Improved Sensor Fault-Tolerant Control Technique Applied to Three-Phase Induction Motor Drive

ABSTRACT


INTRODUCTION
The three-phase induction motor (IM) is an AC electric motor that operates on the electromagnetic induction phenomenon to transfer electrical energy into mechanical energy for industrial applications. With the advantages of structure, powerful features, and high efficiency in operation, IM is one of the most used engines in many fields of industry and transportation [1], [2]. In the early days of its inception, IM was mainly used in fixed-speed applications; today, with the rapid development of the field of power electronics, induction motors have extensive involvement in precision speed control.
Two main groups of strategies are used in the speed control of induction motors: scalar control and vector control. Generally, scalar control corresponding to low-cost drive structures is used in applications that do not require high accuracy [3][4][5]. As opposed to the scalar method, the FOC method corresponding to a highperformance drive structure is established as an engineering solution for speed precision control applications [6][7][8]. Learning based on the control principle of separately excited DC motors, rotor flux and electrical torque components are separated and controlled independently in the FOC strategy. A motor drive applying the typical FOC strategy has four main components, including the motor, controller, converter, and sensors, illustrated in Figure 1. Through the control structure of the drive using the FOC control method, we can recognize the critical role of the sensor's feedback signals in controlling IMD's motor speed. During operation, if the loss of feedback signal due to damaged sensors occurs, it will lead to the failure of the FOC algorithm in controlling the motor  [9][10][11]. Nowadays, to increase the IMD's reliability, FTC techniques have been researched to integrate into the FOC loop to ensure continuous operation even in the event of sensor failure [12], [13]. This paper will analyze and provide an effective FTC solution against failures of the speed encoder and the current sensors. FTC consists of three main processes, performed in sequence, including diagnosing the fault sensors, performing faulty measured signals isolation, and replacing the fault signals with the virtual signs of sensorless techniques. Researchers have published many results on the FTC technique with diverse approaches in many scientific papers. Article [14] presents the sensor fault diagnosis based on rotor resistance observer and current indexes to detect the falses of sensors in IMD. After the fault is identified, the FTC controller isolates the wrong measured signals and applies the appropriate sensorless technique to keep the operation of the drive. This method is highly accurate; however, since the sampling cycle is carried out in an electrical current cycle, this method's performance is not suitable for low-speed controlling applications. The authors in the article [15] propose an approach based on the Axes transformation technique for a current sensor failure diagnosis method. Measured stator currents establish two observers in the stationary coordinate systems, each shifting 120 degrees. The current element on the α-axis of each measured observer will be compared with the α-element of the two estimated observers. The deviation of elements in observers will indicate the health status of the current sensors. The authors use the typical comparison technique between the virtual speed and the measured value of the encoder to determine a speed sensor fault. In [16], the authors present a method without using the model and parameter machine for the FTC technique in IMD using a FOC loop. An asymmetry factor based on the RMS value of phase stator currents is used for detecting the faulty current sensor. In a FOC loop, reference currents combining measured currents in the rotating coordinate are used as the detection function for diagnosing the fault of the encoder. This method is highly effective in diagnosing and compensating for sensor faults in IMD systems applying the FOC technique. In [17], a method using the rotor flux value and stator currents for a diagnosis algorithm to detect the fault of the encoder in IMD. This method separates the two stages of error diagnosis and reconfiguration into two independent processes that facilitate their independent development. Paper [18] proposes a solution to diagnose open circuit faults of the current and speed sensors based on third-difference operators combining the rotor slip algorithm. The open circuit fault of current sensors is prioritized to analyze first, then continue to check the condition of the speed sensor. The advantage of this technique is the fast diagnostic time and avoids the effects of random noises.
After correctly identifying the faulty sensor, FTC will isolate uncertain feedback signals and apply appropriate sensorless techniques, including speed sensorless [19][20][21][22] and current sensorless [23][24][25][26][27], to maintain IMD's operation. In this paper, in order to improve the stability, an improved FTC technique applying mathematical functions for diagnosing the operating status of sensors is integrated with the controller of IMD against the total current and speed sensor faults. The content of the proposed method will be presented in the second section, and the simulation results will be described in the third section. Finally, the fourth part will discuss the method's advantages and disadvantages.

PROPOSED FAULT-TOLERANT CONTROL METHOD
In the second section, an improved FTC function integrated into the FOC controller is proposed to reinforce the reliability and stability of IMD against the single fault occurring by disconnection or complete damage of the sensors.  This paper applies the FOC method with independent magnetic flux and torque control to the IMD drive system. The IMD consists of two current sensors and an encoder powered by a voltage source inverter for speed control, corresponding to Figure 2 Where "γ": rotor flux angular. The current components "iSα, iSβ" combined with the measured rotor speed "ωm" are also used to calculate the rotor flux by the current model.
Where "img": magnetic current, "TR=Lr/Rr": rotor time constant The feedback signals are sent to the FOC control loop to compare with setting values, thereby providing a control voltage signal to the PWM modulator. Then, the PWM modulator will provide switching pulses to an inverter for controlling the motor following the reference speed.

The proposed fault-tolerant control against the total sensor faults
To improve the reliability and sustain of the IMD against the total sensor fault, which occurs when the sensor is disconnected or completely damaged, a fault detection-isolation (FDI) unit is embedded into a FOC loop for determining the operating states of the IM; Figure 3 shows the structure diagram of IMD integrating the FTC function in the FOC-loop for speed control. The measured signals from sensors, including stator currents and an encoder, are feedback to the FDI unit for evaluating the quality of signals for deciding on the healthy of the sensors, then provide the output signals to the FOC loop for speed control.
Two diagnosis functions based on measured currents in (11) are used to check the quality of the current signals from the sensors. 22 Under normal operating conditions, the value of Func_FA and Func_FB is always greater than zero. However, if a total current sensor fault occurs, the values of Func_FA and Func_FB corresponding to each current sensor will equal zero, and the fault flags (FA and FB) will increase to a high level (12). "Ti" is a reasonable period for Func_FA and Func_FB to detect the current fault in time, and "Ti" can be selected at about 2 ms, according to [18]. The health of the current signals is determined via the "Fi" flag (13). When current signals are in a healthy state, "Fi" will be 1; otherwise, "Fi" is zero when any current sensor fails.
AB i F F F = (13) After the condition of the current sensor is determined, the FDI unit applies a diagnosis process to check the health status of the speed sensor corresponding to the formula (14), (15) ref to [17].  (15) Where: "Tw" is a reasonable period for Func_FW to detect the speed senor fault in time, and "Tw" must be greater than "Ti." And "Tw" can be selected at about 3.5 ms, according to [18]. "Threshold_w" is the limitation deviation of the real speed and measured speed in the normal operating condition.
The FW flag determines the health status of the measured speed as in formula (16). If the total speed sensor fault occurs, the fault flags (FW) will increase to a high level.
The fault flags' status and the FDI's corresponding output are indicated in Table 1. The estimated signals can be implemented by applying suitable methods such as MRAS, Sliding mode observer (SMO),.. [19][20][21][22] for the estimated speed (̂); and machine modeling, Luenberger Observer (LO),.. [23][24][25][26][27] for the estimated current (̂, ̂). This paper applies the SMO and LO methods to simulate the estimated signals, and these sensorless techniques have been verified for stability by the Lyapunov function in the reference.

RESULTS AND DISCUSSION
In order to demonstrate the feasibility and efficiency achieved in enhancing the reliability of the IMD, simulation analyses will be performed under various sensor fault cases. The motor parameters used in simulation models are presented in Table 2:  The reference speed of the IMD is kept at zero until 0.5 s, then increases to 750 rpm as a step function, as shown in Figure 4(a). Even though the presence of zero speed last 0.5 seconds and the sudden acceleration of the step function, the FTC function of the FDI unit still implements correctly. There is no confusion in sensor fault detection, and all the fault indication flag remains low during this regular operation.
In the first simulation, a complete failure of the speed encoder occurred at 1 second, and the value of this feedback signal fell to zero immediately, Figure 4(a). The FDI unit applied the diagnosis process based on equations from (11) to (16) to detect speed sensor failure correctly, as shown in Figure 4(b). Corresponding to the second case of Table 1, the output signal of the FDI unit supplied to the FOC control loop is the measured currents and the virtual rotor speed, Figure 4(c). The rotor speed fluctuates during the detection and conversion of the control signal, then quickly stabilizes and maintains regular operation. In the second simulation, a complete failure of a current sensor corresponding to the A-phase occurred at 1.5 seconds, and its value fell to zero immediately, Figure 5(a). Similar to the above speed encoder fault, the FTC function of the FDI unit worked correctly, the "FA" flag increased to a high level, and the other two indication flags remained low, Figure 5(b). Corresponding to the third case of Table 1, the output signals of the FDI unit supplied to the FOC loop are estimated currents and the measured speed, Figure 5(c). The IMD still operates stably, as in Figure  5(d). Although there is a noise pulse of the output current in the conversion process, the IMD system overcomes the transient oscillation and stabilizes quickly. Similar to the second case, the B-phase current sensor fault is simulated in the third case to verify the effectiveness of the proposed FTC solution. The defect occurs with the B-phase measured current at 1.5 s, corresponding to a zero value, as shown in Figure 6(a). The detection and isolation process of the FDI unit still operates correctly, and the B-phase current sensor fault is determined instantaneously, illustrated in Figure 6(b). The output of the FDI unit and the stable operation of the motor are presented in Figures 6(c) and 6(d).
Based on the simulation results, the effectiveness of the proposed solution is demonstrated in accurately detecting and isolating each sensor fault. The FDI unit has provided reasonable control signals to sustain the stable operation of the IMD when sensor failures occur.

CONCLUSION
This paper presents an improved sensor fault-tolerant solution applied to the IMDs by using mathematical functions against the fault current and speed sensor. In the diagnosis algorithm, the current sensor's status is determined priority; then, the speed sensor's status will be checked for the FDI unit to make appropriate decisions. The FTC function can work correctly without confusion in detecting sensor failures. The loss of signal from the sensor will be quickly detected by the proposed FTC function and maintain the stable operation of the IDM when the sensor is disconnected or completely damaged. Compared with FTC methods based on the RMS technique, the advantage of the proposed FTC method is the fast fault detection time; sensor failures are almost immediately detected and determined, whereby the steady state of the speed control is quickly re-established under the operating sensorless mode. The fault-tolerant control method has proven effective against sensor failures and improved the IDM system's reliability. The feasibility of the proposed method has been demonstrated through simulation results with a speed sensor and two current sensor faults.