ScienceDirect Development of a software in the loop ...

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ScienceDirect Energy Procedia 45 (2014) 789 – 798

68th Conference of the Italian Thermal Machines Engineering Association, ATI2013

Development of a software in the loop environment for automotive powertrain systems Gabriele Vandia, Nicolò Cavinaa, Enrico Cortia, Giorgio Mancinia, Davide Moroa, Fabrizio Pontia, Vittorio Ravagliolia a

Department of Industrial Engineering, Alma Mater Studiorum - University of Bologna,Viale del Risorgimento 2, 40136, Bologna, Italy

Abstract In the last years the interest for hybrid vehicles increased mainly for environmental reasons. The dynamic behavior of a vehicle is then influenced by the interaction between the engine and the hybrid system. The final goal of the paper is to realize a software in the loop environment which can be utilized for the development of control strategies for hybrid vehicles. This paper presents the implementation of a simplified engine-driveline model to complete an existing vehicle dynamic model. The engine model is based on maps which are expressed as function of engine speed and load request. Particular care is devoted to the clutch model which allows describing both the situations of engaged and disengaged clutch. The driveline model also permits to change the transmission ratio between engine and wheels depending on the selected gear. The model parts are integrated, taking into account the requirement to use the model in real time simulations, coupling to the engine-driveline with a pre-existing vehicle dynamics model by means of the vehicle driving wheels. The complete vehicle-engine model is used to evaluate the differences in vehicle dynamic behavior when additional masses are added to the vehicle and the position of vehicle center of gravity is changed. © 2013 2013The TheAuthors. Authors. Published by Elsevier © Published by Elsevier Ltd. Ltd. Open access under CC BY-NC-ND license. Selection and peer-review under responsibility of NAZIONALE ATI NAZIONALE. Selection and peer-review under responsibility of ATI Keyword: engine, clutch, driveline,vehicle, model,realtime ;

1. Introduction In the automotive industry simulation models have an important role in the development of new technologies and products. For example in [1] a control-oriented model of a vehicle is developed to project a yaw controller while in [2] a dynamic torsional model is used to investigate the relationship between indicated torque and engine speed frequency components. Control-oriented models are also useful to perform hardware in the loop testing ([3],[4]) and to investigate the interactions between driveline and vehicle dynamics ([5],[6]).The idea at the base of this work is to simulate the vehicle dynamics when two electric motors, mounted on the non-driving wheels, are added to a traditional front wheel drive vehicle, to obtain an hybrid vehicle. Starting from an existing vehicle dynamics model,

1876-6102 © 2013 The Authors. Published by Elsevier Ltd. Open access under CC BY-NC-ND license.

Selection and peer-review under responsibility of ATI NAZIONALE doi:10.1016/j.egypro.2014.01.084

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presented in [7], the authors have developed an engine/driveline model, to simulate the interactions between engine and vehicle dynamics: the contact point between the two models is represented by the driving wheels of the vehicle. The so-obtained model is a complete vehicle-engine model that can be used with different goals: for example to investigate the differences in vehicle dynamic behavior caused by change of position of vehicle center of gravity due to the addition of the electric motors-generators and related batteries to the vehicle. Moreover the model can be used to design appropriate control strategies of the electric motors to avoid the worsening of stability characteristics of the hybrid vehicle. Nomenclature bc kc Fn Jc/e Tc Te Tind Tfric Tpump Td Tw τg/f ωc/e/t ωfr/fl Ψ JZ/XZ JXZ-i ms h hi V h FX-i/Y-i MZ-I δi xi/yi

Clutch damping Clutch stiffness Normal force on clutch plate Clutch/engine inertia Torque transmitted through the clutch Net torque produced by the engine Indicated torque Friction torque Pumping toruque Torque transmitted to the gearbox Torque transmitted to the wheels Selected gear/final transmission ratio Clutch/engine/ transmission rotational speed Front right/left wheel rotational speed Vehicle yaw angle Vehicle yaw/mixed moment of inertia Unsprung mass mixed moment of inertia Vehicle sprung mass Sprung mass roll angle Unsprung mass roll angle Vehicle speed Sprung mass center of gravity vertical distance from vehicle coordinate system center Longitudinal/lateral tire force Tire self-aligning moment Tire toe angle Tire longitudinal/lateral distance from vehicle coordinate system center

2. Engine model Several ways to model the engine are possible: for example in [8] a zero dimensional crank-angle resolved model is used. In [9] and [10] the authors build mean value engine models with control purposes. In [11] the authors express the torque produced by the engine as the sum of different components, such as combustion torque and friction torque, which are calculated through empirical functions. In this work the authors follow the last approach: however the components of the total torque Te are expressed through maps that are function of engine speed and load request instead of being calculated with empirical equations. The engine net torque is expressed through the following equation:

Te ? Tind / T fric / T pump

(1)

Each component of the sum in the right hand of equation (1) is obtained from a map which is function of speed and load request: in figure 1 it is possible to observe an example of those maps.

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Normalized Indicated Torque []

1

0.5

0 100 50

Load Request [%]

0

0

5000 4000 3000 2000 1000

Normalized Friction Torque

b

Normalized Friction Torque []

Normalized Indicated Torque

a

1 0.8 0.6 0.4 100 50

Engine Speed [rpm] Load Request [%]

0

5000 30004000 10002000

Engine Speed [rpm]

Fig. 1. (a) Normalized Indicated Torque map. (b) Normalized Friction Torque map.

Engine speed is calculated through equation (2):

J ey% e ? Te / Tc

(2)

3. Clutch model The torque generated by the engine is transmitted to the driving wheels of the vehicle through the clutch and the gearbox: for simulation reasons it has been necessary to model the clutch in such a way to represent both the situations of engaged and disengaged clutch. For example, when the vehicle speed slows down to zero, it is necessary to decouple engine and vehicle speed to avoid numerical instabilities of the simulator. However this aspect introduces some complications in the simulation model: in fact, when the clutch is disengaged, engine speed and clutch speed are decoupled and there are two independent equations for the two inertias. In this case clutch speed can be calculated through equation (3), whose formulation is similar to equation (2):

J cy% c ? Tc / Td

(3)

Ð

Td ? bc *yc / yt + - k c *yc / yt +

(4)

Tc ? Fn oRsign*ye / yc +

(5)

where Td can be obtained integrating the following expression:

The torque transmitted through the clutch is calculated by the following equation:

When clutch is engaged and it is not slipping (sticking clutch), engine and clutch are coupled into a single inertia and equations (2) and (3) can be reduced to a single equation:

*J e - J c +y% e ? Te / Td

(6)

ye ? yc

(7)

So, when the clutch moves from the disengaged condition to the engaged condition, it is necessary to switch from the two equations system to the one equation system: in simulation models this aspect can lead to numerical instabilities. To avoid these problems the Karnopp model can be used, as explained in [12]: the idea at the base of the Karnopp approach is to use the two equations system for both the situations of engaged and disengaged clutch while changing the expression of the torque transmitted through the clutch. When the clutch is disengaged or it is slipping, the torque transmitted is represented by equation (5) while in the situation of sticking clutch the torque transmitted is represented by the following equation:

Tc ?

*

Ð

+

J e bc *yc / yt + - k c *yc / yt + - J cTe Jc - Je

(8)

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The situations of sticking clutch is reached when two conditions happen: the first one is that the torque transmitted through the clutch is below the maximum transmissible torque, represented by equation (9).

Tcmax ? Fn o stick Rsign*Tc +

(9)

The second condition is that the difference between engine speed and clutch speed must be less than a certain threshold, as stated in (10):

ye / yc

g

(10)

4. Transmission model The transmission model is composed by two simplified model of gear box and a differential gear: the torque transmitted through the clutch is multiplied by a factor, which is function of the selected gear, and distributed to the two driving wheels of the vehicle: Td *v g *v f Tw ? (11) 2 Transmission speed is calculated thanks to wheel speeds, as suggested in [13], which are outputs of the vehicle model:

yt ?

*y fr - y fl + 2v gv f

(12)

Equation for calculating wheel speeds are within the vehicle model. A schematization of the proposed powertrain model is represented in the figure 2.

Fig. 2. Powertrain model schematization.

5. Models integration As previously mentioned in the Introduction, the engine and driveline models presented in this work are developed to complete an existing vehicle dynamics model, shown in [7]. The vehicle model is built in Matlab/Simulink environment: so engine, clutch and driveline models are built in the same environment and then added to vehicle model block diagram. The inputs of the model are steering wheel angle, throttle position, cluch position and selected gear: throttle position can be set by the user or, to simulate maneuvers with a target vehicle speed, controlled by a proportional integral (PI) controller. 5.1. Vehicle dynamics The vehicle model, with which the proposed engine and driveline model is integrated, is a 14 degrees of freedom model suitable for real-time simulations: this model takes into account for both longitudinal and lateral dynamics and allows the user to apply different torques to each wheel. The model is completed by a tire a model which takes into account for wheel slip and rolling resistance. An example of the equations that compose vehicle model is equation (13), which represents vehicle yaw rate, an important parameter of vehicle lateral dynamics.

%% ? J h%% J z[ xz

ÂJ

Gabriele Vandi et al. / Energy Procedia 45 (2014) 789 – 798 XZ /ihi

%% / m hhV% s

Â*F

X /i

sin f i - FY /i cos f i +xi -

Â*F

X /i

cos f i / FY /i sin f i +yi - M Z /i

793

(13)

In the next paragraphs a gear shift simulation will be presented to show the behavior of the proposed engine and clutch models, then the simulation tool will be used to investigate the differences in vehicle dynamic behavior when vehicle mass and the position of center of gravity are changed.

6. Gear shift simulation The first simulated maneuver presented is a gear upshift: the vehicle is running straight at an initial speed of 50 km/h with the a load request of 50 % in 3rd gear. Then the operations for a gear shift are executed like on an actual car: load request is set to 0%, clutch is disengaged (moved to 100% position) and the 4th gear in selected, clutch is engaged and load request set again to 50%. The inputs provided for this simulation are represented in the figure 3. Load request

a

100

Clutch Position [%]

Load Request [%]

Clutch Position

b

100 80 60 40 20 0

80 60 40 20 0

0

2

4

6

8

10

0

2

Time [s]

4

6

8

10

Time [s]

Fig. 3. (a) Throttle input for gear shift simulation. (b) Clutch input for gear shift simulation.

In figure 4 it is possible to observe the results of the simulation : in particular, in figure 4.a, engine and clutch speed are represented showing the transition from engaged to disengaged condition and vice versa. a

Engine & Clutch Speed

b

3200

80

Torque [Nm]

3000

Speed [rpm]

Engine Torque 100

2800 2600

Engine Clutch

2400

60 40 20 0

2200

-20 0

2

4

Time [s]

6

8

10

0

2

4

6

8

10

Time [s]

Fig. 4. (a) Engine and clutch speed during gear shift simulation. (b) Engine torque during gear shift simulation.

At the beginning of the simulation, clutch is sticking and its speed is equal to engine speed: than, at second 4.2 load request is set to 0% and then clutch is disengaged. The gear is changed at second 5: this fact is evident in figure 4.a where clutch speed changes instantaneously and also in figure 5.a, where it is possible to observe a spike in the front right wheel speed. After the gear shift the clutch is reengaged and engine speed becomes equal to clutch speed: then load request is set to 50% and engine speed increases. Two other aspects must be underlined: the first is speed oscillation of both clutch and engine, due to stiffness and damping characteristics of the clutch, visible in figure 4.a. The second aspect concerns wheels speed: when engine is developing a propulsive torque, at the beginning and at the end of the simulation (see figure 4.b) , front wheels (driving wheels) speed is higher than rear wheels speed due to tire slip phenomena, as it is possible to observe in figure 5.a.

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a

Wheel Speed

b

650

70

Speed [km/h]

600

Speed [rpm]

Vehicle Speed 75

550 500

Front Right Rear Right

450

65 60 55 50 45

400 0

2

4

Time [s]

6

8

10

0

2

4

6

8

10

Time [s]

Fig. 5. (a) Wheel speed during gear shift simulation. (b) Vehicle speed during gear shift simulation.

The last result presented is about vehicle speed, which is depicted in the figure 5.b. Vehicle speed increases at the beginning and at the end of the simulation (with a lower gradient after the gear shift since the torque acting on the wheels is lower due to the higher gear inserted) while it slows down when clutch is disengaged (no torque is transmitted to the driving wheels) due to aerodynamic and rolling resistance acting on the vehicle. In the next paragraph, the simulation tool is used to analyze the vehicle dynamic behavior when its mass and the position of the center of gravity are varied. 7. Modified Vehicle As stated earlier in the paper, the idea at the base of this work is to transform a traditional vehicle into an hybrid vehicle by mounting two electric motors on the non-driving wheels of the vehicle. However, to obtain a working hybrid vehicle, it is also necessary to add a power battery and the necessary electronics to control the electric motors: this objects must be installed in the trunk of the vehicle, leading to some changes in vehicle characteristics. Vehicle mass is increased of about 15% of its original value, vehicle center of gravity is moved towards the rear wheels due to the position of the additional mass and finally unsprung mass is increased, because electric motors are mounted on the (non-driving) wheels. This changes can influence the vehicle dynamic behavior, in particular vehicle lateral dynamics: so the complete engine and vehicle model is used to investigate the differences in lateral dynamics response between the original vehicle and the modified one. Two maneuvers are simulated: a step steering wheel input and a sinusoidal steering wheel input. The results of these simulations are shown in the next paragraphs: in the figures, results relative to original vehicle are indicated with as ‘Base’ while results relative to the modified one are indicated as ‘Modified’. 7.1. Step steer simulation The first simulated maneuver is a step input applied to the steering wheel: at the beginning of the simulation the vehicle is running straight at 90 km/h and after one second a 33 degree step is applied to the steering wheel. The simulation is carried out in 4th gear and to control vehicle speed the proportional integral controller, presented in paragraph 5, is used.

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Gabriele Vandi et al. / Energy Procedia 45 (2014) 789 – 798 Steering Wheel Input

b

Vehicle Speed 92

Base Modified

30

91

Speed [km/h]

Steering Wheel Angle [deg]

a

20

10

90 89 88

0

87 0

2

4

6

8

0

10

2

4

6

8

10

Time [s]

Time [s]

Fig. 6. (a) Steering wheel input during step steer simulation. (b) Vehicle speed during step steer simulation.

As depicted in figure 6.b, the PI controller brings the vehicle speed to 90 km/h in both cases after an initial decrease: however, in the case of the Modified vehicle, the action of the PI controller is retarded with respect to the Base vehicle due to the augmented inertia of the vehicle. In the next figure results about load request and engine speed are shown. Load request

a

b

Engine Speed 3600

3550

40

Speed [rpm]

Load Request [%]

50

30 20 10

3500

3450

Base Modified

Base Modified

0

3400 0

2

4

6

8

0

10

2

4

6

8

10

Time [s]

Time [s]

Fig. 7. (a) Throttle request during step steer simulation. (b) Engine speed during step steer simulation.

In figure 7.a load request by the PI controller is depicted: in the case of Modified vehicle load request is higher than Base vehicle and this fact is due to the increased inertia of the Modified vehicle. The higher mass causes more rolling resistance and an increased power request to the engine to keep the vehicle speed at 90 km/h during the maneuver. This tendency can be found also in engine speed: in the final part of the simulation, where vehicle speed is 90km/h for both vehicles, the Modified vehicle has an higher engine speed than the Base vehicle. This fact can by explained in this way: the higher load request causes an higher torque produced by the engine and, consequently, an higher torque applied to the wheels. The higher torque applied to the wheels produces an higher wheel slip and higher wheel speed: engine speed is linked to wheels speed resulting so in an higher value. Results about engine torque and wheel speed are shown in the figure 8. a

Engine Torque

b

80

Wheel Speed [rpm]

Torque [Nm]

60 40 20

Base Modified

0

Wheel Speed 820 810 800

FR Base FL Base FR Modified FL Modified

790 780 770

-20 0

2

4

Time [s]

6

8

10

0

2

4

6

8

10

Time [s]

Fig. 8. (a) Engine torque during step steer simulation. (b) Wheel speed during step steer simulation.

In figure 8.b the front right tire is indicated with acronym FR while front left tire in indicated with acronym FL. The last results presented for the step steer maneuver are relative to vehicle lateral dynamics (see figure 9).

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Gabriele Vandi et al. / Energy Procedia 45 (2014) 789 – 798 Yaw Rate

b

20

Sideslip Angle [deg]

Yaw Rate [deg/s]

a

15 10 5

Base Modified

0

Sideslip Angle 1

Base Modified 0

-1

-2 0

2

4

6

8

10

0

2

4

Time [s]

6

8

10

Time [s]

Fig. 9. (a) Yaw rate during step steer simulation. (b) Sideslip angle during step steer simulation.

Results relative to vehicle lateral dynamics are very interesting: the Modified vehicle has a higher yaw rate and a higher absolute value of the sideslip angle (in this case a negative value of the sideslip angle indicates an oversteering condition) compared to the Base vehicle. To understand this aspect some considerations are necessary: increasing the load on rear wheels allows rear wheels to produce higher lateral forces that oppose to vehicle steering. However moving the center of gravity towards rear wheels has on opposite effect: front wheels increase their ability to turn the vehicle while rear wheels decrease their capability to oppose vehicle turn. In this case the second effect is predominant over the first leading to an increased sensitivity of the vehicle to the steering input: so the Modified vehicle is characterized by a more oversteering behavior than Base vehicle. To complete the analysis results about sine steering input simulation are presented in the next paragraph. 7.2. Sine steer simulation The last simulated maneuver is a sinusoidal steering wheel input with a period of 5 second and an amplitude of 33 degrees: also in this case at the beginning of the simulation vehicle is running straight at 90 km/h and after 1 second sine sequence starts (see figure 10). Steering Wheel Input

b

40

Vehicle Speed 92 91

20

Speed [km/h]

Steering Wheel Angle [deg]

a

0

-20

90 89 88

-40

Base Modified

87

0

5

10

Time [s]

15

20

0

5

10

15

20

Time [s]

Fig. 10. (a) Steering wheel input during sine steer simulation. (b) Vehicle speed during sine steer simulation.

Also in this case simulation is carried out in 4 th gear and vehicle speed is controlled by a PI controller: after 5 seconds speed is about 90 km/h for both vehicles and in the remaining part of the simulation it oscillates around the target value. In figure 11 results about load request and engine speed are depicted.

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Gabriele Vandi et al. / Energy Procedia 45 (2014) 789 – 798 Load request

a

b

Engine Speed 3560 3540

40

Speed [rpm]

Load Request [%]

50

30 20 10

Base Modified

0

3520 3500 3480

Base Modified

3460 0

5

10

15

20

0

5

Time [s]

10

15

20

Time [s]

Fig. 11. (a) Load request during sine steer simulation. (b) Engine speed during sine steer simulation.

Load request and engine speed are characterized by the same oscillations already underlined for vehicle speed: the mean value and the amplitude of the oscillations of these parameters are in both cases higher for the Modified vehicle for the same reasons listed earlier for the step steer maneuver. Engine Torque

b

60

Wheel Speed [rpm]

a

Torque [Nm]

40

20

0

Base Modified

Wheel Speed 810 805 800 795

FR Base FL Base FR Modified FL Modified

790 785 780

-20 0

5

10

15

0

20

5

10

15

20

Time [s]

Time [s]

Fig. 12. (a) Engine torque during sine steer simulation. (b) Wheel speed during sine steer simulation.

In figure 12 results about engine torque and wheels speed are depicted: engine torque, for both vehicles, has an initial peak to keep vehicle speed at 90 km/h and then it is characterized by oscillations that follow the load request. During these oscillations, engine torque for the Modified vehicle has a higher value than the Base vehicle for the same reasons already exposed for the step steer maneuver: same considerations apply to wheels speed, depicted in figure 12.b. Yaw Rate

b

20

Sideslip Angle [deg]

Yaw Rate [deg/s]

a

10

0

-10

Base Modified

-20

Sideslip Angle 1.5 1 0.5 0 -0.5

Base Modified

-1 -1.5

0

5

10

Time [s]

15

20

0

5

10

15

20

Time [s]

Fig. 13. (a) Yaw rate during sine steer simulation. (b) Sideslip angle during sine steer simulation.

Again results about vehicle lateral dynamics are very interesting: the Modified vehicle has a higher peak value of yaw rate and sideslip angle than Base vehicle showing an increased sensitivity to steering input and confirming the results already obtained for the step steer maneuver. 8. Conclusions In this work an engine, clutch and driveline model is presented: engine model is based on maps which are function of engine speed and load request.

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Gabriele Vandi et al. / Energy Procedia 45 (2014) 789 – 798

Particular care is devoted to the clutch model, because, for simulation reasons, both the situations of engaged and disengaged clutch have to be represented: so the Karnopp approach, with its assumptions and simplifications, is chosen and equations of this model are shown. Transmission model is a simplified model which is a characterized by a fixed final transmission ratio and a variable transmission ratio representing the gearbox. The model is then integrated into an existing vehicle dynamics model, built in Matlab/Simulink environment, obtaining a complete engine and vehicle simulator. A simulation of a gear upshift is presented to show the behavior of the proposed model: during the simulation there is a transition from the condition of engaged clutch to disengaged clutch and vice versa to show the numerical stability of the clutch model. Then the idea at the base of this work is presented: a traditional front wheel driving vehicle is transformed into an hybrid vehicle thanks to the addition of two electric motors mounted on the non-driving wheels of the vehicle and other necessary components to store and manage energy. However the equipment added to the vehicle changes the static characteristics of the vehicle, like unsprung mass distribution and location of the vehicle center of gravity. So two simulations, a step steer and a sine steer input, are carried out to evaluate differences in dynamic behavior between the Base vehicle and the Modified vehicle: the results are very interesting showing consistent differences in vehicle lateral dynamics. In particular, the Modified vehicle shows an increased sensitivity to steering input, due to the shift of the vehicle center of gravity towards the rear wheels. To contrast the increased sensitivity to steering input it will be necessary to design appropriate control strategies of the electric motors: in future works the entire model may be used for this purpose. Moreover the model may be used to design strategies for recovering energy during braking, adding models of the electric equipment: with the addition of a specific consumption model or map it will be also possible to evaluate fuel savings in a typical driving cycle, like the New European Driving Cycle NEDC. References [1] Visconti A, Farachi F, Silani E, Savaresi SM, Bittanti S. The Concept of Performance-Oriented Yaw-Control Systems: Vehicle Model and Analysis. SAE Technical Paper. 2002; No. 2002-01-1585. [2] Ponti F, Ravaglioli V, Serra G. Optimal Combustion Positioning Methodology Based On Mfb50 On-Board Estimation. ICEF Technical Paper. 2010; No. 2010-35166. [3] Corti E, Migliore F, Moro D, Capozzella P, Pagano M. Development of A Control-Oriented Model of Engine, Transmission and Vehicle Systems for Motor Scooter HIL Testing. SAE Technical Paper. 2009; No. 2009-01-1779. [4] Sahraeian A, Shahbakhti M, Aslani A R, Jazayeri S A, Azadi S, Shamekhi A H. Longitudinal Vehicle Dynamics Modeling on the Basis of Engine Modeling. SAE Technical Paper 2004. No. 2004-01-1620. [5] Duque E L, Barreto M A, Fluery A T. Math Model to Simulate Clutch Energy During Vehicle Launch. SAE Technical Paper 2009. No. 200936-0401. [6] Cavina N, Olivi D, Corti E, Mancini G, Poggio L, Marcigliano F. Development and Implementation of Hardware in the Loop Simulation for Dual Clutch Transmission Control Units. SAE Technical Paper 2013. No. 2013-01-0816. [7] Vandi G, Moro D, Ponti F, Parenti R, Einaudi G, Vehicle dynamics modeling for real-time simulation. SAE Technical Paper. 2013. No. 201324-0144. [8] Wurzenberger JC, Heinzle R, Schuemie A, Katrasnik T. Crank-Angle Resolved Real-Time Engine Simulation –Integrated Simulation Tool Chain from Office to Testbed. SAE Technical Paper. 2009; No. 2009-01-0589. [9] Gambarotta A, Lucchetti G. Control-Oriented “Crank-Angle” Based Modeling of Automotive Engines. SAE Technical Paper 2011. No. 201124-0144. [10] Wu H, Wang X, Winsor R, Baumgard K. Mean Value Engine Modeling for a Diesel Engine with GT-Power 1D Detail Model. SAE Technical Paper 2011. No. 2011-01-1294. [11] Walter A, Merz B, Kiencke U, Jones S. Comparison & Development of Combustion Engine Models for Driveline Simulation. SAE Technical Paper. 2006; No. 2006-01-0436. [12] Serrarens A, Dassen M, Steinbuch M. Simulation and Control of an Automotive Dry Clutch. Proceeding of the 2004 American Control Conference. 2004:4078-4083. [13] Cheli F, Pedrinelli M, Zorzutti A. Integrated Vehicle and Driveline Modeling. SAE Technical Paper. 2007; No. 2007-01-1583. [14] Genta G. Motor vehicle dynamics: modeling and simulation. Singapore: Word Scientific; 1997. [15] Heywood JB. Internal combustion engine fundamentals. New York: McGraw-Hill; 1998. [16]Guzzella L. Introduction to Modeling and Control of Internal Combustion Engine Systems. Berlin: Springer; 2004. [17] Rajamani R. Vehicle Dynamics And Control. New York: Springer; 2006. [18] Pacejka HB. Tyre and vehicle dynamics. Warrendale: SAE; 2002.