Speed and current sensor fault-tolerant induction motor drive for electric vehicles based on virtual sensors

Abstract

In this work, a sensor fault-tolerant architecture (FTA) for induction motor drives used in electric vehicles (EV) is presented. A bank of observers is designed based on representations of the induction motor model in different reference frames. The fault diagnosis is performed by processing a set of residuals obtained from the bank of observers. The diagnosis method is able to differentiate between single and multiple faults as well as identify the faulty sensor. In addition, virtual sensors are used for the control feedback reconfiguration to obtain a continuous operation of a vector control strategy after a sensor fault. Simulation results of an EV with the proposed FTA validate the effectiveness of the proposal and its robustness against parameter variations. Moreover, results shows a fast control reconfiguration and the ability to return to normal operation if the sensors recover from the faulty condition.

EV model

The simulated EV model is based on an vehicle prototype available at the Applied Electronics Group from the National University of Río Cuarto [4]. For the model description, the chassis is considered as a rigid body and the effect of the suspension is neglected. The EV longitudinal dynamics are expressed as follows [38]:

$$\begin{aligned} {\dot{v}}_x&= \frac{1}{m}\left( 2F_{xr} + 2F_{xf} - F_\mathrm{{aero}} - F_\mathrm{{rod}} - mg \sin \left( \theta \right) \right) \end{aligned}$$

(25)

$$\begin{aligned} {\dot{\omega }}_r&= \frac{1}{J_r}\left( T_r -r F_{xr} - \sigma _\omega \omega _r \right) \end{aligned}$$

(26)

$$\begin{aligned} {\dot{\omega }}_f&= \frac{1}{J_f}\left( -r F_{xf} - \sigma _\omega \omega _f \right) \end{aligned}$$

(27)

where subscripts r and f mean front and rear, respectively; $v_x$ is the longitudinal vehicle speed; $\omega$ is the wheel angular speed; $F_{x}$ is the traction force; $F_{\mathrm{{aero}}}$ and $F_\mathrm{{rod}}$ are the aerodynamic force and the rolling resistance force, respectively; J is the wheel inertia; $\sigma _\omega$ is the viscous friction coefficient of the wheel axis; $\theta$ is the slope of the road with respect to the normal; m is the vehicle mass; r is the wheel radius and g is the gravitational acceleration. In addition, $T_r=N_T T_e$ is the torque applied to the driven wheels, where $T_e$ is the IM electrical torque and $N_T$ is the transmission ratio.

Traction forces are determined by:

$$\begin{aligned} \begin{array}{cc} F_{xi} = F_{Ni} \mu _i \end{array} \end{aligned}$$

(28)

where $i \in \left\{ r, f \right\}$ and $\mu _i$ is the longitudinal friction coefficient of the contact between the tires and the road. This friction coefficient is obtained as follows:

$$\begin{aligned} \mu _i = \text {sign}\left( \sigma _i\right) \left[ A\left( 1 - e^{-B\left| \sigma _i\right| } \right) + C\sigma _i^2 - D \left| \sigma _i\right| \right] \end{aligned}$$

(29)

where A, B, C and D are parameters which depend on the conditions of the patch contact between the wheel and the road. The function $\sigma _i$ denotes the wheels slip, defined by:

$$\begin{aligned} \sigma _i = \frac{\omega _i r - v_x}{\text {max}(\left| \omega _i r\right| , \left| v_x\right| )}. \end{aligned}$$

(30)

Moreover, aerodynamic and rolling resistance forces are obtained, respectively, as follows:

$$\begin{aligned} F_{\mathrm{{aero}}}&= C_a \rho _a A_f (v_x - v_a)^2 \end{aligned}$$

(31)

$$\begin{aligned} F_\mathrm{{rod}}&= mg C_r v_x \end{aligned}$$

(32)

where $C_a$, $\rho _a$, $A_f$ and $v_a$ are the aerodynamic resistance coefficient, the air density, the frontal area of the vehicle and the wind speed, respectively, while $C_r$ is the rolling resistance coefficient.

EV parameters used for simulations are listed in Table 4.