This paper deals with a method of phase current sensor fault reconstruction for permanent magnet synchronous motor (PMSM) drives. A new state variable is introduced so that an augmented system can be constructed to treat PMSM sensor faults as actuator faults. This method uses the PMSM two-phase stationary reference frame fault model and a sliding mode variable structure observer to reconstruct fault signals. A logic algorithm is built to isolate and identify the faulty sensor for a stator phase current fault after reconstructing the two-phase stationary reference frame fault signals, which allows the phase fault signals to be reconstructed. Simulation results are presented to illustrate the functionality of the theoretical developments.
Permanent magnet synchronous motors (PMSMs) are an important category of electric machines, in which the rotor magnetization is created by permanent magnets attached to the rotor. Due to their high efficiency, high ratio of torque to weight, high power factor, faster response, and rugged construction, PMSMs are widely used for high performance variable speed motors in many industry applications. With the development of permanent magnet materials, especially the neodymium-iron-boron (Nd-Fe-B), which has high magnetic energy, high coercive force, and low price, the applications of PMSMs have become more extensive in recent years.
High performance systems usually have demanding requirements on availability, reliability, and survivability [
In recent years, fault-tolerant control has been developed, which can be realized by reconstructing phase currents to substitute current feedback after the fault occurrence. For example, Lu et al. [
Due to the simplicity of the two-axis
Sliding mode techniques are known for their robustness and insensitivity to the so-called matched uncertainty. Therefore these techniques offer great potential for robust fault detection and isolation (FDI) [
The paper is organized as follows. Section
In the
The section proposes a novel method to reconstruct the phase current sensor faults for PMSM drives. Before dealing with the faults, an extended
For system (
Combining systems (
Then, the following augmented system can be obtained:
Therefore, following this transformation, the system is extended and the initial sensor fault problem has become an actuator fault problem. The corresponding extended fault model is
This paper focuses only on sensor faults, which have been transformed into pseudoactuator faults in system (
When
Therefore, there is a matrix
There is a matrix
A fault in the system is a bounded function, such that
The sliding mode observer for system (
If the state estimation errors are defined as
The convergence of the above observer is guaranteed by the following proposition.
Considering the system described by (
For system (
Then, under Assumption
It can be known from above that
This completes the proof.
Proposition
The obtained control algorithm of a sliding mode observer is simple and easy to implement. Because of the excellent robustness of the sliding mode variable techniques, the dependence on the precise mathematical model can be effectively reduced. The performance of the observer can be ensured in the case of a system modeling error, parameter perturbation, and the unknown inputs such as external noise and disturbance. Therefore, it has very strong engineering practicability.
Consider a sliding mode surface:
Proposition
If Assumptions
Selecting the Lyapunov function
Thus, from (
The variables can be defined as
Since
This shows that the sliding mode reachability condition is satisfied. As a consequence, according to sliding mode principle [
This completes the proof.
When the system reaches the sliding mode surface,
Unlike many other methods which use residuals to diagnose the occurrence of sensor fault qualitatively, the method of fault reconstruction presented in this paper estimates the current sensor fault quantitatively. By this way, not only the original appearance of a fault can be reflected vividly, but also more specific fault information can be obtained. It actually becomes the important basis of adopting more targeted measures to eliminate the effect of fault on PMSM drives or achieving the active fault-tolerant control proposal as presented in this paper.
As mentioned previously, a fault on one of the
Generally, for electric motors, only two phase sensors are used. That is based on considerations of cost and the fact that the three phase currents make a vector sum to zero in a star connected system without a neutral line. So, in actual control systems of PMSM, the two phase stator currents,
A linear (3/2) Clarke transformation is applied to transform the three-phase plane coordinate system
For star connected systems without a neutral line,
It can be seen that decoupling can be realized for current in this equation.
As discussed above, practically, currents
From (
In addition, the actual phase current is
Thus, the phase current sensor fault signals can be reconstructed by transformation of the
In the previous literature [
To verify the effectiveness of the method proposed in this paper, the drive tests with respect to two types of faults have been carried out. One tested fault is the incipient fault and the other is the gain sensor fault. The parameters for the PMSM of this study are given in Table
Nominal value for PMSM.
Parameters | Unit | Values |
---|---|---|
Stator resistance ( |
Ω | 2.875 |
Number of pole pairs ( |
Pairs | 4 |
Stator inductance ( |
H | 0.0085 |
Rotor PM flux ( |
Wb | 0.175 |
Rotor moment of inertia ( |
kg⋅m2 | 0.008 |
The matrixes
The matrixes in system (
The matrix
The following saturation function can be used to substitute for the sliding mode signal
The following parameters are chosen:
A sinusoidal signal is added with amplitude 5 A and frequency 150 Hz for
The simulation (Figures
Case
Case
The fault
The fault
Case
A step signal is added with amplitude 5 A from 0.063 s for
The simulation (Figures
Case
Case
The fault
The fault
Case
The simulations show that the fault reconstruction is realized. The fault signal can be estimated to determine the size, location, and time of occurrence of a fault on phase
This paper presents a PMSM phase current sensor fault reconstruction method based on sliding mode variable structure observer. An
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the Natural Science Foundation of China (nos. 61273157 and 61473117), Hunan Provincial Natural Science Foundation of China (nos. 14JJ5024 and 2015JJ5011), and Hunan Province Education Department Project of China (nos. 12A040 and 13CY018).