Current Sensor FTC Method for MPTC of Three-Phase Induction Motor Drives Without Speed Measurement

In encoderless Model Predictive Torque Control (MPTC) of three-phase Induction Motor (IM) drives, current sensors can face different electrical or mechanical faults in harsh industrial environments. In this research, single-phase current sensor Fault-Tolerant Control (FTC) method for MPTC of three-phase IM drives without speed measurement using a flux linkage observer and Model Reference Adaptive System (MRAS) algorithm is proposed. In the presented FTC method, Third-Difference operators, logic circuit module, flux linkage observer, and MRAS algorithm are utilized for fault detection, fault isolation, estimation of stator currents and fluxes, and speed estimation, respectively. In comparison with the conventional current sensor FTC methods, the proposed method can be utilized for encoderless three-phase IM drives. In order to confirm the usefulness and possibility of the proposed encoderless FTC method, experimental studies are performed for a 0.75 kW three-phase IM drive system in different situations. The achieved results demonstrate good performances of the proposed technique during both normal and faulty situations.


Introduction
Three-phase Induction Motor (IM) drives are broadly utilized in various industries such as renewable energy conversion systems, pumps, and electric traction [1][2][3]. Commonly, speed sensors such as encoder or tachometer are used for high-performance control of three-phase IM drives. The use of speed sensor increases the cost of drive system and decreases its reliability. Consequently, speed estimation techniques, such as Extended Kalman Filter (EKF), Sliding Mode Observer (SMO), signal injection techniques, have become a hot research subject in the field of three-phase IM drive systems [4][5][6][7][8].
Model Predictive Torque Control (MPTC) strategy is a recent alternative control technique to Direct Torque Control (DTC) and vector control. In this strategy, the switching states of the inverter are optimized using a cost function. In recent years, different MPTC techniques have been proposed for three-phase IM drives. For example, Habibullah and Lu proposed an encoderless MPTC method using two EKF algorithms [9]. The obtained results in [9] show that the current distortion can be decreased particularly at low speed region. Zhou et al. proposed a control strategy based on MPTC technique using four-switch inverter with suppression of the DC-link voltage offset [10]. Bindal and Kaur introduced a developed MPTC method for three-phase IM drives using fuzzy logic to reduce torque ripples [11]. Feedback correction-based dual reference frame MPTC strategy for encoderless control of three-phase IM drive systems to decrease the electromagnetic torque prediction error was presented by Yan et al. [12]. Bhowate et al. presented a MPTC with online weighting factor computation [13].
A drive system may suffer from electrical or mechanical fault(s), causing safety and dependability difficulties. In other words, Fault-Tolerant Control (FTC) strategies are highly important for motor drive systems [14][15][16][17][18][19][20][21][22][23][24][25]. Generally, FTC strategies can be classified into passive FTC systems and active FTC systems. In spite of the simple structure of a passive FTC system, this approach has less fault-tolerant capabilities [14]. In this case, active FTC systems are preferable.
Single-phase Current Sensor Faults (CSFs) are common in industrial environment due to electrical, thermal, and mechanical stresses. Failure in current sensors can degrade the drive system performance or in some cases can cause the system shutdown. Current sensor FTC strategies are an important field of study for motor drives.
Although different FTC systems have been developed for three-phase motor drives under current sensor failure, there are few current sensor FTC schemes for encoderless three-phase drives. Compared with the previously published papers, the study on encoderless control of three-phase IM drives under single-phase CSF is relatively mature, and an acceptable performance without speed measurement can be achieved.
In this paper, single-phase current sensor FTC strategy for encoderless MPTC of three-phase IM drives using flux linkage observer and Model Reference Adaptive System (MRAS) algorithm is proposed. In the proposed FTC strategy, a Third-Difference (TD) mechanism, flux linkage observer, and MRAS algorithm are utilized for fault detection, estimation of stator currents, and speed estimation, respectively. Through the flux linkage observer, not only the motor currents but also the stator and rotor fluxes used in the control system are estimated. In the presented system, a logic circuit module executes the task of CSF isolation. In other words, in the proposed scheme, a sensorless modified MPTC with a flux linkage observer is used for the healthy IM. After the CSF, the fault detection and isolation units which are based on the TD algorithm and a logic circuit module recognize the CSF condition and select the suitable currents. Then, these currents in cooperation with stator voltages produce the motor speed and fluxes. The motor speed and fluxes are used in the MPTC system. The proposed FTC scheme not only works during the CSF, its performance during normal condition is highly satisfactory as a modified MPTC strategy is used in this condition. According to the previous works in the literature, the following contributions can be presented: • A modified sensorless MPTC for three-phase IM drives under healthy condition using MRAS algorithm is presented. • A current sensor FTC method for MPTC of three-phase induction motor drives without speed measurement is presented. • The motor speed, rotor fluxes, stator fluxes, and motor currents using MRAS algorithm and a flux linkage observer are estimated. • A fault detection and isolation mechanism for the CSF using TD operators and a simple logic circuit module is presented.
Such FTC system can be used in many industrial safety crucial applications such as electric vehicles, ventilation systems, aerospace, and transportation systems. The suggested FTC scheme is experimented under different operating conditions using the TMS320F28335 controller board to demonstrate the applicability of the introduced FTC algorithm.

Literature Review
Generally, active FTC systems include two main parts: (1) fault detection and isolation systems and (2) a control technique for post-fault operation. This section includes two sections. First, different fault detection and isolation systems for motor drives are discussed. Then, some important works to control motor drives during the CSF are presented.
Fault detection is an important section of active FTC systems. In general, fault detection mechanisms can be categorized into four approaches [26,27]: (1) model-based techniques, (2) signal-based techniques, (3) data-driven techniques, and (4) combinations of (1), (2), and (3). Model-based fault detection strategy is an effective approach which is used in many applications [15][16][17][18]22]. In [15,16], artificial neural network and fuzzy logic strategies for the CSF detection were used, respectively. The strategies used in these papers need a large volume of historical information and prior data. Yu et al. used a model-based CSF detection method using three separate observers [17]. These observers can monitor the condition of the sensors in the healthy situation. After CSF, these observers detect the faulty condition. Chakraborty and Verma presented a CSF detection technique using Clarke transformations [18]. In [18], two Clarke transformation matrices were utilized to compare the stator current residual with the predefined threshold to determine the faulty situation. Using three observers in [17] and using different Clarke transformation matrices in [18] increase the complexity of the control system structure. Manohar and Das used a CSF detection mechanism based on the TD operator for IM drives [22]. This mechanism can provide fast and effective fault detection even for a slight change in the stator current.
Another essential part of the FTC system is the post-fault control system. There are two possibilities for post-fault control of IM drives under CSF. In the first approach, when the sensor fault happens, the drive system switches from a closed-loop system to an open-loop system [19] or a current sensorless closed-loop control system [20]. This approach reduces drive system performances conspicuously, and it is not appropriate for many industrial applications. In the second approach, an estimation technique is utilized to acquire the faulty current value. It can be mentioned that in this approach, the structure of the control system remains unchanged. In the second technique, the estimated motor current corresponding to the faulty motor current sensor is utilized in the control system. Consequently, uninterrupted and continuous operation can be realized. Different estimation techniques have been presented in the literature to obtain the value of the faulty current during the post-fault operation. Some of these techniques are reviewed as follows: Yu et al. used three independent adaptive observers for the post-fault control [17]. These observers provide the estimated current value. As mentioned before, this strategy suffers from high complexity due to three observers. In Chakraborty and Verma, the motor currents were reconstructed using the vector rotator concept [18]. In this paper, the motor currents were estimated based on the actual and command stator currents. Thus, the estimated motor currents change slower than the actual currents in transient states. In Lu et al., a method was proposed for motor current rebuilding without utilizing null switching conditions [21]. This strategy was applied to an encoderless synchronous motor drive. In [21], the faulty current was estimated using the DC-link current sensor and switching table. In the paper mentioned above, the reconstructed motor currents were used for high-frequency voltage injection-based rotor position estimation. In Manohar and Das, a flux estimator was employed to estimate the currents in DTC of a three-phase IM drive system under CSF [22]. However, this method needs a speed sensor for the estimation of the motor currents. In addition, DTC technique suffers from high torque ripples during low speed region. In [23], the IM currents were estimated using an EKF during post-fault operation. Although EKF is a good choice to estimate the motor currents in the presence of noises, this algorithm increases the computational burden. The used strategy in [23] also requires a position sensor which increases the drive system cost. In Zhang et al., the reconstruction of the faulty currents was performed based on SMO and the current space vector error projection [24]. This strategy was applied to an encoderless control of a synchronous motor. In [25], a simplified current tracing mechanism was proposed to estimate the currents of a three-phase synchronous motor after CSF based on the sinusoidal features of current. In [28], an adaptive observer with estimation of the stator and rotor resistances was proposed for three-phase IM drive systems via one current sensor. Nevertheless, the presented system in [28] does not discuss the control method reconfiguration. In [29], a coupled FTC was proposed for a primary permanent-magnet linear machine. In this paper, by coupling the faulty mover with the healthy mover, the presented controller can control the faulty mover, in which current sensors fail. In [30], an encoderless current sensor FTC strategy with the SMO was proposed. However, this method suffers from slow dynamics due to several PI controllers and chattering problems due to the SMO.

Proposed Current Sensor FTC Scheme
In three-phase IM drive systems, current sensors are frequently prone to fault(s) [22]. Thus, in order to increase the dependability and safety of three-phase IM drives, FTC of these motors under CSF is critical and vital, especially for some critical industrial applications such as aerospace. In this section, the suggested scheme for current sensor FTC of IM drives is presented. Figure 1 illustrates the proposed current sensor FTC method for the encoderless three-phase IM drive.
The proposed current sensor FTC algorithm works based on a model predictive torque controlled three-phase IM using two current sensors. Two current sensors are placed in aphase and b-phase. Based on this figure, a modified MPTC strategy, fault detection and isolation units, a MRAS estimator and flux linkage observer are combined. Initially, the fault detection and isolation units based on the TD algorithm and a logic circuit module recognize the CSF condition and select to use the actual stator currents or estimated stator currents. Based on the MRAS estimator, the three-phase motor speed is estimated. In addition, using the flux linkage observer, the stator fluxes, rotor fluxes, and stator currents are calculated. It should be pointed out that the reconstructed motor currents used in the MRAS estimator and flux linkage observer block are determined by the fault detection and isolation modules. To compare the proposed scheme with the conventional MPTC, the schematic diagram of the conventional MPTC is given in "Appendix A".

Structure of the Used Encoderless MPTC Strategy for Pre-fault Operation
The used control strategy in this research is in accordance with a recently presented MPTC-based method [9]. It is worth noting that in [9], a modified encoderless MPTC strategy using two EKFs was proposed for a healthy three-phase IM drive. However, the use of two EKFs considerably increases the control structure complexity and memory size needed for the real time implementation. The approach in [9] is suitably modified to make it appropriate for the current sensor FTC technique. The stator fluxes and electromagnetic torque at the instant (n + 1) can be predicted as illustrated in (1)- (3): where From (1)-(5), it is observed that the stator fluxes and torque equations are affected by estimation errors of the fluxes and motor speed. In this study, the values of fluxes and speed are estimated based on a flux linkage observer and MRAS algorithm as shown in the next section.
To compensate the time delay, the prediction of motor variables such as stator fluxes and electromagnetic torque is done at the instant (n + 2) [31]. The stator fluxes and electromagnetic torque at the instant (n + 2) can be predicted as demonstrated in (6) where i s ds (n + 2) i s ds (n + 1) Since the frequency of the rotor flux is too low compared with the sampling frequency, in (9) and (10), it is assumed that ψ s r (n + 1) ψ s r (n) [9]. In addition, i s ds (n + 1) and i s qs (n + 1) in (9) and (10) are obtained based on (4) and (5).
To achieve the optimal voltage vectors for inverter feeding, the following cost function is considered: where [9] i m ∞ i f |i s (n + 2)| > i max 0 otherwise (15) As can be seen from (14), the term i m is added to the cost function to protect over current.
In Fig. 2, the estimated speed is compared with the desired speed to produce the desired electromagnetic torque. According to the stator voltages, stator currents, and estimated values of the fluxes and speed, the stator fluxes and electromagnetic torque are predicted at the instant (n + 2). Finally, the optimal voltage vectors for inverter feeding are achieved based on the cost function.

Estimation Mechanisms for the Rotor Speed, Stator Currents, and Fluxes Based on MRAS and Flux Linkage Observer
As can be realized from Fig. 2, the values of fluxes and speed are required in the control system. In this paper, a MRAS and flux linkage observer module is used for estimation of the rotor speed, stator currents, and fluxes.

Rotor Speed Estimation Using MRAS
MRAS algorithm has been proved to be an efficient and straightforward approach for encoderless control of threephase IM drives [7]. The speed estimation technique in this study is based on the conventional MRAS based on the rotor flux. The structure of the conventional MRAS for speed estimation is illustrated in Fig. 3. As shown in Fig. 3, the rotor fluxes in the reference model (ψ s dr1 ,ψ s qr1 ) are computed using the voltages and currents. Moreover, the rotor fluxes in the adjustable model (ψ s dr2 ,ψ s qr2 ) are computed according to the currents and estimated speed. The error between the reference model quantities and adjustable model quantities is fed to the adaptation mechanism to produce the rotor speed. It can be mentioned that the proposed encoderless FTC system can work for all speed estimation strategies. Here, MRAS is used only as a sample.

Stator Currents and Fluxes Estimation Based on a Flux Linkage Observer
In the rotational reference frame, the motor dq fluxes (ψ e dm , ψ e qm ,ψ e ds ,ψ e qs ,ψ e dr ,ψ e qr ),ˆ sl , andθ e can be shown as (16) (22) θ e ˆ e dt (23) where L m1 L m L ls L lr L ls L lr + L m L lr + L m L ls (24) In addition, the dq currents in terms of motor fluxes can be written as [32]: Based on (16)-(26), the flux linkage observer module for estimation of the stator currents and fluxes is shown in Fig. 4.

Fault Detection
In the proposed encoderless FTC algorithm, the fault detection is done by TD of the three-phase IM line currents. This method is able to detect even a slight change in the motor currents [33]. In this research, two TDs are utilized in phases a and b to detect the fault. The TDs can be determined using some simple calculations as (28) and (29): Under healthy and faulty conditions, the TD related to any line current generates very small and high impulse amplitudes, respectively. The fault detection is based on the comparison between the absolute value of the TD and a predefined threshold (T ), as shown in Table 1.
The selection of an appropriate value for threshold is a cumbersome task. Nevertheless, to obtain the value of T , some simulations based on Fig. 2 during different operating conditions were carried out. The parameters and nominal values of the 4-pole, 50 Hz, 0.75 kW wye-connected three-phase IM drive as well as the controller and inverter parameters in simulations are given in "Appendix B". Tables 2, 3, 4, 5, 6 show the absolute values of TD a and TD b at the CSF occurrence during different operating conditions.
As shown in Tables 2, 3, 4, 5, 6, the absolute values of TD a and TD b at the CSF occurrence produce high impulse amplitude (in the range of 1.02 A to 16.6 A). It should be pointed out that under normal state, the absolute values of TD a and TD b produce very small impulse amplitude (less than 0.01 A). These tables show that T 0.6 A, gives an acceptable performance of the proposed FTC method for all the fault condition.

Fault Isolation
The dq currents in the stationary reference frame (superscript "s") and during healthy condition can be shown as ( (32) It is seen that the stator d-axis current only depends on the stator a-phase current, while the stator q-axis current depends on the stator a-phase and b-phase currents. It means that when the fault occurs in phase a,î s ds andî s qs (estimated values of the stator dq currents) should be utilized in the control system. Furthermore, when the CSF occurs in phase b, i s ds andî s qs should be utilized in the control system. Additionally, during healthy mode, i s ds and i s qs should be used. Based on the above discussion, the fault detection and isolation scheme are shown in Fig. 5.
As can be seen from the schematic diagram of Fig. 5, after the fault detection process using TD operator, for continuous operation of the drive system, the logic circuit module selects the appropriate value of motor dq currents based on the X and Y values.
When X 0 and Y 0, it indicates that the sensors are healthy, and the dq currents are obtained from the actual dq currents.
When X 0 and Y 1, it means that the b-phase CSF happens. In this condition, the d-axis current is obtained from the actual d-axis current and the q-axis current is obtained from the estimated q-axis current.
When X 1 and Y 0, it can be concluded that the aphase CSF happens. In this case, the dq currents are obtained from the estimated dq currents.
In summary, Fig. 6 illustrates the detailed flowchart for the faulty sensor identification and suitable selection of the motor currents.

Experimental Evaluation
The usefulness of the proposed FTC system for a MPTC-based three-phase IM drive is confirmed with a TMS320F28335 controller board from a prototype developed in the laboratory. The picture of the experimental setup of a 0.75 kW wye-connected three-phase IM drive using the proposed FTC algorithm is displayed in Fig. 7.
The proposed FTC technique code for the TMS320F28335 controller board is generated using PSIM software. In all tests, the electromagnetic torque is calculated based on the IM equations. The parameters and nominal values of the experimented three-phase IM as well as the controller and inverter parameters are given in "Appendix B". In tests, the sensor output is made zero in the software. It should be pointed out that the sensor faults do not essentially mean an open-circuit fault; any malfunctions in current In many industrial applications, such as railway traction and electric vehicles, the drive system should be able to control the IM for the entire speed range [34][35][36]. For this aim, different operating conditions such as high speed (Figs. 11,13,and 14), medium speed (Figs. 8, 10, and 12), and low speed ( Fig. 9) are considered in tests.
Additionally, in many industries, the drive system should be able to control the machine during light or mid-load conditions such as small fan and electric vehicle applications and heavy load conditions such as electric traction and cooling pumps [37,38]. In tests, Figs. 9 and 13 are presented to evaluate the control system performance during light or mid-load conditions, while Fig. 11 is presented to evaluate the control system performance during the heavy load condition. Figure 8 displays the results of the suggested FTC scheme under the condition mentioned above. In Fig. 8, the reference speed is changed from 110 rad/s to 70 rad/s, τ l 0 N.m and ψ * s 1 Wb. It is seen that the actual and estimated speeds follow the reference speed. As shown in Fig. 8(f), the amplitudes of the estimated fluxes have constant values and the estimated stator flux amplitude tracks the command stator flux. As can be seen from Figs. 8b and 8c, the actual dq currents are sinusoidal and balanced in this condition. As shown in Fig. 8d, the values of X and Y are 0 and 0, respectively. Thus, i s ds and i s qs are selected as feedback currents. Figure 8e shows the torque performance during healthy condition. In his test, the average value of the torque during the steady-state and no-load condition is around 0.25 N.m. Figure 9 demonstrates the experimental results of the proposed FTC strategy during normal condition and different speeds. In this test, the reference speed is changed from 5 rad/s to 17 rad/s to 75 rad/s, τ l is changed from 0 N.m to 2 N.m (no-load condition to 39% of the nominal load) at t 70.5 s, and ψ * s 1 Wb. It is observed that the actual and estimated speeds track the command speed during low and high speeds. Furthermore, in this condition, the dq currents are sinusoidal and balanced. Additionally, the values of X and Y are both 0. Finally, the average value of torque is equal to the applied mechanical load. In this test, the average value of the torque during the steady-state and after the load is around 0.33 N.m which is similar to the average value of the torque in Fig. 9.

Performance of the Proposed FTC Strategy When a-phase and b-phase Sensors are Healthy
The achieved results in Fig. 9 clearly show the excellent performance of the introduced FTC strategy during normal mode and under different speeds and load condition.  Figure 10 shows the performance of the suggested FTC algorithm when the sensor fault happens in phase a, while the sensor in phase b is healthy. In this experiment, the drive system was initially working with healthy sensors and at t 14 s, the a-phase sensor output is made zero using a simple switching block in PSIM. In this test, the reference speed is 70 rad/s, τ l 0 N.m, and ψ * s 1 Wb. Figure 10a and f shows undisturbed estimated speed, actual speed, and estimated fluxes during the post-fault operation. The amplitudes of the estimated stator and rotor fluxes in Fig. 10f depict the constant operations of the fluxes even during a-phase current sensor failure. As discussed before, when the CSF happens in phase a, actual dq currents have incorrect values (see Fig. 10b and c). As can be seen from Fig. 10d, after the sensor fault, the values of X and Y are 1 and 0, respectively. Thus,î s ds andî s qs are selected as feedback signals. Figure 10e demonstrates acceptable ripples of the torque signal during post-fault operation as the average value of the torque before the CSF is around 0.23 N.m and the average value of the torque after the CSF is around 0.32 N.m. Figure 10 shows that the proposed system can suitably detect the fault and swaps from the actual motor currents to the estimated motor currents under such a situation. Figure 11 displays the performance of the proposed method during load condition. As shown in Fig. 11, in this test, the drive system starts with healthy sensors and under no-load condition. Then, a mechanical load equal to 5.1 N.m (nominal load) is applied. Afterward, a-phase CSF happens. In Fig. 11, the reference speed is 150 rad/s and ψ * s 1 Wb. Figure 11a shows that the estimated and actual speeds can track the command speed. The speed error is presented in Fig. 11b. Based on Fig. 11b, the average value of the speed error is near zero. As shown in Fig. 11c, i s ds and i s qs are used during normal mode. In addition,î s ds andî s qs are used during

Performance of the Proposed FTC Strategy When a-Phase Sensor is Healthy and b-Phase Sensor is Faulty
The performance of the proposed FTC algorithm under such a situation is illustrated in Fig. 12. In this scenario, during pre-fault operation, the reference speed is 90 rad/s and after the CSF, the reference speed is changed from 90 rad/s to 120 rad/s, τ l 0 N.m, and ψ * s 1 Wb. Fig. 11 Performance of the proposed FTC strategy during load condition when a-phase sensor is faulty and b-phase sensor is healthy; a * r ,ˆ r , r _actual , b r _actual −ˆ r , c X &Y , d |ψ s |&|ψ r |  Figure 12f also shows the constant values of fluxes during different modes and speeds. As shown in this scenario and during post-fault operation, i s ds has a correct value, while the value of i s qs has a wrong value (see Fig. 12b and c). As can be observed from Fig. 12d, in this condition, the values of X and Y are 0 and 1, respectively. It means that i s ds andî s qs are used in the control system. Figure 12e shows the torque signal has low ripples during different conditions and its variation is proportional to the motor speed. In this test, the average value of the torque during the steady-state and after the CSF is around 0.34 N.m, while the average value of the torque during the steady-state and before the CSF is around 0.25 N.m. Fig. 13 Performance of the proposed FTC strategy during load condition when a-phase sensor is healthy and b-phase sensor is faulty; a * r ,ˆ r , r _actual , b X &Y , c τ e &τ l , d |ψ s |&|ψ r | Fig. 14 Comparison between the proposed FTC strategy in this paper and the presented FTC strategy in [22] when a-phase sensor is healthy and b-phase sensor is faulty Figure 13 shows experimental results of the suggested FTC strategy during post-fault operation. In this case, the three-phase IM drive system starts with both healthy current sensors and b-phase current sensor information is assumed to be lost. In Fig. 13, before t 19.27 s, the drive system is under no-load condition, and after t 19.27 s, the load torque is equal to 3 N.m (59% of the nominal load). In addition, the reference speed is 150 rad/s and ψ * s 1 Wb. Figure 13a and d illustrates uninterrupted and continuous speed and fluxes tracking performances under this scenario. The values of X and Y during post-fault mode are depicted in Fig. 13b. The X and Y statuses show that a-phase sensor is healthy and b-phase sensor is faulty. The estimated q-axis current and the actual d-axis current are utilized based on the X and Y values. As seen from Fig. 13c, the torque response of the three-phase IM has reasonable ripples (0.35 N.m) compared to the previous scenarios and its average value after the mechanical load is equal to the applied load. Figure 14 displays the comparison of the torque response between the proposed FTC strategy in this paper and the presented FTC strategy in [22] after the CSF. In both tests, a-phase sensor is healthy and b-phase sensor is faulty. In addition, to have a fair comparison in both tests, an encoder was used for the speed measurement. In Fig. 14, the reference speed is 140 rad/s, τ l 0 N.m and ψ * s 1 Wb. As shown, the average values of the torques are close to zero for both two experiments. As can be clearly seen, the MPTC in this paper outperforms the presented DTC system in [22] in terms of steady-state torque ripple. In addition, in the proposed FTC strategy, in this paper, the speed encoder is not needed, while in the presented FTC strategy in [22], the speed encoder is needed.

Conclusion
This research has presented an implementation of a FTC strategy for encoderless MPTC of a three-phase IM drive against single-phase current sensor failure. The used control system is based on modifications of the MPTC strategy. For the detection and isolation of the faulty sensor, a TD and logic circuit module are used. In the suggested FTC scheme, the rotor speed estimation is based on the conventional rotor flux-based MRAS algorithm and the stator currents are estimated using a flux observer. Through the flux observer, not only the stator currents but also the stator and rotor fluxes which are utilized in the modified MPTC strategy are estimated. The proposed FTC technique does not need an extra sensor and noticeable changes in the control system structure during post-fault operation. Extensive experimental results have shown that the three-phase IM drive system is able to detect and isolate the CSF and switch to the corresponding post-fault control strategy. The proposed encoderless FTC method works satisfactorily during different operation conditions such as normal, faulty, and load conditions. As shown in this paper, the MRAS algorithm was used to estimate the motor speed. Nevertheless, this algorithm can be easily polluted by noises. To solve this problem, an EKF can be developed in the suggested encoderless MPTC method. The parameters dependency is one main drawback of the suggested control. This issue degrades the performance of the drive system. In future work, the motor parameters such as resistances in the proposed control system will be estimated during different operating conditions.

Appendix A
In Fig. 15: