New Real-time Algorithm For Control Allocation of In-Wheel motor vehicle轮毂电机电动汽车转矩分配算法 - 图文

F2014-EPT-068

A New Real-time Algorithm For Control Allocation of In-Wheel-Motor Electrical

Vehicle

Zhengyi, He; Quanhui, Du; Hao, Zhang

China Automotive Engineering Research Institute, P.R.China

KEYWORDS –In-wheel motor electric vehicle, Control allocation, Real-time algorithm

ABSTRACT –

The main goal of this paper is to develop a geometry based algorithm to solve the control allocation problem for electric vehicle using in-wheel motors. The proposed method do not require iterative computations, hence the computation effort can be greatly reduced and can be used in real-time application. The theoretical basis and details of the algorithm are discussed this paper. It is also shown that the proposed method also can be used in several other four-wheel drive vehicles. The effectiveness of the proposed control allocation algorithm has been validated by the software tests. 1. Introduction

As to four-wheel independent drive vehicle(4WD) using four in-wheel motors, the four motors can be used as the actuators to generate the desired traction and active yaw-moment. This arise a new problem called control allocation problem. Control allocation deals with the problem of distributing the yaw moment command and desired traction force command to several actuators(four in-wheel-motors), while the output of actuators(four in-wheel-motors) satisfying the given constraints.

It is noticed that the previous published papers [1-6] on control allocation problem are all focus on discussing the methods which require many iteration times, such as interior-point algorithms, low computational efficiency is the major problem for those control allocation algorithms.

In general, the control allocation problem can be formulated as linear programming problem. However, when the number of variables in a linear programming problem is great than three or more, it is difficult to use geometry method to calculate the feasible solutions. In this paper, we develop a geometry based method to get the feasible solutions while the control allocation has four variables.

The major contribution of this paper is that we use geometry method to develop real-time algorithm for control allocation problem, which does not require iteration computation. As to the proposed method, there is no problem on the performance of convergence rate and computational efficiency.

2. Details of The Proposed Method 2.1 The Control Allocation Problem The control allocation problem of four-wheel independent drive vehicle(4WD) using four in-wheel motors, can be described by Table 1. F_Pedal denotes the desired force computed from acceleration pedal position, Ffl denotes desired front-left motor output force, etc. Ffl_B_max denotes front-left motor maximum braking torque, etc. k is defined as the front force divided by total force, M defined as the desired yaw moment torque.

Table 1. the control allocation problem of four-wheel-drive vehicle

Cost function Input variables. Auxiliary relaxation variables ΔF, ΔM Output variables. Output variables. Equation constraints(1) Inequality constraints(2). Problem A Min |ΔF |, Min |ΔM |. F_Pedal, k, M ΔF= F_Pedal_Modi - F_Pedal, ΔM = M_Modi – M. solution of Ffl, Ffr, Frl, Frr F_Pedal_Modi, M_Modi Frr+Ffl+Frl+Ffr=F_Pedal+ΔF, (Ffr-Ffl)Lf+(Frr-Frl)Lr=M+ΔM. Ffl_B_max

Then the above problem A in the Table 1 can be rewritten as problem B. At the same time, we can calculate the four motors force using the following equations,

Ffl=Ff-0.5Df, (4) Ffr=Ff+0.5Df, Frl=Fr-0.5Dr, Frr=Fr+0.5Dr,

As to problem B, the following problem should be solved, 1）to get the set of feasible solutions of Ff,Fr 2）to get the set of feasible solutions of Df,Dr

3）modify F_Pedal so that the constraints about M is always satisfied, because desired yaw moment M greatly influence the stability of vehicle

4）If necessary, modify M so that problem B has one solution at least.

Figure1. Architecture of the proposed control allocation method as to problem B

2.2 The Properties of The Feasible Sets of (Ff, Fr), (Df, Dr) Theorem 1: the feasible solutions of (Ff, Fr) should lie in the rectangular area HIJK, which can be seen in figure 2,

H: (max(Ffl_B_max +0.5Df, Ffr_B_max -0.5Df), min(Frl_ T_max+0.5Dr, Frr_ T_max-0.5Dr)), I: (min(Ffl_T_max+0.5Df, Ffr_ T_max -0.5Df) , min(Frl_ T_max+0.5Dr, Frr_ T_max-0.5Dr)), J: (min(Ffl_T_max+0.5Df, Ffr_ T_max -0.5Df) , max(Frl_B_max+0.5Dr, Frr_B_max-0.5Dr)), K: (max(Ffl_B_max +0.5Df, Ffr_B_max -0.5Df), max(Frl_B_max+0.5Dr, Frr_B_max-0.5Dr)). Proof:

According to the inequalities in Table 2, we have,

Ffl_B_max

We can get,

max(Ffl_B_max +0.5Df, Ffr_B_max -0.5Df)

From,

Frl_B_max

We can get,

max(Frl_B_max+0.5Dr, Frr_B_max-0.5Dr)

It is noted that the rectangular area HIJK can be described by inequalities (5),(6). QED.

Figure2. Graph to determine the feasible solution sets of Fr, Ff.

Theorem 2: when F_Pedal>0.

The intersection line segment between HIJK and the line described by equation (1.1) exists, if the necessary conditions that (Df, Dr) lies in the rectangular area UVWX is satisfied, which can be seen in figure3. Proof:

When F_Pedal>0, line defined by equation (1.1) should lie between point I and point K in figure 2, which can be written as the following inequalities.

inequality (7):max(Ffr_B_max?0.5?Df,Ffl_B_max?0.5?Df) ?max(Frr_B_max?0.5?Dr,Frl_B_max?0.5?Dr)

?F_Pedal/2?min(Ffr_T_max?0.5?Df,Ffl_T_max?0.5?Df) ?min(Frr_T_max?0.5?Dr,Frl_T_max?0.5?Dr)?inequality (8):（Ffr_B_max?0.5?Df）（+Frr_B_max?0.5?Dr）?F_Pedal/2（Ffr_B_max?0.5?Df）（+Frl_B_max?0.5?Dr）?F_Pedal/2 （Ffl_B_max?0.5?Df）（+Frr_B_max?0.5?Dr）?F_Pedal/2（Ffl_B_max?0.5?Df）（+Frl_B_max?0.5?Dr）?F_Pedal/2F_Pedal/2?（Ffr_T_max?0.5?Df）（+Frr_T_max?0.5?Dr）F_Pedal/2?（Ffr_T_max?0.5?Df）（+Frl_T_max?0.5?Dr）F_Pedal/2?（Ffl_T_max?0.5?Df）（+Frr_T_max?0.5?Dr）F_Pedal/2?（Ffl_T_max?0.5?Df）（+Frl_T_max?0.5?Dr）?inequality (9):

2Ffr_B_max+2Frr_B_max?F_Pedal?Df+Dr?F_Pedal?2Ffl_B_max?2Frl_B_max2Ffl_B_max+2Frr_B_max?F_Pedal?Dr?Df?F_Pedal?2Ffr_B_max?2Frl_B_maxF_Pedal?2Ffl_T_max?2Frl_T_max?Df+Dr?2Ffr_T_max+2Frr_T_max?F_PedalF_Pedal?2Ffr_T_max?2Frl_T_max?Dr?Df?2Ffl_T_max+2Frr_T_max?F_Pedal?inequality (10): max(2Ffr_B_max+2Frr_B_max?F_Pedal,F_Pedal?2Ffl_T_max?2Frl_T_max)?Df+Dr?min(F_Pedal?2Ffl_B_max?2Frl_B_max,2Ffr_T_max+2Frr_T_max?F_Pedal)max(2Ffl_B_max+2Frr_B_max?F_Pedal,F_Pedal?2Ffr_T_max?2Frl_T_max)?Dr?Df?min(F_Pedal?2Ffr_B_max?2Frl_B_max,2Ffl_T_max+2Frr_T_max?F_Pedal)We should notice that rectangular area UVWX is denoted by inequality (10). QED.

Figure3. Graph which can be used to determine the feasible solution of Dr, Df.

Remark 1: when F_Pedal≤0, the point K in figure 2 should lie on left behind of the line Ff+Fr=0. This means that

max(Ffr_B_max?0.5?Df,Ffl_B_max?0.5?Df)?max(Frr_B_max?0.5?Dr,Frl_B_max?0.5?Dr)?0 (11)

Theorem 3: the feasible sets of (Df, Dr) should lie in the rectangular area PQRS, which shown in figure 3,

P: (Ffr_B_max-Ffl_T_max, Frr_T_max-Frl_B_max), Q: (Ffr_T_max-Ffl_B_max, Frr_T_max-Frl_B_max), R: (Ffr_T_max-Ffl_B_max, Frr_B_max-Frl_T_max), S: (Ffr_B_max-Ffl_T_max, Frr_B_max-Frl_T_max). Proof:

From inequalities (2) in Table 1, we have,

Ffr_B_max

Ffr_B_max-Ffl_T_max

It is noted that the rectangular area PQRS can be denoted by inequality (12). QED.

Theorem 4:

The rectangular area HIJK in Figure 2 always exist, if (Df , Dr) lie in the area PQRS in Figure 3. Proof:

The necessary and sufficient conditions that rectangular area HIJK in Figure 2 always exist, can be written as,

.

If (Df , Dr) lie in the rectangular area PQRS in Figure 3, then we can get the following inequalities,

min( Frr_T_max?0.5?Dr,Frl_T_max?0.5?Dr)?max(Frr_B_max?0.5?Dr,Frl_B_max?0.5?Dr)min(Ffr_T_max?0.5?Df,Ffl_T_max?0.5?Df)?max(Ffr_B_max?0.5?Df,Ffl_B_max?0.5?Df)