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Automotive Innovation

, Volume 1, Issue 2, pp 140–146 | Cite as

Torque Distribution Strategy of Electric Vehicle with In-wheel Motors Based on the Identification of Driving Intention

  • Bo Peng
  • Huanhuan ZhangEmail author
  • Feihu Xuan
  • Wenwen Xiao
Article

Abstract

A driver’s intention is recognized accurately by employing fuzzy identification and a logic threshold including acceleration intention and steering intention. Different torque distribution control strategies are developed for different intentions and the driver’s torque demand is amended by fuzzy identification so that the response of the vehicle is more consistent with the driver’s intention of operation. Finally, a simulation model is built using MATLAB/Simulink to validate the control strategy. Simulation results show that the system accurately identifies the driver’s intention and improves the acceleration performance and steering stability of the vehicle.

Keywords

Fuzzy recognition Torque distribution Driving intention In-wheel motors Steering stability 

1 Introduction

The electric vehicle with in-wheel motors does not have traditional transmission components, such as a clutch. Each wheel is driven by a separate motor and the vehicle thus allocates individual driving torques to the wheels, i.e., it is possible for the vehicle to adopt any driving torque distribution among the wheels [1, 2]. Electric vehicles having in-wheel motors therefore have an advantage over internal combustion engine vehicles and central-motor-driven vehicles [3, 4]. In previous work, a driving force distribution method was developed on the basis of the minimum tire load [5]; a control allocation method was used in a hierarchical structure to optimize the drive and braking torque distribution and thus improve the handling and stability of a vehicle [6]; and a driving force distribution algorithm was developed on the basis of control allocation [7], where the algorithm establishes an objective function and constraints based on economic requirements, optimizing the torque allocation of the vehicle to ensure the best economic performance.

The shortcoming of present torque distribution strategies is that they do not effectively (consider) a driver’s driving intention when achieving driver’s desired performance.

At the same time, the torque distribution usually has only single target. Furthermore, the strategies fail to consider the different conditions of the desired running performance. Finally, the combined driving intention recognition of vehicle control strategies rarely considered the torque distribution. A fuzzy control method has been proposed where the driver’s operation of the accelerator pedal is converted to a target speed of the motor drive in the effective control of the total output torque demand of a plug-in hybrid electric vehicle [8]. Recognition of the driving intention based on hybrid vehicle control strategies has been developed [9], and fuzzy inference identification of the driving intent has been used to amend the demand for automotive torque during acceleration, but the torque distribution has been not addressed. A method directly controlling the yaw moment that adapts to identified driver behavior has been presented [10], where the intention of lane changing is obtained and the yaw moment required to adjust the distribution of the left and right wheel drive torques is determined according to the prediction of the driver behavior.

This paper considers the driver intention and divides the driving intention into linear acceleration intention and steering intention. The linear acceleration intention is further divided into adjustment acceleration and urgent acceleration to improve the vehicle accelerating performance and steering stability.

The remaining of this paper is structured as follows. The recognition of driving intention is presented in the next section, including the recognition of the intention of linear acceleration and recognition of steering intention. In the third section, different torque distribution strategies are developed based on acceleration intention and steering intention, respectively. Furthermore, a driving intention identification model is established in the fourth section. Finally, conclusions are introduced and limitations are discussed.
Fig. 1

Process of the fuzzy inference of driving intention

2 Recognition of Driving Intention

2.1 Recognition of the Intention of Linear Acceleration

Acceleration is divided into adjustment acceleration and urgent acceleration. Adjustment acceleration is acceleration that is not immediately crucial, with the driver accelerating or decelerating gradually through control of the accelerator pedal. Urgent acceleration is time-crucial acceleration where high speed is required rapidly.

2.1.1 Identification Parameters and Methods

Our aim is to obtain the intention of the driver and to take an appropriate action, such as operation of the steering wheel or pedals, thus changing the running state of the vehicle. Previous operations of the driver can thus be used to obtain identification parameters. The literature has highlighted that the opening of the accelerator pedal and the rate at which the pedal is opened reflects the intention of the driver [8]. This paper thus uses these indicators in the recognition of accelerating intention.

The driver’s intention is difficult to describe accurately with a mathematical model and is thus treated as a fuzzy concept [8]. Fuzzy reasoning is effective in simulating human reasoning. The present paper therefore uses fuzzy reasoning to identify the driver’s acceleration intention. The process of fuzzy inference of the driving intention is shown in Fig. 1. The function of fuzzification is to transform the exact amount of input into a fuzzy quantity, and the input of fuzzy control is usually a deviation and the deviation rate of change. The fuzzy rule includes a series of rules expressed by fuzzy linguistic variables. Fuzzy inference is based on the fuzzy concept. The fuzzy implication and inference rules of fuzzy logic is used to obtain the model control function and simulate the human decision process. The function of defuzzification is to transform the fuzzy variables obtained from fuzzy inference into those of can be used for control.

2.1.2 Construction of the Model for Recognizing the Acceleration Intention

The acceleration intention is identified by the accelerator pedal opening and accelerator opening rate of change. The fuzzy domain of the accelerator opening is [0, 100] and the fuzzy subset is [S, M, B], where S stands for ‘small’, M for ‘medium’, and B for ‘big’. The fuzzy domain of the accelerator opening rate of change is [− 200, 200] and its fuzzy subset is [N, S, M, B], where N stands for ‘negative’, S for ‘small’, M for ‘medium’, and B for ‘big’. Figure 2 shows the membership functions of the accelerator pedal opening while Fig. 3 shows the membership functions of the accelerator pedal opening rate of change.
Fig. 2

Membership functions of the accelerator pedal opening

Fig. 3

Membership functions of the accelerator pedal opening rate of change

Expertise and real-vehicle acceleration test statistics provide the acceleration situation for different pedal states. Fuzzy inference rules of the acceleration intention are presented in Table 1.
Table 1

Fuzzy inference rules of acceleration intention

Opening

Opening rate

 

N

S

M

B

S

Aa

Aa

Aa

Aa

M

Aa

Aa

Aa

Ea

B

Aa

Ea

Ea

Ea

Aa adjustment acceleration, Ea emergency acceleration

2.2 Recognition of Steering Intention

The steering intention is relatively easy to identify, so it is recognized using a logic threshold. The angle of the steering wheel is taken as the steering intention parameter. A steering intention (i.e., an intention to change direction) is recognized when the steering wheel angle is nonzero. However, the process of straight driving involves small nonzero angles of the steering wheel, and a steering intention is therefore recognized in practice when the steering wheel angle changes by more than a threshold.

3 Torque Distribution Strategies

3.1 Torque Distribution Strategy for Acceleration Intention

Single-axis drive can meet the acceleration demand when adjustment acceleration is recognized. Single-axis drive uses the front wheels and the total torque demand is divided between left and right wheels equally:
$$\begin{aligned} T_{\mathrm{Z}}= & {} 2K\cdot T_{\max }, \end{aligned}$$
(1)
$$\begin{aligned} T_\mathrm{fr}= & {} T_\mathrm{fl} =0.5T_{\mathrm{Z}}, \end{aligned}$$
(2)
where \(T_{\mathrm{Z}} \) is the total desired torque, K is the accelerator opening, \(T_{\max } \) is the maximum torque that a single motor can provide, \(T_\mathrm{i}\) denotes torques of the driving wheels, and \(i=\hbox {fl},\hbox {fr},\hbox {rl},\hbox {rr}\), respectively, denotes the front-left, front-right, rear-left, and rear-right wheels.
The aim of urgent acceleration is to reach a high speed in a short time and four-wheel drive is thus used to generate greater torque output for such acceleration. If the driver’s reaction time and the intensity of the accelerator pedal are insufficient for urgent acceleration, it is necessary to compensate the torque and thus increase the torque output. The total torque demand is therefore
$$\begin{aligned} T_{\mathrm{Z}} =4\beta K\cdot T_{\max }, \end{aligned}$$
(3)
where \(\beta \) is the torque correction factor determined by fuzzy reasoning according to the determined urgency of the driver torque demand. The input parameters are the accelerator opening and the accelerator opening rate of change. Table 2 gives the rule base of the torque correction factor fuzzy inference.
Table 2

Fuzzy rule base of the compensation torque correction coefficient

AP

DAP

 

S

M

B

S

S

S

S

M

S

S

M

B

S

M

B

In Table 2, AP is the accelerator pedal opening and DAP is the accelerator opening rate of change. The range of the torque correction factor is [1.0, 1.3]. AP, DAP and the correction coefficient of the torque compensation range are set using the membership functions shown in Figs. 45 and 6.
Fig. 4

Membership functions of the accelerator pedal opening

Fig. 5

Membership functions of the accelerator pedal opening rate of change

Fig. 6

Membership functions of the torque correction coefficient

During acceleration and especially urgent acceleration, the front-axle load is shifted to the rear axle. This will be accompanied by changes in the adhesion limits of the front and rear wheels. At the same time, to maximize the use of front- and rear-wheel adhesion, the front and rear torques are allocated in proportion. The front and rear torque distribution ratio can be determined by the front and rear load of vehicle, finally improving the emergency acceleration.

Ignoring air lift during acceleration and torque generated by the rolling resistance of the coupling components, front- and rear-axle loads after load transfer have been proposed previously [11]:
$$\begin{aligned} F_\mathrm{zf}= & {} G\left( \frac{b}{L}\cos \alpha -\frac{h_\mathrm{g} }{L}\sin \alpha \right) -\left( \frac{G}{g}\frac{h_\mathrm{g} }{L}+\frac{\sum {I_\mathrm{w}} }{Lr}\right) \frac{\hbox {d}u}{\hbox {d}t}, \end{aligned}$$
(4)
$$\begin{aligned} F_\mathrm{zr}= & {} G\left( \frac{a}{L}cos\alpha +\frac{h_\mathrm{g} }{L}sin\alpha \right) +\left( \frac{G}{g}\frac{h_\mathrm{g} }{L}+\frac{\sum {I_\mathrm{w} } }{Lr}\right) \frac{\hbox {d}u}{\hbox {d}t},\nonumber \\ \end{aligned}$$
(5)
where G is the vehicle weight, L is the length of the wheelbase, a and b are, respectively, the distance between the center of mass and the front and rear axes, \(h_\mathrm{g} \) is the vehicle centroid height, \(\alpha \) is the road slope angle, U is the longitudinal speed, \(I_\mathrm{w}\) is the moment of inertia of the wheel, r is the wheel radius, and G is acceleration due to gravity.
Front and rear torques are, respectively,
$$\begin{aligned} T_\mathrm{fr}= & {} T_\mathrm{fl} =\frac{0.5F_\mathrm{zf} }{F_\mathrm{zf} +F_\mathrm{zr} }T, \end{aligned}$$
(6)
$$\begin{aligned} T_\mathrm{rr}= & {} T_\mathrm{rl} =\frac{0.5F_\mathrm{zr} }{F_\mathrm{zf} +F_\mathrm{zr} }T . \end{aligned}$$
(7)

3.2 Torque Allocation Strategy Based on the Steering Intention

Steering may lead to lateral instability, the occurrence of understeer or flick and other dangerous situations. The yaw rate and sideslip angle are two important parameters characterizing the stability of a vehicle. The torque is therefore distributed to maintain steering stability when a steering intent is recognized. The torque distribution controls the yaw rate and sideslip angle and generates an additional yaw moment. Increasing the yaw moment is beneficial to steering and vehicle stability.

Coordinate distribution control steering performance by coordinately changing front outer and inner rear-wheel torque. So as not to alter the torque demand of the vehicle, the total torque change is always zero in the whole driving, and the yaw moment is controlled with proportional-integral-derivative controllers. Torque is allocated according to
$$\begin{aligned} T_\mathrm{Z}= & {} 2K\cdot T_{\max }, \end{aligned}$$
(8)
$$\begin{aligned} T_\mathrm{fl}= & {} 0.5T_\mathrm{z}, \end{aligned}$$
(9)
$$\begin{aligned} T_\mathrm{fr}= & {} 0.5T_\mathrm{z} -\Delta M/2, \end{aligned}$$
(10)
$$\begin{aligned} T_\mathrm{rl}= & {} \Delta M/2, \end{aligned}$$
(11)
$$\begin{aligned} T_\mathrm{rr}= & {} 0. \end{aligned}$$
(12)
Here \(\Delta M\) is the additional yawing movement and can be obtained according to:
$$\begin{aligned} \Delta M= & {} \lambda \left( K_{\mathrm{p}\gamma } \Delta \gamma +K_{\mathrm{i}\gamma } \int {\Delta \gamma \hbox {d}t} +K_{\mathrm{d}\gamma } \frac{\hbox {d}\Delta \gamma }{\hbox {d}t}-K_{\mathrm{p}\beta } \Delta \beta \right. \nonumber \\&\left. -\,K_{\mathrm{i}\beta } \int {\Delta \beta \hbox {d}t} -K_{\mathrm{d}\beta } \frac{\hbox {d}\Delta \beta }{\hbox {d}t}\right) \nonumber \\&+\,(1-\lambda )\left( K_{\mathrm{p}\gamma } \Delta \gamma +K_{\mathrm{i}\gamma } \int {\Delta \gamma \hbox {d}t} +K_{\mathrm{d}\gamma } \frac{\hbox {d}\Delta \gamma }{\hbox {d}t}\right) ,\nonumber \\ \end{aligned}$$
(13)
where \(\Delta \gamma \) is the difference between the actual yaw rate and the ideal yaw angular velocity and \(\Delta \beta \) is the difference between the actual sideslip angle and the ideal sideslip angle. \(\lambda =0\) when \(\beta <2^{\circ }\) and \(\lambda =1\) when \(\beta \ge 2^{\circ }\). When the sideslip angle is small, the steering control target is the yaw rate. When the sideslip angle is greater than \(2{^{\circ }}\), the vehicle must be controlled by sideslip angle and yaw rate at the same time.

4 Simulation

A driving intention identification model is established by using MATLAB/Simulink and the vehicle model has nine degrees of freedom. The simulation parameters are presented in Table 3.
Table 3

Simulation parameters of the vehicle

Parameters

Value

Unit

Vehicle mass (m)

1482.7

kg

Body rotational inertia about the X axis (\({I}_\mathrm{x})\)

346.73

kg m\(^{2}\)

Body rotational inertia about the Y axis (\({I}_\mathrm{y})\)

1675.8

kg m\(^{2}\)

Body rotational inertia about the Z axis (\({I}_\mathrm{z})\)

1808.8

kg m\(^{2}\)

Wheel rotational inertia (\({I}_\mathrm{w})\)

5.11

kg m\(^{2}\)

Distance between the front axle and centroid (a)

1.225

m

Distance between the rear axle and centroid (b)

1.437

m

Centroid height (\({h}_\mathrm{g})\)

0.49

m

Front wheel base (\({B}_\mathrm{f})\)

1.438

m

Rear-wheel base (\({B}_\mathrm{r})\)

1.438

m

Wheel rolling radius (r)

0.285

m

Motor peak torque (T)

300

N m

While vehicle accelerating, the acceleration pedal opening is shown in Fig. 7. The peak road adhesion coefficient is 0.3 when the brake pedal opening is zero. At 16 s, steering wheel angle step 0.6 rad/s, and it is shown in Fig. 8.
Fig. 7

Accelerator pedal opening

Fig. 8

Change in the steering wheel angle

Fig. 9

Velocity response

The velocity response is shown in Fig. 9. Results of driving intention identification are shown in Fig. 10.

Results of driving intention identification are shown in Fig. 10 as follows: Adjustment acceleration—emergency acceleration—adjustment acceleration—emergency acceleration—adjustment acceleration—emergency acceleration—adjustment acceleration—steering. The opening degree rate of change is initially large, and the acceleration pedal opening then decreases and increases in a cyclic manner. At 16 s, the recognition result is steering travel.

For the same driver input, Fig. 11 compares the vehicle speed change with and without a torque distribution strategy for the identified intention of driving.
Fig. 10

Driving intention identification

Figure 11 shows that the torque distribution strategy based on driver intention recognition improves the acceleration performance of the car; the time taken to accelerate from 0 to 73 km/h with intention identification reduced by about 1 s, compared to that of without intention identification. This improvement is due to the system recognizing an urgent intention to accelerate and using four-wheel drive to appropriately increase the compensation torque. The torque distribution ratio is determined by the front- and rear-wheel load, and thus greatly improves the dynamic performance of the vehicle.

Figures 12 and 13 show the responses of the vehicle yaw rate and sideslip angle with and without the driving intention recognition control strategy, respectively.
Fig. 11

Speed comparisons with and without a torque distribution strategy

Fig. 12

Response of the yaw rate

Fig. 13

Response of the sideslip angle

Figure 12 shows that, when the vehicle speed is high, the steering control effect is obvious and the yaw rate control reaches a steady state quickly. Without control, the yaw rate is too high, and it takes some time to reach the required steady state. Figure 13 shows that when controlled, the sideslip angle response is better and a steady state is achieved rapidly. The sideslip angle increases very quickly and it is impossible to keep vehicle in a steady state without control. The torque distribution strategy based on the identification of the driver intent improves the vehicle steering stability in extreme conditions. Torque distribution results are shown in Fig. 14.
Fig. 14

Torque distribution

5 Conclusions

By operating the state of driving behaviors to build a recognition model can accurately identify the driver’s intentions. The desired torque distribution is involved in this recognition model. This improves the acceleration performance and steering stability of the vehicle.

Main limitations of the present paper lie in two aspects: the accuracy of fuzzy rules and the formulation of standards, which are worked out depending on plenty of experiments and experience. In future work, we will investigate the identification of driving intention in a full range of driving conditions and develop appropriate torque distribution strategies.

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Copyright information

© Society of Automotive Engineers of China (SAE-China) 2018

Authors and Affiliations

  • Bo Peng
    • 1
  • Huanhuan Zhang
    • 1
    Email author
  • Feihu Xuan
    • 1
  • Wenwen Xiao
    • 1
  1. 1.College of Automotive EngineeringShanghai University of Engineering ScienceShanghaiChina

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