Control strategy for four-wheel independent drive electric vehicles under failure of motor drive systems

Abstract

Four-wheel independent drive electric vehicle cannot follow the driver’s command when one or more motor drive systems fail, which may lead to some serious accidents when the vehicle is running. In order to deal with this problem, a control strategy is proposed in this paper to maintain the stability of 4WID electric vehicle under the failure of motor drive systems. Firstly, failure states of motor drive systems are analysed and classified into Failure-Driving mode and Failure-Stopping mode according to the ability of the vehicle to drive safely. Secondly, a two-layer-control model is designed to maintain the vehicle performance and stability by controlling the remaining normal working motor drive systems for Failure-Driving mode. Thirdly, a control algorithm is designed to help the driver stop the vehicle safely in Failure-Stopping mode. Simulation based on Matlab/Simulink and veDYNA demonstrate that the proposed control strategy can maintain the stability of the 4WID electric vehicle in both Failure-Driving mode and Failure-Stopping mode.

Keywords

4WID direct yaw-moment control electric vehicle fuzzy logic motor drive system two-layer-control model

Introduction

As a solution for energy and environmental problems, electric vehicles (EVs) are receiving considerable attention (Maeda et al., 2012). Some solutions, such as the Tesla MODEL S, have performed extremely well with improved motor and batteries. A four-wheel independent drive (4WID) EV is a vehicle that is driven by four motors (in-wheel or hub) independently. The design of 4WID EVs permits packaging flexibility by eliminating the central drive motor, the associated transmission and drive-train components (including the transmission, the differential, the universal joints and the drive shaft; Tahami et al., 2004). As each wheel of 4WID EV can be controlled independently, yaw-moment control is used to improve its lateral dynamics (Demirci and Gokasan, 2013; Kim et al., 2008; Sakai et al., 1999; Tahami et al., 2003).

In 4WID EVs, the motor drive system consists of a motor, inverter and sensors (current sensors, speed sensors, etc.). As there are four motor drive systems in a 4WID EV, the failure rate of a 4WID EV is higher than an EV with one motor drive system, and the failure of motor drive systems may cause serious accidents when the vehicle is running (Mutoh et al., 2008; Wang and Wang, 2011).

In the research field of EVs, fault-tolerant control methods have been designed to ensure the system’s stability when speed sensors, current sensors, position sensors, etc., failure happens (Diallo et al., 2004; Gaied, 2014; Jeong et al., 2005; Parsa and Toliyat, 2007; Yang et al., 2010). These studies on fault-tolerant control focused on how to diagnose the fault state of the constituting components and how to compensate for the failed situation, but cannot deal with the situation when the drive system fails to generate a driving force (Mutoh and Tomita, 2006). Miyazaki and Ohmae (2005) studied the characteristics of vehicle motion when one inverter in the two-wheel independent drive EV breaks down, and control methods are proposed to improve the instability that occurs when one inverter breaks down. The failsafe performance of a front-and-rear-wheel independent drive-type EV has been studied (Mutoh and Nakano, 2012). Chu et al. (2012) proposed a rule-based strategy to enhance drive capability and lateral stability when failure happens in a distributed electric drive vehicle.

For a 4WID EV, the primary target of the control is safety. If motor drive systems fail, the remaining normal working motor drive systems can be used to maintain the driving performance as usual and drive safely. This study aims to give some contributions in this field; all of the motor drive failures are classified and analysed as Failure-Driving mode or Failure-Stopping mode. Furthermore, on the one hand, a control strategy is proposed to maintain the vehicle’s stability and desired performance in Failure-Driving mode; on the other hand, as the vehicle cannot be driven safely in Failure-Stopping mode, a control strategy is presented to help the driver stop the vehicle safely. The rest of the paper is structured as follows: system modelling is studied in the next section; we analyse the vehicle behaviour at the time of failure; the proposed control strategy is designed; our simulation and the results are introduced and finally, the main conclusion and future works are summarized.

Vehicle modelling

Vehicle model

The proposed method is based on an eight-degrees-of-freedom (8DOF) vehicle model, which is shown in Figure 1. Four degrees of freedom related to the vehicle body are longitudinal velocity ( $v_{x}$ ), lateral velocity ( $v_{y}$ ), yaw rate ( $r$ ) and roll angle ( $ϕ$ ). The other four degrees of freedom are the velocities of the four wheels ( $w_{fl}$ , $w_{fr}$ , $w_{rl}$ and $w_{rr}$ ). The equations of the 8DOF vehicle model can be expressed as

Longitudinal motion:

m {\overset{\cdot}{v}}_{x} = (F_{xfl} + F_{xfr}) \cos δ - (F_{yfl} - F_{yfr}) \sin δ + F_{xrl} + F_{xrr}

(1)

Lateral motion:

m {\overset{\cdot}{v}}_{y} = (F_{xfl} + F_{xfr}) \sin δ + (F_{yfl} + F_{yfr}) \cos δ + F_{y rl} + F_{yrr}

(2)

Yaw motion:

\begin{matrix} I_{z} \overset{\cdot}{r} = l_{f} (F_{xfl} \sin δ + F_{yfl} \cos δ) - \frac{T_{f}}{2} (F_{xfl} \cos δ - F_{yfl} \sin δ) + \\ l_{f} (F_{xfr} \sin δ + F_{yfr} \cos δ) + \frac{T_{f}}{2} (F_{xfr} \cos δ - F_{yfr} \sin δ) - \\ l_{r} (F_{xrl} + F_{xrr}) + \frac{T_{r}}{2} (F_{xrr} - F_{xrl}) \end{matrix}

(3)

Roll motion:

J_{sx} \overset{\cdot\cdot}{ϕ} = ϕ (mg h_{cg} - κ_{ϕ}) - m h_{cg} {\overset{\cdot}{v}}_{y} - \overset{\cdot}{ϕ} β_{ϕ}

(4)

Wheels rotational motion:

{\begin{matrix} I_{w} {\overset{\cdot}{ω}}_{fl} = T_{dfl} - T_{bfl} - R_{eff} F_{xfl} \\ I_{w} {\overset{\cdot}{ω}}_{fr} = T_{dfr} - T_{bfr} - R_{eff} F_{xfr} \\ I_{w} {\overset{\cdot}{ω}}_{rl} = T_{drl} - T_{brl} - R_{eff} F_{xrl} \\ I_{w} {\overset{\cdot}{ω}}_{rr} = T_{drr} - T_{brr} - R_{eff} F_{xrr} \end{matrix}

(5)

where m is the mass of the vehicle; $F_{xfl}$ , $F_{xfr}$ , $F_{xrl}$ and $F_{xrr}$ are respectively the longitudinal forces of the four wheels; $F_{yfl}$ , $F_{yfr}$ , $F_{yrl}$ and $F_{yrr}$ are respectively the lateral forces of the four wheels; $δ$ is the front wheel steering angle; $I_{z}$ is the yaw inertia moment; $l_{f}$ is the distance from the front axle to the centre of gravity (CG); $l_{r}$ is the distance from the rear axle to the CG; $T_{f}$ is the length between two front wheels; $T_{r}$ is the length between two rear wheels; $J_{sx}$ is the moment of inertia around the longitudinal axis; $h_{cg}$ denotes the height of the CG; $κ_{ϕ}$ is the roll stiffness; $β_{ϕ}$ is the roll damping; $I_{w}$ is the wheel moment of inertia; $T_{dfl}$ , $T_{dfr}$ , $T_{drl}$ and $T_{drr}$ are respectively the driving torque of the four wheels; $T_{bfl}$ , $T_{bfr}$ , $T_{brl}$ and $T_{brr}$ are respectively the four brake torque of the four wheels; and $R_{eff}$ is the effective tyre radius.

Figure 1.

Eight-degrees-of-freedom (8DOF) vehicle model.

Tyre model

The tyre–road forces highly influence the vehicle dynamics. The tyre–road model proposed by Dugoff et al. (1970) is used in this study. For the Dugoff tyre model, the tyre forces are directly related to the tyre–road friction coefficient in more transparent equations than other tyre models (Rajamani, 2011). Let $λ$ be the longitudinal slip ratio of the tyre and $α$ be the side-slip angle. Let $C_{x}$ be the cornering stiffness of the tyre and $C_{y}$ be the longitudinal tyre stiffness. Then longitudinal tyre force ( $F_{x}$ ) and lateral tyre force ( $F_{y}$ ) are given by

F_{x} = C_{x} \frac{λ}{1 - λ} \cdot f (L)

(6)

F_{y} = C_{y} \frac{\tan (α)}{1 - λ} \cdot f (L)

(7)

where $f (L)$ is given by

f (L) = {\begin{matrix} L (2 - L), L < 1 \\ 1, L \geq 1 \end{matrix}

(8)

and $L$ is given by

L = \frac{μ F_{z} (1 - λ)}{2 \sqrt{C_{x}^{2} \cdot λ^{2} + C_{y}^{2} \tan^{2} α}}

(9)

where $μ$ is the tyre–road friction coefficient and $F_{z}$ is the vertical tyre force.

Vehicle behaviour analysis at the time of failure

For the purposes of controlling the vehicle when motor drive systems fail, we should first study the failure dynamics of vehicle. A simulation case is conducted to analyse the vehicle dynamics when the motor drive system fails. The known parameters of the 4WID EV model are listed in Table 1.

Table 1.

Specification of vehicle model.

Parameter	Symbol	Unit	Value
Vehicle mass	$m$	kg	1830
Vehicle moment of inertia about Z-axis	$I_{z}$	kg m²	3819
Distance from front axle to rear axle	$l$	m	3.05
Distance from front axle to CG	$l_{f}$	m	1.4
Distance from rear axle to CG	$l_{r}$	m	1.65
Front track width	$T_{f}$	m	1.6
Rear track width	$T_{r}$	m	1.6
The height of CG	$h_{cg}$	m	0.45
Effective radius of wheels	$r_{eff}$	m	0.326

CG, centre of gravity.

In this simulation, the vehicle runs in a straight line and the drive torque of the four wheels is set to 40 Nm. At 2 s, the front left motor drive system fails and the drive torque of the front left wheel drops to 0 Nm. Simulation results are shown in Figures 2 –5.

Figure 2.

Drive torque in motor drive system failure simulation.

Figure 3.

Vehicle trajectory in motor drive system failure simulation.

Figure 4.

Yaw rate in motor drive system failure simulation.

Figure 5.

Side-slip angle in motor drive system failure simulation.

As is shown in Figure 2, before 2 s, the four wheel’s drive torque is 40 Nm. At 2 s, the front left motor drive system fails, and the drive torque of front left wheel drops to 0 immediately. Figure 3 shows that the vehicle rotates to left and cannot follow the target trajectory after failure occurs at 2 s. It can be seen from Figures 4 –6 that a sudden change in yaw rate, side-slip angle and longitudinal speed are caused by the front left motor drive system failing at 2 s.

Figure 6.

Longitudinal speed in motor drive system failure simulation.

It can be seen from the simulation results that the vehicle cannot follow the driver’s commands when the motor drive system fails. A control method should be designed to deal with this situation.

Control strategy design

Failure mode

Failure of the motor drive system may be caused by motors, inverters or sensors and Fault Detection and Isolation (FDI) of motor drive system is not discussed in this paper. If the failed motor is separated from the power supply after failure happens, the motor can still rotate freely under all the electric failures of the motor drive system, and the failed wheel can still be used as a non-driven wheel if the motor can still rotate freely. In this paper, only the electric failure of motor drive system is considered. It is apparent that the work state for each motor is a binary variable, either work or fail. The work state of each motor drive system is defined by

S_{i} = {\begin{matrix} 0 & wheel & fails \\ 1 & wheel & works \end{matrix}

(10)

where $S_{i}$ , with $i = fl, fr, rl, rr$ , is the work state of each motor drive system, and ${S_{fl}, S_{fr}, S_{rl}, S_{rr}}$ stands for the vehicle work state. As each motor drive system has two work states, the vehicle has 16 works states. Except for the states where all motor drive systems work and all motor drive systems fail, the vehicle has 14 failure states. In the vehicle failure states, if two left/right motor drive systems fail, the lateral force generated by the two right/left wheels is much bigger than the failure side, and the vehicle will rotates to the failure side. In order to maintain the stability of a 4WID EV, there should be at least two motor drive systems on the opposite side without failure. From the point discussed above, 14 failure states can be classified into Failure-Driving mode or Failure-Stopping mode. Failure-Driving mode includes the failure states that have at least one motor drive without failure on the left and right side; the other failure states are classified into Failure-Driving mode. The failure mode of 4WID EVs can be defined as

η = (S_{fl} | S_{rl}) & (S_{fr} | S_{rr})

(11)

where is the failure mode. $η = 1$ stands for Failure-Driving mode and $η = 0$ stands for Failure-Stopping mode.

The control algorithms for Failure-Driving mode and Failure-Stopping mode are different. In Failure-Driving mode, a Failure-Driving controller is proposed so that the vehicle can still be driven safely; In Failure-Stopping mode, a Failure-Stopping controller is designed to stop the vehicle safely.

Control for Failure-Driving mode

A double-layer-control-model is proposed in Failure-Driving mode – fuzzy logic-based direct yaw-moment control (DYC) in the upper layer and a torque distribution algorithm in the lower layer. Figure 7 shows the block diagram of the controller in Failure-Driving mode. In the upper direct yaw-moment control layer, a fuzzy-logic-based controller is designed to calculate the deviation of the drive torque; in the lower torque distribute layer, a driving torque calculator and a torque distributor are proposed to distribute the recalculated drive torque to the driven wheels.

Figure 7.

Controller for Failure-Driving mode.

The yaw rate of the vehicle and side-slip angle are in close connection with the vehicle’s stability, and yaw moment control is effective for enhancing the vehicle stability. The aim of yaw moment control is to adjust the yaw rate and side-slip angle to the desired yaw rate and side-slip angle. In our research, it is assumed that the side-slip angle is small, and yaw rate can reflect vehicle’s steady state when the side-slip angle is small. The two-degree-of-freedom (2DOF) vehicle model is widely used to calculate the desired yaw rate and side-slip angle in the application of active stability control of the vehicle (Boada et al., 2005; Rajamani, 2011; Tahami et al., 2003). Equations for the 2DOF vehicle model can be written as

\overset{\cdot}{r} = \frac{l_{f}^{2} C_{f} + l_{r}^{2} C_{r}}{I_{z} v_{x}} r + \frac{l_{f} C_{f} - l_{r} C_{r}}{I_{z}} β - \frac{l_{f} C_{f}}{I_{z}} δ

(12)

\overset{\cdot}{β} = (\frac{l_{f} C_{f} - l_{r} C_{r}}{{mv}_{x}^{2}} - 1) r + \frac{C_{f} + C_{r}}{m v_{x}} β - \frac{C_{f}}{m v_{x}} δ

(13)

As can be seen from Equations (12) and (13), the 2DOFs are the motion of yaw rate and motion of side-slip. In our study, the 2DOF model is enough to calculate the desired yaw rate and side-slip angle. The equation between reference yaw rate and front wheel angle can be described as

r_{ref} = \frac{v_{x} / l}{1 + \frac{m}{l^{2}} (\frac{l_{f}}{C_{r}} - \frac{l_{r}}{C_{f}}) v_{x}^{2}} δ = \frac{v_{x} / l}{1 + {Kv}_{x}^{2}} δ

(14)

and

K = \frac{m}{l^{2}} (\frac{l_{f}}{C_{r}} - \frac{l_{r}}{C_{f}})

(15)

where K is the stability coefficient of the vehicle, and $k_{1}$ and $k_{2}$ are respectively the effective cornering stiffness of the front and rear axle. The desired yaw rate described in Equation (14) cannot always be obtained because low friction of snow or an icy road is unable to enable the tyre forces to support a high yaw rate. Hence the desired yaw rate must be limited by a function of the tyre road friction coefficient (Rajamani, 2011). The upper limit function of ideal yaw rate is set as

r_{up} = 0.85 \frac{μ g}{v_{x}}

(16)

where $μ$ is the tyre road friction coefficient, $g$ is the gravitational acceleration and the desired yaw rate $r_{d}$ can be written as

r_{d} = min {| r_{ref} |, | r_{up} |} \cdot sign (r_{ref})

(17)

DYC is a yaw moment control method that distributes proper traction and braking forces on the right and left tyres to provide a very effective means of stabilizing the vehicle characteristics. According the yaw motion equation in Equation (3), applying different torque to the left-side and right-side wheels can directly control the yaw rate. As the torque of each wheel can be adjusted independently, DYC can be applied to 4WID EV conveniently.

A fuzzy-logic controller is proposed in this paper to calculate the deviation yaw-moment (Figure 8). Fuzzy control is a non-linear control method, which can be used to deal with a complicated non-linear dynamic control problem (Efstathiou, 1988; Wang and Jordan, 1994). The number of applications of fuzzy logic to vehicle control has increased significantly over the last few years (Bauer and Tomizuka, 1996; Boada et al., 2005; Tahami et al., 2002).

Figure 8.

Structure of the fuzzy-logic controller.

There are two inputs in the fuzzy-logic controller: $e (r)$ and $ec (r)$ . $e (r)$ is the error between the real yaw rate and the desired yaw rate, and can be written as

e (r) = r - r_{d}

(18)

$ec (γ)$ is the error rate of change, which can be defined as

ec (r) = \overset{\cdot}{e} (r)

(19)

The number of linguistic variables describing the fuzzy subsets of a variable varies according the application. Fuzzy controllers with seven fuzzy sets are predominant, as they perfectly match a human’s perception of linguistic values (Kovacic and Bogdan, 2005). Seven fuzzy sets are used for both inputs $e (r)$ and $ec (r)$ , which is defined as

{e (r), ec (r)} = {NB, NM, NS, ZE, PS, PM, PB}

(20)

where NB is Negative Big, NM is Negative Medium, NS is Negative Small, ZE is Zero, PS is Positive Small, PM is Positive Medium and PB is Positive Big.

Various combinations of shapes and distributions of fuzzy sets result in a variety of possible controller structures. The triangular membership function with a linear distribution of fuzzy sets is the most widely used in the design of fuzzy logic controllers (Pedrycz, 1994). The triangular membership function is chosen as the membership function of the fuzzy logic controller’s inputs and output. The membership function for $e (r)$ is shown in Figure 9, and the membership function for $ec (r)$ is shown in Figure 10.

Figure 9.

Membership function for yaw rate error.

Figure 10.

Membership function for yaw rate error of change.

For the fuzzy controller’s output, either an absolute controller output or controller output increment are usually generated. A controller output increment is used in this paper, and the control output $Δ T$ is the deviation torque applied to left and right motor drive systems, which is defined as

{Δ T} = {NB, NM, NS, ZE, PS, PM, PB}

(21)

The membership function for $Δ T$ is shown in Figure 11.

Figure 11.

Membership function for deviation torque.

The rule-base is a set of rules that define the relation between the input and output of the fuzzy controller, and the rule-base can be found using the available knowledge in the area of designing the system. The knowledge required to generate the fuzzy rules can be derived from the understanding of the behaviour of the dynamic system under control and offline simulation. These rules in this paper are based on expert knowledge and the extensive simulations performed offline. The fuzzy rule-base for DYC is shown in Table 2.

Table 2.

Fuzzy rule-base for yaw moment controller.

U		E
		PB	PM	PS	ZE	NS	NM	NB
	PB	PB	PB	PB	PM	NS	NS	NS
	PM	PB	PB	PM	PS	NS	NS	NS
	PS	PB	PM	PM	PS	NS	NS	NM
EC	ZE	PM	PM	PS	ZE	NS	NM	NM
	NS	PM	PS	PS	NS	NM	NM	NB
	NM	PS	PS	PS	NS	NM	NB	NB
	NB	PS	PS	PS	NM	NB	NB	NB

PB, Positive Big; PM, Positive Medium; PS, Positive Small; ZE, Zero; NS, Negative Small; NM, Negative Medium; NB, Negative Big; EC; EC, Error Change.

In Failure-Driving mode, if one motor drive system fails, the remaining three motor drive systems can be controlled, but the control of three driven wheels is complex, so we chose two wheels as the driven wheels and the other wheel as a non-driven wheel. In the situation when one wheel fails, the rule to choose driven wheels is defined as

{\begin{matrix} D_{fl} = S_{fl} \times S_{fr} \\ D_{fr} = S_{fl} \times S_{fr} \\ D_{rl} = S_{rl} \times S_{rr} \\ D_{rr} = S_{rl} \times S_{rr} \end{matrix}

(22)

where $D_{fl}$ , $D_{fr}$ , $D_{rl}$ and $D_{rr}$ are respectively the driven state of the four wheels. means that the front left wheel is chosen as the driven wheel; means that the front left wheel is chosen as the non-driven wheel. According to Equation (22), if one wheel in the front/rear fails, the front/rear two wheels are set as driven wheels, and the rear/front two wheels are set as driving wheels. In the situation when two wheels fail, the remaining two wheels would be set as driven wheels; the other two wheels with failure are set as non-driven wheels.

The driving torque calculator in Figure 7 is used to calculator the driving torque in Failure-Driving mode. is a one-dimension map where the input is the accelerator pedal position and output is the desired driving torque $T'$ of each motor drive. As there are only two driven wheels in Failure-Driving mode, the driving torque should be doubled in order to achieve the same driving performance as usual. The desired driving torque of each motor drive in Failure-Driving mode can be described as

T' = 2 K_{normal} θ_{c}

(23)

In the torque distributor shown in Figure 7, the desired torque of the four motor drive systems can be expressed as

{\begin{matrix} {T'}_{fl} = D_{fl} \times (T' + Δ T) \\ {T'}_{fr} = D_{fr} \times (T' - Δ T) \\ {T'}_{rl} = D_{rl} \times (T' + Δ T) \\ {T'}_{rr} = D_{rr} \times (T' - Δ T) \end{matrix}

(24)

where $T_{fl}^{'}$ , $T_{fr}^{'}$ , $T_{rl}^{'}$ and $T_{rl}^{'}$ are respectively the four desired torques of the four motor drive systems. As the desired driving torque $T'$ is doubled, the four desired torques may be higher than the maximal motor torque $T_{\max}$ . Hence the desired torque must be limited by the maximal motor torque $T_{\max}$ . The target torque of the four motor drives can be written as

T_{i} = min {| {T'}_{i} |, T_{\max}} \cdot sign (T_{i}^{'})

(25)

According the algorithms designed above, the control strategy for each failure case in Failure-Driving mode can be explained as follows. If the front left motor drive system fails, $S_{fl} = 0$ , then $D_{fl} = D_{fr} = 0$ and $T_{fl} = T_{fr} = 0$ . The front two wheels are used as non-driven wheels, and the rear two wheels are used to maintain the performance and stability of the vehicle. The control strategy under failure of the front right motor drive system is the same as the strategy of front left motor drive system failure. If the rear left motor drive system fails, $S_{rl} = 0$ , then $D_{rl} = D_{rr} = 0$ and $T_{tl} = T_{tr} = 0$ . The rear two wheels are used as non-driven wheels, and the front two wheels are used to maintain the performance and stability of the vehicle. The control strategy under failure of the rear right motor drive system is the same as the strategy of the rear left motor drive system failure. If the front left and rear right motor drive systems fail, the failed two wheels are used as non-driven wheels, and the remaining two wheels are used to maintain the performance and stability of the vehicle. If the front right and rear left motor drive systems fail, the failed two wheels are used as non-driven wheels, and the other two wheels are used to maintain the performance and stability of the vehicle.

Control for Failure-Stopping mode

In Failure-Stopping mode, because two motor drive systems in the same side fail or three motor drive systems fail at the same time, the vehicle cannot be driven normally. In the case of driving in a straight line, the drive torque of the four motor drives should be set to zero. If the vehicle is turning or changing lane in Failure-Stopping mode, the different torque on two sides of vehicle may cause deflection of driving directions. The vehicle should be stopped in Failure-Stopping mode, but the driver has the option to drive in a real-world application. In our study, a control strategy is presented to improve the performance by controlling the remaining normal working motor drive systems (Figure 12).

Figure 12.

Flow chart of torque distribution in Failure-Stopping mode.

Taking the two left motor drive failures for an example, over-steering happens when vehicle turns left. By applying the braking force to the two right wheels, yaw moment decreases effectively and over-steering can be adjusted. The driving torque of the two right motor drive systems is reduced. The driving torque drops until it equals the maximum braking force torque. The driving torque remains unchanged after it is equal to the maximum braking force torque.

Simulation results

Two simulation cases are conducted based on Matlab/Simulink and veDYNA (Figure 13). The vehicle dynamics program veDYNA is developed and commercially distributed by TESIS DYNAware. The veDYNA simulation results show good agreement with real vehicle behaviour (Butz et al., 2002).

Figure 13.

Human machine interface of the driving simulator.

Failure-Driving mode simulation

Friction coefficient on road surface is set to 0.8. The simulation case of Failure-Driving mode is set as follows: for 15 s, the vehicle accelerates after start-up until its speed is 80 km/h; the steering wheel is turned 70° to the left at 15 s; the front left motor drive system failed at 17 s.

Simulation results are shown in Figures 14 –16.

Figure 14.

Vehicle trajectories in Failure-Driving mode simulation.

Figure 15.

Yaw rate in Failure-Driving mode simulation.

Figure 16.

Torque in Failure-Driving mode simulation.

Figure 14 shows the trajectories of the vehicle. It can be seen that the trajectories with control can follow the reference, and the vehicle without control is over-steered because the front left motor drive system fails when the vehicle turns left. In Figure 15, after the failure happened, the value of yaw rate cannot follow the reference value without control, but the value of yaw rate can follow the reference value with control.

As is shown in Figure 16, torque of the front left wheel reduces to 0 after it failed at 17 s; the torque of the front right wheel reduced to 0 at 17.5 s because of the proposed control strategy adjusting; the torque of the two rear wheels are doubled to maintain normal driving performance. Meanwhile, the yaw moment controller adjusted the output torques of the two rear wheels to maintain the stability of the vehicle.

These simulation results show that the control strategy in Failure-Driving mode can maintain the performance and stability like driving normally. The simulation results of any other case of Failure-Driving mode are similar to this simulation case.

Failure-Stopping mode simulation

The simulation case of Failure-Stopping mode is set as follows: for 15 s, the vehicle accelerates after start-up until its speed is 80 km/h; the steering wheel turns 70° to the left at 15 s; the front left wheel and two rear wheels failed at 17 s. Simulation results are shown in Figures 17 and 18.

Figure 17.

Vehicle trajectories in Failure-Stopping mode simulation.

Figure 18.

Torque in Failure-Stopping mode simulation.

As is shown in Figure 17, trajectories of the vehicle with control are different from the reference, but they are better than the vehicle without control.

As can be seen from Figure 18, the torque of the front left and two rear wheels reduces to 0 at once. The driver should stop the vehicle as soon as possible for safety.

Conclusion and future works

In this paper, the control strategy for a 4WID EV under failure of motor drive systems is studied. Two motor drive failure modes are defined for vehicles in terms of safety, and the control strategy is designed respectively to the two failure modes. Simulation results clearly demonstrate that the proposed control strategies can maintain the stability of the vehicle when the motor drive fails. This study would be useful to enhance the safety of 4WID EVs. For future work, a new design for control strategy may be investigated when the 4WID EV’s main ECU fails.

Footnotes

Declaration of conflicting interest

The authors declare that there is no conflict of interest.

Funding

This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.

References

Bauer

Tomizuka

(1996) Fuzzy logic traction controllers and their effect on longitudinal vehicle platoon systems. Vehicle System Dynamics 25: 277–303.

Boada

Diaz

(2005) Fuzzy-logic applied to yaw moment control for vehicle stability. Vehicle System Dynamics 43: 753–770.

Butz

Chucholowski

Wolter

(2002) Modeling techniques and parameter estimation for the simulation of complex vehicle structures. High Performance Scientific and Engineering Computing. Berlin: Springer, pp. 333–340.

Chu

Luo

Han

. (2012) Rule-based traction system failure control of distributed electric drive vehicle. Journal of Mechanical Engineering 10: 15.

Demirci

Gokasan

(2013) Adaptive optimal control allocation using Lagrangian neural networks for stability control of a 4WS–4WD electric vehicle. Transactions of the Institute of Measurement and Control 35: 1139–1151.

Diallo

Benbouzid

MEH

Makouf

(2004) A fault-tolerant control architecture for induction motor drives in automotive applications. IEEE Transactions on Vehicular Technology 53: 1847–1855.

Dugoff

Fancher

Segel

(1970) An analysis of tire traction properties and their influence on vehicle dynamic performance. SAE Technical Paper.

Efstathiou

(1988) Expert systems, fuzzy logic and rule-based control explained at last. Transactions of the Institute of Measurement and Control 10: 198–206.

Gaied

(2014) Wavelet-based prognosis for fault-tolerant control of induction motor with stator and speed sensor faults. Transactions of the Institute of Measurement and Control. In press.

10.

Jeong

Sul

Schulz

. (2005) Fault detection and fault-tolerant control of interior permanent-magnet motor drive system for electric vehicle. IEEE Transactions on Industry Applications 41: 46–51.

11.

Kim

Hwang

Kim

(2008) Vehicle stability enhancement of four-wheel-drive hybrid electric vehicle using rear motor control. IEEE Transactions on Vehicular Technology 57: 727–735.

12.

Kovacic

Bogdan

(2005) Fuzzy Controller Design: Theory and Applications. Boca Raton, FL: CRC press.

13.

Maeda

Fujimoto

Hori

(2012) Four-wheel driving-force distribution method based on driving stiffness and slip ratio estimation for electric vehicle with in-wheel motors. In: 8th IEEE Vehicle Power and Propulsion Conference, pp. 1286–1291.

14.

Miyazaki

Ohmae

(2005) Driving stability for electric vehicle with independently driven two wheels in case of inverter failure. In: 2005 IEEE European Conference on Power Electronics and Applications, p. 9.

15.

Mutoh

Nakano

(2012) Dynamics of front-and-rear-wheel-independent-drive-type electric vehicles at the time of failure. IEEE Transactions on Industrial Electronics 59: 1488–1499.

16.

Mutoh

Tomita

(2006) Failsafe control methods for EVs with the structure driven by front and rear wheels independently. In: EVS22, 22nd International Battery, Hybrid Fuel Cell Electric Vehicle Symposium and Expo, pp. 23–28.

17.

Mutoh

Takahashi

Tomita

(2008) Failsafe drive performance of FRID electric vehicles with the structure driven by the front and rear wheels independently. IEEE Transactions on Industrial Electronics 55: 2306–2315.

18.

Parsa

Toliyat

(2007) Fault-tolerant interior-permanent-magnet machines for hybrid electric vehicle applications. IEEE Transactions on Vehicular Technology 56: 1546–1552.

19.

Pedrycz

(1994) Why triangular membership functions? Fuzzy Sets and Systems 64: 21–30.

20.

Rajamani

(2011) Vehicle Dynamics and Control. Berlin: Springer.

21.

Sakai

Sado

Hori

(1999) Motion control in an electric vehicle with four independently driven in-wheel motors. IEEE/ASME Transactions on Mechatronics 4: 9–16.

22.

Tahami

Farhangi

Kazemi

(2004) A fuzzy logic direct yaw-moment control system for all-wheel-drive electric vehicles. Vehicle System Dynamics 41: 203–221.

23.

Tahami

Kazemi

Farhanghi

. (2002) Fuzzy based stability enhancement system for a four-motor-wheel electric vehicle. SAE Technical Paper.

24.

Tahami

Kazemi

Farhanghi

(2003) A novel driver assist stability system for all-wheel-drive electric vehicles. IEEE Transactions on Vehicular Technology 52: 683–692.

25.

Wang

Jordan

(1994) An experimental investigation of the dynamic performance of fuzzy logic control. Transactions of the Institute of Measurement and Control 16: 142–148.

26.

Wang

(2011) Fault-tolerant control with active fault diagnosis for four-wheel independently driven electric ground vehicles. IEEE Transactions on Vehicular Technology 60: 4276–4287.

27.

Yang

Cocquempot

Jiang

(2010) Optimal fault-tolerant path-tracking control for 4WS4WD electric vehicles. IEEE Transactions on Intelligent Transportation Systems 11: 237–243.

U		E
		PB	PM	PS	ZE	NS	NM	NB
	PB	PB	PB	PB	PM	NS	NS	NS
	PM	PB	PB	PM	PS	NS	NS	NS
	PS	PB	PM	PM	PS	NS	NS	NM
EC	ZE	PM	PM	PS	ZE	NS	NM	NM
	NS	PM	PS	PS	NS	NM	NM	NB
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	NB	PS	PS	PS	NM	NB	NB	NB

U		E
		PB	PM	PS	ZE	NS	NM	NB
	PB	PB	PB	PB	PM	NS	NS	NS
	PM	PB	PB	PM	PS	NS	NS	NS
	PS	PB	PM	PM	PS	NS	NS	NM
EC	ZE	PM	PM	PS	ZE	NS	NM	NM
	NS	PM	PS	PS	NS	NM	NM	NB
	NM	PS	PS	PS	NS	NM	NB	NB
	NB	PS	PS	PS	NM	NB	NB	NB

U		E
		PB	PM	PS	ZE	NS	NM	NB
	PB	PB	PB	PB	PM	NS	NS	NS
	PM	PB	PB	PM	PS	NS	NS	NS
	PS	PB	PM	PM	PS	NS	NS	NM
EC	ZE	PM	PM	PS	ZE	NS	NM	NM
	NS	PM	PS	PS	NS	NM	NM	NB
	NM	PS	PS	PS	NS	NM	NB	NB
	NB	PS	PS	PS	NM	NB	NB	NB