Sensorless Fault-Tolerant Control of an Induction Motor Based Electric Vehicle

1. Introduction

Recently, fault-tolerant control (FTC) has begun to concern a wider range of industrial applications such as aerospace, automotive, nuclear power, manufacturing, etc. The past two decades have therefore seen considerable research on Fault Tolerant Control (FTC). FTC systems are designed to allow recovery from damage and system faults. When it comes to electrical drives used in safety critical applications or industrial processes where system faults may lead to enormous costs, FTC systems are crucial [1]. Stator, rotor and shaft faults together constitute up to 47% of recorded induction motor faults [1, 2]. Specifically, we address the case in which the faults affecting the controlled system can be modeled as functions (of time) within a finitely parameterized family.

Then, we design a controller, which embeds an internal model of this family, whose purpose is to generate supplementary control actions which compensate for the presence of any of such faults, regardless their entity.

In other words, the control reconfiguration does not rely upon an explicit FDI (Fault Detection and Isolation) design but, indeed, is achieved by a proper design of a dynamic controller, which is implicitly fault tolerant to all the possible faults whose model is embedded in the regulator. To increase the reliability and the continuous operation of electromechanical systems interest in fault tolerance has grown [3, 4]. Indeed, extensive research has been conducted toward fault-tolerant alternating-current motor drives in industrial applications [5, 6]. Fault tolerance is no longer limited to high-end systems but also to railway [7], and automobile applications. It becomes an important means to increase the reliability, availability, and continuous operation of electromechanical systems among the automotive ones [8]. Since the early 1990s there has been resurgence in electric vehicles (EVs) research, stimulated by various factors such as rising oil prices, environmental concerns, cost reduction of power electronics and motor drives, and a marked improvement in energy storage technologies [9]. Electric vehicles (EVs) have become very attractive in replacing conventional internal combustion engine vehicles because of environmental and energy issues. They have received a great attention from the research community. Control methodologies have been actively developed and applied to EVs to improve the EVs performances [10, 11]. A classical EV traction system is studied using an induction motor drive. A separated excited DC load is thus controlled to impose the same behavior of the mechanical power train to the induction motor.

However, this control needs accurate information about rotor speed. The extended kalman filter (EKF) has been successfully applied for sensorless control of induction motor. Consequently, it is considered to be the best solution for the speed and flux estimation using the stator currents and stator voltages of the induction motor drive [12-13].

This paper is organized as follows. In Section 2, the nonlinear model of IM in presence of faults and dynamic of EV are presented. The sensorless sliding mode control (SMC) for the IM is designed in Section 3. The proposed fault tolerant control strategy is described in Section 4. Section 5 is devoted to the presentation of the simulation results obtained for various fault-free situations and fault scenarios when the proposed scheme is applied to the IM. Section 6 presents the experimental results, which shows the effectiveness of the proposed control scheme. Finally, conclusion is provided in Section 7.

 

2. Modeling of the Traction System

2.1 Induction motor model in presence of faults

The induction motor state model developed in the stationary reference frame in presence of faults is given by:

with:

where:

with:

σ is the coefficient of dispersion, Ls, Lr, M are stator, rotor and mutual inductance, respectively. Rs, Rr are respectively stator and rotor resistance.Tr is the rotor time constant .

The presence of electrical faults generates asymmetry of the IM yielding some slot harmonics in the stator winding. In the two-phase model, it is possible to model this effect thinking of a sinusoidal component, which corrupts the stator currents, i.e:

These assumptions allow us to express the deviation of the stator currents values in presence of faults values as [14]:

with:

nf : faults number,

where:

fi is the characteristic frequency of the fault and ݂fa is the fundamental frequency.

The frequency dependent on the kind of fault, which belongs to the two possible classes (rotor or stator faults), and unknown amplitude and phase. The latter depending on the fault severity. In particular it is easy to realize that, defining the exosystem:

with:

The additive perturbing terms in (7) can be thought as a suitable combination of the exosystem state, namely:

with:

In this way, the uncertainty on the amplitude and phase of the additive sinusoidal terms in the faulty condition reflects in that on the initial state of the exosystem. In view of this, it is readily seen that the model of the IM in presence of faults is given by (1) with the exogenous input Vf equal to:

Fig. 1.Traction system scheme of the EV

2.2 Modeling and dynamics of the EV load torque emulator

The EV model and the contact law between wheel and road may be taken into account for a dynamic modeling. But the slip phenomenon is complex and requires specific controllers for good dynamic performance [15].

The road load is then given by [16]:

with Fad is the aerodynamic drag force, Fro is the rol ling resistance force, Fpr is the profile force of the roa d, and Fsf is the Stokes or viscous friction force.

The vehicle velocity vev is obtained using the classical dynamics relationship with the traction and road load forces, Ft and Fw [17]:

with Mev the mass of the vehicle.

The mechanical equation used to describe each wheel drive is expressed by:

where Jtm is the moment of inertia, Tm is the motor t orque, TB is the load torque accounting for friction an d windage, and TL is the load torque.

The gearbox leads to the gearbox torque TW and the rotation speed ωW respectively is given by:

The load torque in the motor referential is then given by:

where N is the transmission ratio, ηtr is the transmissi on efficiency, and RW is the wheel radius.

 

3. Sensorless Sliding Mode Control

3.1 Sliding mode control of IM

Sliding Mode Control is considered to be the appropriate methodology for the robust nonlinear control of induction motor drives due to its order reduction, disturbance rejection, strong robustness and simple implementation by means of power converter [18]. The surfaces proposed by J.J.Slotine are given by:

with k1 and k2 are positive gains.

The corresponding derivative are:

After simplification calculates derivatives of the sliding surfaces are given in matrix form as follows:

with:

The condensed form of (24) is given by:

And check the condition of Lyapunov stability , must have:

Equating (25) and (26) we have:

The law equivalent control is given by:

The law of attractive control is given by:

where: v1 > |F1|, v1 > |F2|

Selecting the gain ki is such that the desired value is imposed at the output of each regulator. The global control ensuring both is given by:

3.2 Speed observer

In an induction motor drive, the Kalman filter is used to obtain unmeasured state variables (rotor speed ωr, rotor flux vector components Φra and Φrβ). The induction motor state model used by the EKF is developed in the stationary reference frame and summarized by:

The discrete induction motor state model used by the EKF is summarized by:

where w(k) represents the disturbances vector applied to the system inputs. It also represents modeling uncertainties; v(k) corresponds to system output measurement noises. It is supposed that the random signals v(k) and w(k) are Gaussian noises not correlated and with null average value. They are characterized by covariance matrixes, Q and R respectively, which are symmetrical and positive definite. with:

● Estimation of error covariance matrix

● Kalman filter gain

● Update of the error covariance matrix

The speed adaptive mechanism is then given by [19]:

where: and .

kp, ki are positive gains.

Thus, the speed value can be estimated by a simple PI controller, to minimize the error ε defined by the following expression:

 

4. Fault-Tolerant and Load Drive Controller

The fault scenario considered in this paper addresses electrical faults caused both by rotor and stator failures of the IM. Fig. (2) shows the proposed flexible architecture for fault tolerant control purposes that maintains maximum performance and the overall system failure rate at an acceptable level. The IM drive will be evaluated using a controlled load drive. This load drive has to impose the same rotation speed as imposed by the mechanical power train (Load characteristics of Electric Vehicle). To provide the right set point to the DC machine rotation speed, the mechanical model is used with the IM torque as input.

Fig. 2.The proposed fault tolerant control scheme

The objective of this technique is to provide an internal model that generates an additive term uad zero in the absence of faults that are added to the nominal control to compensate the effect of faults on the system. The new control is then expressed by:

The term is used to compensate known terms, which allows to give a suitable form to the system dynamics of the error, on the basis of which the unknown term uad calculated [20]. The instantaneous difference between the derivative of the system state and the set value becomes:

where:

For the determination of uad we consider the following system:

Whose dynamics is derived from the system (39):

The Eq. (41) can be written in matrix form:

with:

4.1 Internal model

Assuming that the characteristics of ωi faults (number nf and thus the matrices sf and Γ pulses) are perfectly known, consider the following Sylvester equation [21]:

F and G are matrices of suitable dimensions such that F is an arbitrary stable (Hurwitz), and G selected such that the pair (F, G) is available:

Ms is the unique solution of the Sylvester equation and is non-singular. The internal model takes the following form (known Sf) :

Consider the system (40), uad is selected so as to:

And the expression (42) of becomes:

The new error variable is considered:

We derive with respect to time, taking into account the dynamics of the internal model and the faults:

The equations describing the dynamics of closed-loop errors are:

We need to find the expression of which cancels the error of observation of faults and allows at the same time to reject their effect because it also cancels. Is the Lyapunov function of (51), we have:

After development and derivative with respect to time, becomes:

Finally is written as following:

In this case the choice of is given by:

Then the system (51) becomes:

Finally the objective of the control is achieved by adopting the procedure performed and may compensate for the effect of faults on the system and replicate (e→0) in the internal model. and reproduce (e→0) in the internal model.

 

5. Simulation Results

In order to evaluate the proposed fault-tolerant sliding control strategy performance, simulations have been carried-out for an electric vehicle using a 1 kW induction motor with squirrel cage rotor based powertrain, supplied by a 3-leg VSI and a 1 kW separated excited DC machine supplied by a 4-quadrant chopper. The model of EV consists of a mass of 1.5 t, a wheel radius of 0.3 m, and a vehicle width of 1.6 m. The adaptation coefficients are chosen in function of speed and torque limitations: N=20. The nominal parameters values of the studied induction motor and separated excited DC machine are shown in appendix.

5.1 Simulation of the sliding mode control

Figs. 3 and 4 illustrate the simulation models developed for the performance of the SMC. Firstly, no- perturbations, then at t=8 sec, introducing perturbations in the parameters 80% in rotor resistance (Rr) and stator resistance (Rs), after at t=9 sec occurrence of a single fault in the stator. A trapezoidal trajectory with a reverse operation is imposed as set point of the vehicle velocity vev_ref. The rotation speed of the machine is closed to the speed generated by the mechanical model.

Fig. 3.One fault affects the motor in the stator

Fig.4.Two faults affect the motor in the stator and rotor

Then, two faults are introduced at t=9 sec, one in the stator and the other in the rotor.

From these results, we can see that the proposed control is robust to parameter perturbations and load torque, but is insufficient in case of faults. Increased strength reduces the error on the speed and flux but does not negate the effect of faults on the currents.

Fig. 5.One fault affects the motor in the stator with using the proposed FTC scheme

Fig. 6.Two faults affect the motor in the stator and rotor with using the proposed FTC scheme

5.2 Tests of the FTC approach

The proposed fault-tolerant control strategy has been simulated on a 1 kW induction motor drive whose ratings are summarized in Appendix.

Then, two faults are introduced, one in the stator and the other in the rotor.

 

6. Experimental Results

6.1 Test bench

The test bench used to validate the proposed approach is illustrated in Fig. 7. It is made up of a 1-kW induction motor drive whose ratings are given in the Appendix.

Fig. 7.Photograph of the experimental setup

The experimental test-bench main components are a Static power electronics convertor from Semikron composed of a diode rectifier (AC-DC converter) and a three-leg voltage source IGBT inverter (DC-AC converter), current sensors of Hall, an optical encoder attached to the motor shaft, and a dSPACE 1104 development board, which is interfaced to a standard PC.

In this section experimental results are presented validating the proposed control on the experimental viewpoint. To this purpose, a closed loop control system has been realized that is composed of the above IM, supplied by a voltage source inverter, The IM has been operated with a rotor flux of 1 Wb. Both the controller and the observer have been implemented on a plat form involving a dSPACE1104 micro controller, operating under the Matlab/Simulink environment. The use of the dSPACE plat form is particularly important since it allows rapid prototyping of the control system and a real-time execution of it.

The bloc diagram of the proposed fault tolerant controller used in the experimental set-up is presented in Fig. 8.

Fig. 8.Experimental test setup: schematic diagram

6.2 Experimental tests

The experimental results obtained are presented in Figs. (9-12) show clearly the effectiveness of the FTC scheme that occurs during the application of the fault by removing all defects thanks to the FTC strategy. In faulty conditions, it is found that the observer has better performance for high and low speeds. We see that the speed follow up the reference quickly and perfectly for the SMC which confirms the robustness of this technique.

Fig. 9.Reference, real and estimated of IM speeds in faulty conditions (upper plot) in case of single fault affect the IM at time t=9s, and healthy conditions (lower plot) with using the proposed FTC scheme

Fig. 10.Induction motor currents in faulty conditions (upper plot) in case of single fault affect the IM at time t=9s, and healthy conditions (lower plot) with using the proposed FTC scheme

Fig. 11.Reference, real and estimated of IM speeds in faulty conditions (upper plot) in case of two faults affect the IM at time t=9s, and healthy conditions (lower plot) with using the proposed FTC scheme

Fig. 12.Induction motor currents in faulty conditions (upper plot) in case of two faults affect the IM at time t=9s, and healthy conditions (lower plot) with using the proposed FTC scheme

 

6. Conclusion

This paper has presented a sensorless fault-tolerant sliding mode control strategy of induction motor based on electric vehicle application, suitable for dealing with electrical faults. A fault tolerant control based on SMC strategy is designed to steer the flux and the speed to their desired references in presence of rotor and stator resistance variations. The simulation and experimental results show the robustness of the proposed control scheme, and the results presented in this paper confirm that the EKF observer is more efficient. This controller presents high robustness in presence of the internal and the external perturbations.