Improvement of EV Maneuverability and Safety by Dynamic Force Distribution with Disturbance Observer

Multi-wheel driven EV is referred to as an over-actuated system in the motion control synthesis process. It is meaningful to use the redundant actuators to maintain the control reliability and thus improve the dynamics of EV. In this paper, a dynamic optimum force distribution method which utilizes redundant motors is discussed. Besides, we also mention a disturbance observer to estimate the tire friction conditions. Incorporated with active yaw moment control, the proposed method is evaluated by the experiments. The results show the proposed method can improve dynamics and keep handling stability of the EV.


INTRODUCTION
For the reason of environmental protection and energy conservation, researches about electric vehicle (EV) have been put forward greatly in recent years.
In-wheel motored EV is a newly developed vehicle. As Fig.1 shows, the driving electric motors are installed into wheels. That motored wheel can be controlled independently [1]. Based on this kind of configuration, it is easy to perform force control directly and realize complexity motion control without traditional power train or mechanical parts. Therefore, it inevitably stimulates the researches about the "by-wire" control.
Multi-in-wheel driven EV is looked on as an over actuated system. It is meaningful to take advantage of redundant in-wheel motors to improve control reliability and dynamics of that kind of EVs.
Since that, EVs must be controlled much more adaptable than before.
Force control of motored wheels is the basement for all advanced motion control strategies. To obtain an optimum "force control" by using all of the controllable driving motors, which include redundant ones, is the main theme of dynamic force distribution.
For the next generation EVs, there is a potential requirement for the development of dynamic force distribution control, which has properties of dependable, adaptable and optimizable [8]. However there are fewer researches on this topic. So far there is even no practical application of this research to be realized on a multi-in-wheel driven EV.
In this paper, we discuss a dynamic force distribution method and apply it by incorporating with the maneuverability assistant control system, which is well known as active yaw moment control. y optimal force control of motored wheels, traction fo oment can be obtained by on r dangerous road co Fig. 1 "UOT March II" and its in-wheel motors B rce between tire and road could be generated instantly.
Due to such precise traction force generation, yaw moment, which effects EV yaw rate, can be controlled exactly [2]. We will use this active controllable yaw moment to improve maneuverability and keep safety throughout yaw rate control.
Normally, the active yaw m ly controlling two motored wheels on the different sides of EV. However, if all wheels are motored, the same yaw moment can be obtained by force control of different groups of motored wheels.
When EV drives in a critical o ndition, the redundant driving motors can be used for avoiding the tire slip or wheel lock. In other case, for example, when one motored wheel suddenly fails and can not produce the nominal control effect, the redundant ones can be used to make up the difference and prevent controllability from degrading.
To use the redundant motors, tire working conditions sh se

As a , a fo
The proposed method will be evaluated by the ex ould be well considered. Although many kinds of expensive sensors can be used for the detection of tire friction forces, it is difficult to clearly know that values in real time. Therefore, in this paper we also propose an estimation method based on a disturbance observer.
The remainder of this paper is organized as follows: ction 2 mentions the analysis of vehicle dynamic; section 3 discusses estimation of tire friction force; section 4 mentions dynamic force distribution; section 5 mentions the evaluation of force distribution integrated with active yaw moment control; section 6 mentions conclusions and future works. n example of multi-wheel-driven EV ur-wheel-driven EV is studied in this paper. The free body diagram is shown in Fig. 2.
periments of the yaw rate control. Therefore, it is natural to consider the horizontal motion of EV. We assume that the front steering is controlled by the driver. The steering angles of left and right sides are equal. Four motored wheels can be controlled independently.
We also assume that the front steering angle f and side slip angle of EV body are very small.
In this paper, we also assume that the steering angle is small and the longitudinal velocity is constant. From Eq.1 to Eq.5, the linear dynamics of EV planar motion can be written as: From Eq.6, the transfer functions from steering angle an yaw moment to yaw rate can be written as: d parameters [4]. n is the damping coefficient. n is the natural frequency of control system. where n n . In this study we define 1.5 n n .

ESTIMATIONS
A friction conditions tribution. It is well know sa se the measured longitudinal and l accelerations to estimate th motored wheel can be expressed as: s mentioned above, it is necessary to know the tire for dynamic force dis n that the tire friction forces, which are shown in Fig.3, tisfy: We u ateral e normal forces acted on the wheels. Normal forces could be estimated in real time [6]. It is easy to estimate observer, which is sh

Force on the Lateral Direction
the traction force by a disturbance ow in Fig.4.
Yaw momentˆz x M , which is generated by the left and right traction forces, can also be estimated. The es n timator is show in Fig.5, which is a common idea in the researches of control of wheelchair [5].
Rewrite the Eq.1 and Eq.2 as follows The front and rear lat follows eral forces can be calculated as In Eq.13 and Eq.14, deviation of side slip angle obtained with the side slip angle estimation, wh can be ich is published by [7]. According to Eq.6, the der ative variable iv can be written as: In this study, we assume that the slip angles and road conditions of left and right tire are equal. We can get the lateral force of each tire as:  Fig.6 shows, the control effectors are the required force ( athematic Statement of Dynamic Fo bution D namic force distribution is used to utilize the redundant drivi namic distribution is stated as a kind of inverse optimal control problem.
As for the inverse control problem, the control effectors, for example the w moment, are defined first. According to those required control effectors, control inputs of the system will be generated by the force distribution.  T n the maximum mains. T possible to get unique solutions. However, it is that redundancy makes it possible to optimize some other criterions. For example, the tire work load inimized by actively controlling redundant actuators. Considering the above mathematic descriptions, the force distribution problem can be stated as: Cost function

Cost Function
re work load as: Fig. 6 Outline of dynamic force distribution Considering the tire friction conditions, which are shown in Fig.3 y is about 10 km/h. The friction co steering angle is kept as a constant value. The driving force is also kept constant.
In this experiment, the EV is controlled to follow a desired behavior, which is the neutral steering

Evaluations
Using that experiment, we evaluate our proposed dy een the reference yaw rate and the real one becomes larger and larger. Fig. 9 also shows that the proposed force distribution method can improve the turning performance much better than what of the equal distribution method does. Fig.10 shows the corresponding force commands which are generated by the dynamic force distribution fo Further, it is well known that the lateral acceleration of the EV is also important for the handling characteristic of the EV. We also discuss the effect of proposed control method on the lateral acceleration of EV. We compare the equal force distribution method nstrained quadratic programming problem [3]. We in this paper do not prepare to talk about these mathematic theorem and numerical algorithms in details.
What we should mention is that there are two efficient methods for solving constrained quadratic programming problem till nowadays. One is the "Active set method" and the other is "Interior-point m is study we use the "Active set method", which has the less computation load and high accuracy in the small dimensional case.

Active Yaw Moment
main goal of active yaw moment control e maneuverability or maintain stability in cri driving situations. In those cases, it is difficult for drivers to con ystem is expected to work as a drive assistant.
However, the required yaw moment or total force cannot be a direct input command for the force control of tire. In this paper active yaw moment control is implemented with dynamic force distribution. It i generate force commands for force control by optimally managing redundant driving motors. Fig.7 shows the block diagram of whole control system.
In the integrated control system, yaw moment control is the high level controller. It calculated the active yaw moment which is required for yaw rate control. This yaw moment controller integrates yaw rate feed ntrol with yaw moment feed forward control.

Experiment
The design of experiment is show is controlled to turn a constant radi n in Fig.8. The EV ip The initial velocit efficient is about 0.3~0.4. During experiment, the characteristic. In this experiment, we try to realize that neutral steer performance by controlling yaw rate of EV.
namic force distribution method by comparing the equal distribution method, which distribute the left and right forces in an equal way.
Without any control method, as Fig.9 shows, EV can not follow the desired neutral steering. The error betw r the driving motors. Fig. 7 Block diagram of integrated control system Ge rated driving mmands [Nm] co Acceleration time with the proposed method. The effect of proposed dynamic force distribution on the lateral acceleration is shown in Fig.11. The experiment results indicate that the maximum lateral acceleration is enlarged by the proposed method. However, in the case of equal force distribution, the effect on the lateral acceleration of EV is not so much as the proposed method.
From the results mentioned above, it can be shown that the dynamic optimum force distribution improves th c dynamic optimum force distribution method will be real [ 9.
[3] Peng  e handling characteristics of EV. Besides that we also try different control methods, which act as the outer-loop yaw rate controller. A 2-DOF controller is designed and integrated with the proposed dynamic force distribution method. Experiment results also show a quite well corporation of proposed force distribution with the higher level control law.

CONCLUSIONS AND FUTURE WORKS
In this paper, we discuss the dynamic force distribution for motion control of multi-wheel-driven EVs. We evaluate that method by the experiments. The results show that the method can greatly improve the handling dynamics of that kind of EV, especially when it derives in a dangerous condition.
We also discuss the technologies about dynami force distribution in this paper. For example, the yaw rate control logic and tire force observation.
In the future, the estimation of tire working conditions should be improved. For example, the lateral friction force can be known easily and accurately. Based on the obtained information of tire forces, the ized on-line more easily.  Fig. 11 Description of the experiment The turning radius is 15 meters; steering angle is 200 degree; acceleration torque of four motors is about 932 Nm, the longitudinal acceleration is about 0.13g; the gains are changed.