automob. Eng., vol. 218, no. 10, pp. 1125–1134, Oct. 2004. [28] D. Zhang, J. Chen, T. Hsieh, J. Rancourt, and M. R. Schmidt, “Dynamic modelling and simulation of two-mode electric variable transmission,” Proc. Instrum. Mech. Eng.—Part D J. Automob. Eng., vol. 215, no. 11, pp. 1217–1223, Nov. 2001. [29] S. R. Cikanek and K. E. Bailey, “Regenerative braking system for a hybrid electric vehicle,” in Proc. Amer. Control Conf., May 8–10, 2002, vol. 4, pp. 3129–3134. [30] L. U. Gokdere, K. Benlyazid, E. Santi, C. W. Brice, and R. A. Dougal, “Hybrid electric vehicle with permanent magnet traction motor: A simulation model,” in Proc. Int. Conf. IEMD, May 9–12, 1999, pp. 502–504. [31] S. M. Lukic and A. Emado, “Modeling of electric machines for automotive applications using efficiency maps,” in Proc. Elect. Insul. Conf. and Elect. Manuf. Coil Winding Technol. Conf., Sep. 23–25, 2003, pp. 543–550. [32] C. Shukang, P. Yulong, C. Feng, and C. Shumei, “The torque pulsation analysis of a starter generator with concentrated windings based hybrid electric vehicles,” in Proc. IEEE IEMDC, Jun. 1–4, 2003, vol. 1, pp. 218–221. [33] E. Hansen, L. Wilhelm, N. Karditsas, I. Menjak, D. Corrigan, S. Dhar, and S. Ovshinsky, “Full system nickel-metal hydride battery packs for hybrid electric vehicle applications,” in Proc. 17th Annu. Battery Conf. Appl. and Adv., Jan. 15–18, 2002, pp. 253–260. [34] X. He, “Battery modeling for HEV simulation model development,” presented at the SAE Tech. Paper Series, World Congr., Detroit, MI, Mar. 2001, Paper 2001-01-0960. [35] X. He and J. W. Hodgson, “Modeling and simulation for hybrid electric vehicles—I: Modeling,” IEEE Trans. Intell. Transp. Syst., vol. 3, no. 4, pp. 235–243, Dec. 2002.

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[36] ——, “Modeling and simulation for hybrid electric vehicles—II: Simulation,” IEEE Trans. Intell. Transp. Syst., vol. 3, no. 4, pp. 244–251, Dec. 2002. [37] A. C. Baisden and A. Emadi, “ADVISOR-based model of a battery and an ultra-capacitor energy source for hybrid electric vehicles,” IEEE Trans. Veh. Technol., vol. 53, no. 1, pp. 199–205, Jan. 2004. [38] M. Ehsani, K. M. Rahman, and H. A. Toliyat, “Propulsion system design of electric and hybrid vehicles,” IEEE Trans. Ind. Electron., vol. 44, no. 1, pp. 19–27, Feb. 1997. [39] Y. Yang, M. Parten, J. Berg, and T. Maxwell, “Modeling and control of a hybrid electric vehicle,” in Proc. 52nd IEEE VTS—Fall VTC, Sep. 24–28, 2000, vol. 5, pp. 2095–2100. [40] J. Van Mierlo and G. Maggetto, “Vehicle simulation program: A tool to evaluate hybrid power management strategies based on an innovative iteration algorithm,” Proc. Instrum. Mech. Eng.—Part D J. Automob. Eng., vol. 215, no. 9, pp. 1043–1052, Sep. 2001. [41] ——, “Innovative iteration algorithm for a vehicle simulation program,” IEEE Trans. Veh. Technol., vol. 53, no. 2, pp. 401–412, Mar. 2004.

Fazal U. Syed received the B.S. degree in electrical engineering from the Technical University of Budapest, Budapest, Hungary, in 1992 and the M.S. degree in electrical engineering from Wayne State University, Detroit, MI, in 1995, where he is currently working toward the Ph.D. degree. He joined Servotech Engineering in 1995 and worked on various vehicle, engine, electrical, and electronic control design projects. He joined Ford Motor Company’s Hybrid Electric Vehicle Program as a Lead Design Engineer in September 2002. He has published technical papers in various conferences. He is the holder of various U.S./European patents and patent pending in the area of diesel and hybrid electric vehicle controls. Mr. Syed received the 2005 Henry Ford Technology Award, which is the highest technical achievement recognition and most prestigious award in the Ford Motor Company, for his work related to development of the hybrid electric vehicle control system.

Ming L. Kuang received the M.S. degree in mechanical engineering from the University of California, Davis, in 1991. He joined Ford Motor Company’s Electric Vehicle Programs as a Control System Engineer in April 1991, where he was responsible for electric vehicle (EV) and hybrid EV (HEV) system/power train control development. In 1995, he joined Ford Research Laboratory as a Research Engineer, conducting research on traction control, antilock brakes, and interactive vehicle dynamics (IVD) or vehicle stability control. In 2000, he joined a production HEV program as an HEV Control Technical Expert, leading the vehicle control system development and implementation for hybrid vehicle programs. He has published numerous technical papers in ASME, ACC, AVEC, International Electric Vehicle Symposium, and International Modelica Conferences. He is the holder of 29 U.S./European patents and has a patent pending in the area of IVD and EV/HEV controls. Mr. Kuang received the 2005 Henry Ford Technology Award, which is the highest technical achievement recognition and most prestigious award in the Ford Motor Company.

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John Czubay (M’92–S’97–M’98) received the M.S. degree in control systems from Wayne State University, Detroit, MI, in 1997. He is a Research Engineer with the Research and Innovation Center, Ford Motor Company, Dearborn, MI. His research focuses on the development of advanced control algorithms for new power train technologies to continually reduce the impact that automobiles have on the environment. His interests include the application of control theory to hybrid electric and clean-diesel-powered vehicles. His work includes the use of simulation and rapid prototyping for the rapid and robust development of real-time control algorithms for embedded controllers. Mr. Czubay is a member of the Society of Automotive Engineers.

Hao Ying (S’88–M’90–SM’97) received the B.S. and M.S. degrees in electrical engineering from Donghua University (formerly China Textile University), Shanghai, China, in 1982 and 1984, respectively, and the Ph.D. degree in biomedical engineering from the University of Alabama at Birmingham in 1990. He is a Professor with the Department of Electrical and Computer Engineering and a Full Member of the Barbara Ann Karmanos Cancer Institute, Wayne State University, Detroit, MI. He was in the faculty of the University of Texas Medical Branch at Galveston between 1992 and 2000. He was an Adjunct Associate Professor with the Biomedical Engineering Program, University of Texas at Austin, between 1998 and 2000. He has published one research monograph/advanced textbook entitled Fuzzy Control and Modeling: Analytical Foundations and Applications (New York: IEEE Press, 2000), 72 peer-reviewed journal papers, and 102 conference papers. He is an Associate Editor of four international journals (International Journal of Fuzzy Systems, International Journal of Approximate Reasoning, Journal of Intelligent and Fuzzy Systems, and Dynamics of Continuous, Discrete & Impulsive Systems—Series B: Applications and Algorithms). He has been a Guest Editor for several journals. He was invited to serve as a Reviewer for more than 50 international journals, which are in addition to major international conferences and book publishers. Prof. Ying is an elected Board Member of the North American Fuzzy Information Processing Society (NAFIPS). He served as the Program Chair for the 2005 NAFIPS Conference as well as for the International Joint Conference of NAFIPS Conference, the Industrial Fuzzy Control and Intelligent System Conference, and the NASA Joint Technology Workshop on Neural Networks and Fuzzy Logic held in 1994. He served as the Publication Chair for the 2000 IEEE International Conference on Fuzzy Systems and as a Program Committee Member for over 20 international conferences.