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ABSTRACT

The continuous increase of pollutants and fine particulates is

mainly caused by cars circulating worldwide. Therefore, it is

necessary to replace internal combustion engines with the

cleanest electric motors. The short term solution is

represented by Hybrid Electric Vehicles (HEVs) due to its

environmental and efficiency characteristics. In the present

paper a dynamic feed-forward mathematical model for a

hybrid vehicle performance analysis is proposed. Torque and

power, pollutant emission, fuel consumption, battery pack

state of charge, as well as speed and acceleration have been

evaluated by means of simulation of United State and

Japanese standard driving cycles. In order to carry out

simulations on a real hybrid configuration, the model has been based on the powertrain installed on the Toyota Prius

(Toyota Hybrid System - THS). A mathematical sub-model

of each vehicle component has been implemented to simulate

the real vehicle behavior in all possible running conditions.

To do so, a rule-based control strategy was also implemented

to manage the energy flows during vehicle motions taking

into account battery pack state of charge, vehicle speed,

engine and motor torques, as well as power generation in

regenerative breaking condition. In order to assess the

effectiveness and accuracy of the implemented mathematical

model, different simulations on standard driving cycles have

been carried out, and results have been compared with

experimental data found in scientific literature. The

comparison shows a well evident agreement between

simulated and experimental data in different running

conditions. Furthermore, in an acceleration test from 0 km/h

to 100 km/h, the response of the simulated vehicle has been

evaluated, and results showed a good agreement between

simulated and experimental data. The developed

mathematical model is a powerful tool to study the dynamics

of powertrain system and the interaction between

components. It is also possible to try out new control

strategies able to reduce fuel consumption and pollutants

emissions maintaining at the same time the required performance.

INTRODUCTIONToday, evermore stringent anti-pollution laws and the

pressing need for energy saving are driving the technologica

development of increasingly efficient propulsion [1].

Hybrid propulsion systems are nowadays a short-medium

term solution for obtaining higher efficiency targets and

lower pollutant emissions thanks to the interconnection of

two propulsion systems. At present the most common

solution is the combination of an internal combustion engineand an electric motor.

Both industrial and scientific research have given great

impetus to such technology.

As regards the car industry, in 1997 Toyota Motor Corp

marketed their first hybrid vehicle, the Prius, first in Japan

and then worldwide in 2001. Honda followed suit with their

Insight, marketed in 2000. Since then, Toyota has been

working on several THS (Toyota Hybrid System) propulsion

versions, which will be marketed in Europe from 2010, all

based on a hybrid Series/Parallel configuration.

The research community has mainly focused on energy-flow

optimization and overall vehicle-propulsion management, so

as to further reduce fuel consumption and pollutants. So, to

optimize these flows and performance, there are two main

approaches: experimental and numerical modeling.

This latter approach is preferred, especially by the scientific

community, because mathematical models ensure fas

technological low-cost development which can then be tested

experimentally for optimized solutions.

Hybrid Vehicles Performances Analysis: Feed-

Forward Dynamic Approach

2010-01-1443

Published

05/05/2010

S. Brusca, A.T. Galvagno, R. Lanzafame and M. MessinaUniv. of Catania

Copyright © 2010 SAE Internationa

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Mathematical models [2], depending on level of accuracy, are

divided into three main categories: static, quasi-static and

dynamic. The first two [3 and 4], feature a backward vehicle

simulation, while the last is a forward one. In the first case,

the simulation starts from the cycle-imposed speed which,

with backward calculations, is able to determine the

consumption of the fuel needed to run the imposed cycle. In

forward models, the simulated vehicle speed is controlled bythe driver, as in reality, to follow the imposed cycle; this

provides actual fuel consumption, pollutant emissions and

predicts vehicle perfor mance.

The main advantages of using a static or quasi-static model

lie in simpler implementation of the model and quicker

computations, but this also entails less accurate results in

dynamic simulations and inadequacy in simulating vehicle

performance. By contrast, dynamic models, being more

complex to accomplish and requiring more computing time,

obtain more accurate results in dynamic simulations as well

as predicting the real performance of simulated vehicles.

Besides, these models best lend themselves to the study and

development of control strategies for engines and the

generation and storage of electricity.

The present work deals with the study of a hybrid vehicle, by

implementing a dynamic mathematical model to simulate the

Toyota Prius THS performance.

DYNAMIC MODELA feed-forward mathematical model was studied and

implemented for a vehicle with hybrid Series/Parallel

propulsion.

Figure 1 shows the Simulink® environment/mathematical

model of the Toyota Prius THS, listing all the main elements:

• Driver

• Control Unit (CU)

• Internal Combustion Engine (ICE)

• Electric Motor (MG1)

• Electric Power generator (MG2)

• Power Split Device (PSD)• Battery

• Wheel and vehicle Dynamics

(See Figure 1 after last section of paper)

This model is a feedback model, where the control parameter

is the simulated vehicle speed. A brief description of each

component is given below.

DRIVER In the Driver subsystem, driving-cycle imposed speed and

feedback simulated speed are compared. The comparison

error is managed by two PID controllers, one for the

accelerator, the other for the brake, the function of which is to

control the related variable, in this case the vehicle simulated

speed so as to follow, as faithfully as possible, the referencevariable which is the driving-cycle imposed speed. Within the

PID controller, equation 1 is solved:

(1)

where Kp, Ki and Kd respectively are the gains from

proportional, integrative and derivative effects of th

controller, e(t ) is error and u(t) is controller response. The

controller response corresponds to a signal proportional to the

pressure exerted by the driver on the accelerator and brake

pedals.

Controllers calibration was done using the Ziegler-Nichols

methodology [5].

The output signal of the Driver subsystem ranges from 0 to 1

which correspond to the two pedal end-strokes. These signal

are used as input signals for the Control Unit subsystem.

CONTROL UNITThe Control Unit, together with the Power Split Device, is the

most important part of the THS system. All the signals from

other subsystems converge in this subsystem, allowinginteraction between propulsion, generation and storage

components.

THS has five possible operational modes which vary

according to the power and speed requirements imposed by

the driving cycle. The control unit receives as input the

accelerator and the brake signals, the state of charge (later

SOC) of the storage system and the generated and required

power from electrical machines. Taking into account all these

signals, the control unit activates one of the five possible

operational modes.

In the first mode (Fully Electric), only the electric motor(MG1) propels the vehicle, while the ICE remains off. This

condition occurs during starting and low-speed drives and

requires at the same time vehicle speeds lower than 45 km/h

and battery SOC over 50%. If these two conditions are no

simultaneously verified, the control unit activates the second

operational mode.

The second mode applies when vehicle speed is over 45 km/

h, and when the power generate by MG2 (moved from ICE)

is greater than power required from MG1. In this mode, the







ICE and MG1 together generate the torque necessary to set

the vehicle in motion. In this operational mode the Control

Unit evaluates if the motor MG2 can provide the power

required by the motor MG1 (delta_P=(C MG1 − C MG2) <0), if

so it actives both the ICE to MG1.

If the vehicle speed is over 45 km/h, the power generate by

MG2 is lower than power required from MG1 and the SOC isgreater than 50%, the CU activates the third mode. In this

case, the MG1, besides to uses MG2 energy, also drains

energy from the storage system.

The fourth mode is activated during vehicle deceleration and

braking. In this case MG1 becomes an electric power

generator and recharges the storage system.

The fifth mode is activated when the vehicle stops and the

SOC is less than 50%. Then, the ICE works at its maximum

efficiency point, allowing the MG2 to increase the SOC of

the storage system.

PROPULSION AND GENERATION

SYSTEMSThe propulsion systems, ICE and MG1, and the power

generation system MG2, are complex structures in which

thermo-chemical and electro-mechanical transformations take

place. These systems have been simulated through the use of

their characteristic curves that allow to link torques and

power to rotational speed of moving parts.

For ICE, MG1, and MG2 the torque can be evaluated by

equation 2:

(2)

where stands for maximum torque at the rotational

speed considered, is system pulsation, α represents the

accelerator pedal position, J is the total polar moment of

inertia and P aux is the power absorbed by any accessories,

assumed constant as rotational speed varies.

The C max can be deduced from the characteristic curves for

ICE, MG1, and MG2. In Figure 2, the ICE characteristiccurves [6] is shown as an example.


Within the ICE subsystem there is a further submodel which

determines the specific fuel consumption and pollutant

emissions.

The fuel flow rate is calculated from power balance equation

3:

(3)

where P IC E is the power output of ICE subsystem, η ICE

represents ICE efficiency which varies as supplied power and

rotational speed vary (see Figure 2), Hi is the lower heating

value of the fuel and ṁcomb is the fuel flow rate.

Solving equation 3 and integrating over time, the fue

consumption is obtained for the chosen driving cycle.

To evaluate the CO2 production, equation 4 is applied [4]:

(4)

where mcomb is fuel mass used, mmC is carbon molar mass

mmO is oxygen molar mass, mm H is hydrogen molar massand H_C is the hydrogen/carbon fuel ratio.

PSD (POWER SPLIT DEVICE)Figure 3 shows the Power Split Device used to connect the

two power sources and the THS system generator. It is an

epicyclic train composed of a sun gear, a ring gear and a

planetary carrier, to which the generator, the motor and the

ICE are connected. On the shaft connecting the ring gear and

the MG1 there is a gearing which transfers the engine-

generated torque to the wheels via a silent chain.

ICE-generated power is conveyed to the wheels(mechanically) and generator (electrically). The former

consists in transferring power from the planetary carrier to

the ring gear, the latter in power transfer from the planetary

carrier to the PSD sun gear, to which the generator is

connected. The energy transferred to it is turned into

electricity which is stored in the batteries or sent to the MG1.

To calculate the torque and rotation speed of each PSD

component, the power equilibrium between the various shafts

and the ratios of torques to rotation speeds have been

examined and solved. In order not to complicate the model

the inertial PSD torques were deliberately overlooked

entailing a slight fuel saving.







Figure 3. Power Split Device

From calculations made in the other subsystems, the PSD

input variables are known: C ICE the torque supplied by the

ICE, the MG1 rotation speed and C MG1, the MG1

torque. From these inputs, the output variables were defined

by solving equations 5, 6 and 7 [7]:

(5)

(6)

(7)

where is MG2 rotation speed and C MG2 is MG2

torque, is the ICE rotation speed, and z is the number

of teeth of the sun and ring gear.

Knowing the ICE and MG1 torques which propel the vehicle,

the torque from the shaft connected to the PSD ring gear

which is transferred to the wheels through a system made upof a silent train and a series of cogwheels was calculated as

per equation 8:

(8)

where C prop is the torque generated by the PSD subsystem

resulting from the torques supplied by both power sources

and τ stands for the transmission ratio related to al

components between the PSD and the drive wheels.

ELECTRIC STORAGE SYSTEMThe subsystem dealing with electric power storage [8

features equations used to obtain the state of charge (SOC) o

the storage batteries: 38 modules of 7.2 V nominal. Thissubsystem solves equation 9:

(9)

where SOC 0 stands for the initial storage battery charge, and

within the integral:

(10)

where I batt is the charge/discharge current, and C batt is the

system storage capacity; from equation 10 it follows that if

the I batt is negative the storage system is discharged and vice

versa for charging.

The power supplied or absorbed from the storage system

( P batt ), can be evaluated by equation 11:

(11)

where V oc and Rbatt indicate idle voltage and power storageinternal resistance, the latter being different in charge and

discharge phases, both functions of SOC, as reported in

Figure 4 [9].


WHEEL AND VEHICLE DYNAMICSWithin these two subsystems, the simulated vehicle speed is

defined by solving the unidimensional equation of motion. In

this model it is assumed that vehicle motion is rectilinear and

that the wheels do not skid either during braking or

acceleration; this simplifies the equations but produces lowerfuel consumption.

The Wheel subsystem calculates the horizontal componen

traction force F t which provides vehicle acceleration or

deceleration through equation 11:

(12)







where C prop is the torque generated by the PSD subsystem

resulting from the torques supplied by both engines, C braking

is braking system torque proportional to the brake pedal

position, C inertia the torque inertia at the wheels and Rwheel

the wheel radius.

In the Vehicle Dynamics subsystem, the motion equation is

solved along the vehicle's trajectory.

(13)

where F p is the projection of the gravitational force along the

vehicle's trajectory, F r is the friction generated by the tire

rolling along the asphalt, due to the rolling friction

coefficient, F a is the aerodynamic friction caused by the

vehicle impacting the air, mv is the vehicle mass and v ̇vehicle is

the vehicle acceleration.

Integrating and solving equation 12 in relation to speed, we

get the feedback signal which allows the subsystem Driver,

once the difference between cycle-imposed speed and actual

vehicle speed is known, to send the most suitable acceleration

or braking inputs to obtain a f aithful reproduction of the

imposed cycle.

SIMULATIONS AND DISCUSSION OFRESULTSAll parameters concerning the system's components were put

into the mathematical model in order to carry out simulations

and evaluate the effectiveness of the model. As stated above,up to now two versions of Prius are on the market, the THS

and the 2nd generation called THS-II. Basing on data from

the two versions [10], it has been noticed that the

improvements in the second series mainly consist in a more

efficient ICE, a larger motor and generator, and some small

details in the control system such as extending the generator's

range. Apart from that, nothing has changed in the dynamic

equations which govern the vehicle. The simulation regarded

the THS model.

All vehicle characteristics, efficiency maps and characteristic

curves, were obtained from official Toyota Motor Corp.,

from the ADVISOR 2002 and from scientific literature [11].

Figure 5 a) shows the response of proposed model to the

UDDS standard cycle (Urban Dynamometer Driving

Schedule) in terms of speed and state of charge of the power

storage system (SOC at the cycle beginning equal to 70%;

SOC at the cycle end equal to 62 %). The model closely

follows the imposed cycle; notice how the simulated speed

faithfully follows the reference cycle speed whereas SOC

trend is similar to that seen in [12].

Figure 5 a) shows also the threshold of 45 km/h. The ICE is

activated when the vehicle speed overcomes this threshold

(see Figure 5 b).

For each SOC starting value, during UDDS cycle, the THS

Control Unit manages power sources in or der to obtain a fina

SOC value of about 60%. This THS strategy is designed to

optimized the fuel consumption [12].


Figure 5 b) and c) shown the ICE and MG1 torques

respectively. The ICE is activated when vehicle speed

overcomes the threshold of 45 km/h, while the electrical

motor (MG1) is activated when vehicle acceleration is greater

than zero and vehicle is moving (vvehicle > 0 km/h)

Table 1 shows a comparison between the simulation results

of the proposed model, experimental data [13] and

ADVISOR 2002, related to the UDDS driving cycle. They

confirm the effectiveness of the proposed model, with limited

errors, both in terms of fuel consumption and pollutant

emissions.

(See Table 1 after last section of paper)

Being a dynamic model, the simulated vehicle's performance

can be assessed. Figure 6 shows the model's response to an

acceleration test using a driving cycle from 0 km/h to 100

km/h. Table 2 compares the simulation results with the

experimental data [14]. Since the experimental test refers to

an acceleration test from 0 to 60 mph, it also was used to

validate the numerical simulation.


Table 2. Performance Comparison

To verify the reliability of the proposed model versus

different imposed cycles, other simulations were performed

with different standard cycles. Figure 7 shows the response of

the model to Japanese 10-15 mode standard cycle, made up

of three urban cycles (Japanese 10 mode) and an extra-urban

one (Japanese 15 mode). Also in this case the model response

follows the imposed cycle perfectly in terms of speed, while

the SOC remains nearly constant from start to end.








Table 3 shows a numerical comparison between the

experimental data [11], results from ADVISOR 2002

simulations, and results of proposed model simulation. It

seems clear how, even with other driving cycles than the one

used for setting the model, the model can accurately provide

the fuel consumption to complete the cycle.

(See Table 3 after last section of paper)

CONCLUSIONSIn this work, a feed-forward dynamic model of Toyota

Hybrid system has been developed. The characteristics of all

vehicle components were entered into the model, and a “rule-

based” control system was implemented to manage

interaction between vehicle components, making it easy to

predict the general behavior of a real vehicle. The model

performed simulations of the UDDS standard cycle and other

cycles to evaluate the model's response. The results confirmthat the model can simulate the actual vehicle accurately and

that the control strategy implemented closely follows that of

the first generation Toyota Prius. Compared to previous

model studies [15], this one can assess vehicle performance

as well as fuel consumption and pollutant emissions. This

represents a remarkable target to help popularise hybrid

motor vehicles in a market looking for ever better

performance and lower fuel consumption.

REFERENCES1. Chan C. C., “The state of the art of electric and hybrid

vehicles”, Proceedings of the IEEE , 90 (2), 247-275, 2002.2. Gao D. W., Mi C. and Emadi A., “Modeling and

Simulation of Electric and Hybrid Veicles”, Proceedings of

the IEEE , 95 (4), 729-745, 2007.

3. Markel T., Brooker A., Hendricks T., Johnson V., Kelly

K., Kramer B., O'Keefe M., Sprik S., and Wipke K.,

“ADVISOR: A systems analysis tool for advanced vehicle

modeling”, J. Power Sources, 110 (2), 255-266, 2002.

4. Fiorenza, S., Lanzafame, R., and Messina, M.,

“Development of a Quasi-Static Backward Code for the

Simulation of an Integrated Starter Alternator Vehicle,” SAE

Technical Paper 2007-01-4125, 2007.

5. Hwang H., Choi J., Lee W., Kim J., “A Tuning Algorithmfor The PID Controller Utilizing Fuzzy Theory”,

International Joint Conference on Neural Networks , 4,

2210-2215, 1999.

6. http://www-personal.engin.umd.umich.edu

7. Sasaki S., “Toyota's newly developed hybrid powertrain”,

Proceedings of the 10th International Symposium on Power

Semiconductor Devices and ICs, 1, pp. 17-22, 1998.

8. Liu J., Peng H., “Modeling and Control of a Power-Split

Hybrid Vehicle”, IEEE Transactions on Control Systems

Technology, 16 (6), 1242-1251, 2008.

9. Advisor 2002 program libraries files.

10. Muta, K., Yamazaki, M., and Tokieda, J., “Development

of New-Generation Hybrid System THS II - Drastic

Improvement of Power Performance and Fuel Economy,”

SAE Technical Paper 2004-01-0064, 2004.

11. Rousseau, A., Sharer, P., and Pasquier, M., “Validation

Process of a HEV System Analysis Model: PSAT,” SAETechnical Paper 2001-01-0953, 2001.

12. Kelly K. J., Mihalic M. and Zolot M., “Battery Usage

and Thermal Performance of the Toyota Prius and Honda

Insight During Chassis Dynamometer Testing”, The

Seventeenth Annual Battery Conference on Applications and

Advances, Long Beach, California, 2002.

13. Liu J., Peng H. and Filipi Z., “Modeling and Analysis of

the Toyota Hybrid System”, Proceedings of the 2005 IEEE/

ASME Advanced Intelligent Mechatronics Conference,

Monterrey, California, 2005.

14. Douba M., “Performance and Emissions of The Toyota

Prius”, Prius Data Exchange Workshop, USCAR, Ott. 1999.

15. Fiorenza, S., Lanzafame, R., and Messina, M., “Analysis

of Rules-Based Control Strategies for Integrated Starter

Alternator Vehicles,” SAE Technical Paper 2008-01-1314,

2008.

DEFINITIONS/ABBREVIATIONS

THSToyota Hybrid System;

ICEInternal combustion engine;

MG1Electrical Motor;

MG2Electrical Power generator;

PSDPower Split Device;

u(t)Accelerator/Brake control signal;

KpPropor tional gain;

Kiintegrative gain;





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http://www-personal.engin.umd.umich.edu/




http://www-personal.engin.umd.umich.edu/




e(t )error between imposed cycle speed and simulated

speed;

Kdderivative gain;

Ctorque [Nm];

angular pulsation;

α

propulsion system command signal;

J polar inertial moment [kg*m^2];

P power [W];

η

efficiency;

Hilower heating value [J/kg];

ṁcomb

fuel flow rate [kg/s];

mCO2

CO2 mass produced [kg];

mcomb

fuel mass used [kg];

mmC

carbon molar mass [g/mol];

mmO

oxygen molar mass [g/mol];

mmH

hydrogen molar mass [g/mol];

H_Chydrogen/carbon fuel ratio;

generator angular pulsation [s^(−1)];

internal combustion engine angular pulsation [s^(−1)];

electric motor angular pulsation [s^(−1)];

z ring

teeth number of ring gear;

z sun

teeth number of sun gear;

C MG 2

generator torque [Nm];

C ICE

internal combustion engine torque [Nm];

C MG 1

electrical motor torque [Nm];

C prop

tractor torque [Nm];

τ

gear ratio;

SOCstorage system state of charge;

SOC 0

initial state of charge;

SȮCtemporary variation of state of charge;

I batt

current in storage system [A];







V batt

tension in storage system [V];

P batt

storage system power [W];

V oc

storage system idle tension [V];

F t

traction force [N];

C braking

braking torque [Nm];

C inertia

inertial torque [Nm];

Rwheel

wheel radius [m];

F p

gravitation force [N];

F r

rolling friction force [N];

F a

aerodynamic friction force [N];

mv

vehicle mass [kg];

vvehicle

vehicle speed [m/s]

v̇vehicle

vehicle acceleration [m/s^2];

UDDSUrban Dynamometer Driving Schedule.







Figure 1. Toyota Prius THS dynamic model schematization

Figure 2. Maximum torque curve and ICE efficiency map







Figure 4. Power storage internal resistance as charge varies

Figure 5. a) Model response to UDDS cycle; b) ICE torque; c) Electric Motor (MG1) torque







Figure 6. Acceleration test

Figure 7. Response of model to Japan 10-15 cycle







Table 1. UDDS cycle Consumption / Emission comparison

Table 3. Japan 10-15 Cycle consumption comparison

The Engineering Meetings Board has approved this paper for publication. It has

successfully completed SAE's peer review process under the supervision of the session

organizer. This process requires a minimum of three (3) reviews by industry experts.

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ISSN 0148-7191

doi:10.4271/2010-01-1443

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