A Review on Predictive Control Technology for Switched Reluctance Motor System

: The signiﬁcance of employing control strategies on a switched reluctance motor (SRM) is that they can reduce vibration noise and torque ripple. With the rapid development of digital system processors, predictive control (PC), as a modern control approach, is increasingly applied to enhance the dynamic performance and operational efﬁciency of SRMs. This review provides a comprehensive overview of the current state of research on PC strategies of SRMs and classiﬁes PC technologies, such as generalized predictive control (GPC), hysteresis predictive control (HPC), deadbeat predictive control (DPC), and model predictive control (MPC). It summarizes the PC schemes from the aspects of predictive current control (PCC), predictive torque control (PTC), and other PC, and it discusses the current trends in technology development, as well as potential research directions. The insights presented herein aim to facilitate further investigations into predictive control techniques for SRM.

Predictive control (PC) offers a different approach compared to conventional controllers, as it can manage restrictions and nonlinearities [65]. Additionally, it takes into account the discrete characteristics of the power converter when determining control actions [66]. Simple implementation and effective dynamic response are other features of PC [67]. These features make PC a promising strategy for SRM control. PC has proven effective for AC drives and power converters, including induction motors [68][69][70][71], and permanent magnet synchronous motors [72][73][74][75]. PC becomes more interesting when implemented in intricate systems, such as multilevel inverters [76] and multiphase drives [77].
SRMs possess a salient pole structure, which is a key component of torque generation mechanism. Therefore, SRM characteristics, including torque and magnetic linkage, are contingent on the rotor position. Concurrently, these properties are influenced by the phase current.
In Figure 1, the phase flux linkage curve of a 12/8 SRM under a constant current excitation of 10 A is displayed, juxtaposed with the relative positioning of the stator and rotor poles. When the stator pole is situated between two rotor poles, the relative gap between the rotor and stator poles reaches its peak. This position is known as the unaligned position. From Figure 1, at the unaligned position, due to the large air gap, the flux linkage is at its minimum. Conversely, when the stator and rotor poles are in alignment, the air gap shrinks to its smallest size, leading to the flux linkage reaching its zenith. Additionally, the flux linkage is influenced by the excitation current. With a higher current input, the incremental rise in flux linkage is diminished because of an elevated magnetic flux density, leading to a reduced saturation level of the magnetic core. As illustrated in Figure 2a, the flux linkage increment from 10 A to 15 A is notably less than the growth observed from 5 A to 10 A.   The motor operates in accordance with Faraday's law of electromagnetic induction. The motor has m phases, and every phase winding conforms to equation 1. As illustrated in Figure 2, the flux linkage of the SRM demonstrates a pronounced nonlinearity. While mathematical approaches can be employed to model the flux linkage, the precision of such techniques is considerably constrained. Typically, information regarding the magnetic flux linkage is derived using a three-dimensional look-up table (LUT) approach.
Where ek, ψk, and t, respectively, represent the induced electromotive force, flux linkage, and time of the kth phase winding. k = 1, 2, …, m. There is a correlational mapping between the rotor position angle θph, the phase current ik, and the flux linkage ψk. The interrelation between the flux linkage and inductance Lk is represented in the subsequent equation: k ph k k ph k k ψ θ i L θ i i (2) where Lk denotes the phase inductance, ik signifies the phase current, and θph corresponds to the rotor position. Every phase circuit adheres to the voltage balance equation based on Kirchhoff's voltage law.
where Uk denotes the phase voltage, and Rk signifies the phase resistance. The motor operates in accordance with Faraday's law of electromagnetic induction. The motor has m phases, and every phase winding conforms to Equation (1). As illustrated in Figure 2, the flux linkage of the SRM demonstrates a pronounced nonlinearity. While mathematical approaches can be employed to model the flux linkage, the precision of such techniques is considerably constrained. Typically, information regarding the magnetic flux linkage is derived using a three-dimensional look-up table (LUT) approach.
where e k , ψ k , and t, respectively, represent the induced electromotive force, flux linkage, and time of the kth phase winding. k = 1, 2, . . ., m.
There is a correlational mapping between the rotor position angle θ ph , the phase current i k , and the flux linkage ψ k . The interrelation between the flux linkage and inductance L k is represented in the subsequent equation: where L k denotes the phase inductance, i k signifies the phase current, and θ ph corresponds to the rotor position. Every phase circuit adheres to the voltage balance equation based on Kirchhoff's voltage law.
where U k denotes the phase voltage, and R k signifies the phase resistance. The mechanical equilibrium equation can be derived using pertinent mechanical principles, as follows: where T e stands for the electromagnetic torque produced by the motor, and T L indicates the load torque. J and D are constant parameters corresponding to the moment of inertia and the viscous friction coefficient, respectively. ω represents the motor's actual speed.
The electromagnetic torque of one phase of SRM can be expressed as: where T k represents the electromagnetic torque of the kth phase. k = 1, 2, . . ., m.

Power Converter Topology
As shown in Figure 3, using a single phase of a three-phase half-bridge converter as an example, the functioning of the converter is demonstrated. Each phase has three potential World Electr. Veh. J. 2023, 14, 221 4 of 23 switching states: Figure 3a depicts the state with a positive phase voltage V dc , involving S 1 and S 2 . In Figure 3b, there is a state where a negative voltage, V = −V dc , is directed to the machine terminals, routing the phase current back to the source via the diode. Figure 3c displays a freewheeling mode, where V = 0 V. In this state, the present phase current flows through the diode and switch S 2 .
where Tk represents the electromagnetic torque of the kth phase. k = 1, 2, …, m.

Power Converter Topology
As shown in Figure 3, using a single phase of a three-phase half-bridge converter as an example, the functioning of the converter is demonstrated. Each phase has three potential switching states: Figure 3a depicts the state with a positive phase voltage Vdc, involving S1 and S2. In Figure 3b, there is a state where a negative voltage, V = −Vdc, is directed to the machine terminals, routing the phase current back to the source via the diode. Figure 3c displays a freewheeling mode, where V = 0 V. In this state, the present phase current flows through the diode and switch S2.

Predictive Control Basics
In predictive control, the best input sequence, u(k), is determined by forecasting future states using a stable, discrete-time model. The objective is to guide the state x toward the reference Γ* using the ideal input sequence u(k) for each sample interval. This optimal solution is derived by addressing the constrained finite-horizon control challenge using a cost function or a designated predictive model. The chosen u(k) is then deployed in the succeeding sampling interval, k + 1. Under this approach, the chosen input u(k) can be employed regardless of whether or not a modulator is present, affecting the closed-loop controller's efficiency and switching frequency traits. In this review, PC techniques of SRMs are categorized according to the standard shown in Figure 4 [79]. Table 1 provides a detailed introduction to the characteristics of each prediction method.

Predictive Control Basics
In predictive control, the best input sequence, u(k), is determined by forecasting future states using a stable, discrete-time model. The objective is to guide the state x toward the reference Γ* using the ideal input sequence u(k) for each sample interval. This optimal solution is derived by addressing the constrained finite-horizon control challenge using a cost function or a designated predictive model. The chosen u(k) is then deployed in the succeeding sampling interval, k + 1. Under this approach, the chosen input u(k) can be employed regardless of whether or not a modulator is present, affecting the closed-loop controller's efficiency and switching frequency traits. In this review, PC techniques of SRMs are categorized according to the standard shown in Figure 4 [79]. Table 1 provides a detailed introduction to the characteristics of each prediction method.     One of the primary shortcomings of predictive control methods is their vulnerability to parameter discrepancies and measurement noise. In real-world scenarios, parameter shifts are inevitable, stemming from the nonlinear nature of physical systems, aging, temperature variations, or other external influences. Without the inclusion of elements to reduce the steady-state error of MPC, the impact of parameter changes on the performance of predictive methods could worsen [80]. This issue can generally be mitigated by extending the prediction's receding horizons, implementing active disturbance rejection strategies [81], or utilizing filtering methods, such as the Kalman filter [82]. Another approach is to combine online parameter estimation methods with predictive control methods, which can alleviate the disturbance effects caused by parameter changes and enhance the robustness of predictive controllers [83].

Generalized Predictive Control
Employing a linearized version of the plant model is a classic methodology in predictive control for tackling the constrained finite-horizon optimization control challenge. GPC leverages the model to determine the best control action. This is performed using a predictive model built on transfer functions and a cost function [84]. The schematic representation of this method can be seen in Figure 5. The forecasting phase can be executed using methods such as Kalman filtering or traditional predictive models, for instance, the Diophantine equations [85]. These equations utilize the linearity of the model to split the response into two components. The first component, known as the natural response, is influenced by variables previously used. The second component, referred to as the forced response, is dependent on future execution variables [86]. These components are represented as yf and Gũ(k + j) in Figure 5, indicating the natural response and forced response, respectively. Subsequently, the forecasted value at the sampling interval j is juxtaposed with the reference value Γ* via the cost function. A step is then introduced to minimize the cost function, leading to the determination of the optimal input sequence û (k + j).
A defining feature of GPC is its extended prediction horizon, which demands fewer computational resources compared to other predictive control techniques [87]. GPC offers a precise solution to the constrained finite-horizon optimization control challenge and has the potential to include a modulation phase, ensuring consistent switching frequency. However, the predictive model in GPC only accounts for the average model, neglecting The forecasting phase can be executed using methods such as Kalman filtering or traditional predictive models, for instance, the Diophantine equations [85]. These equations utilize the linearity of the model to split the response into two components. The first component, known as the natural response, is influenced by variables previously used. The second component, referred to as the forced response, is dependent on future execution variables [86]. These components are represented as y f and Gũ(k + j) in Figure 5, indicating the natural response and forced response, respectively. Subsequently, the forecasted value at the sampling interval j is juxtaposed with the reference value Γ* via the cost function. A step is then introduced to minimize the cost function, leading to the determination of the optimal input sequence û (k + j).
A defining feature of GPC is its extended prediction horizon, which demands fewer computational resources compared to other predictive control techniques [87]. GPC offers a precise solution to the constrained finite-horizon optimization control challenge and has the potential to include a modulation phase, ensuring consistent switching frequency. However, the predictive model in GPC only accounts for the average model, neglecting the nonlinearity associated with the converter or machine [78].

Hysteresis Predictive Control
HPC operates based on principles similar to conventional hysteresis controllers. The distinction lies in its ability to extract the best input sequence u(k) from a predictive portrayal of the error signal, thereby bolstering its dynamic response. Figure 6 shows the operational diagram of HPC. Instead of directly modulating the output variable, this method manages the real-time error between the reference and forecasted states, making sure the output y(k) remains within a predetermined boundary. Furthermore, it can integrate with techniques such as space vector modulation to achieve an almost consistent switching frequency [88]. Yet, HPC is not widely favored in the literature due to the necessity of determining the device parameters when using the predictive model. This issue removes a key advantage of hysteresis controller, its capacity to effectively regulate an average reference without pre-existing insight into system properties.

Deadbeat Predictive Control
DPC addresses the constrained finite-horizon optimization control challenge by directly determining the optimal input sequence using the predictive model [67]. Utilizing machine parameters, the current state x(k), and the previously computed best input sequence u(k), the upcoming input sequence u(k + j) is forecasted by the predictive model, which brings the error to nil. Figure 7 shows the basic block diagram of this procedure. The intent is to accomplish a zero error in the forthcoming sampling period, which results in y(k +1) equating to Γ*. Thus, the model's representation can be described as

Deadbeat Predictive Control
DPC addresses the constrained finite-horizon optimization control challenge by directly determining the optimal input sequence using the predictive model [67]. Utilizing machine parameters, the current state x(k), and the previously computed best input sequence u(k), the upcoming input sequence u(k + j) is forecasted by the predictive model, which brings the error to nil. Figure 7 shows the basic block diagram of this procedure. The intent is to accomplish a zero error in the forthcoming sampling period, which results in y(k +1) equating to Γ*. Thus, the model's representation can be described aŝ In (6), the ideal input sequence û(k + j) ensures that the output y(k + j) = y(û (k + j)) = Γ*. Within the motor system, this reference sequence is normalized based on the DC link voltage V dc to determine the duty cycle. This duty cycle is then relayed to the modulation phase. At this stage, the PWM signal is dispatched to the motor driver, guaranteeing an operation with a consistent switching frequency. quence u(k), the upcoming input sequence u(k + j) is forecasted by the predictive model, which brings the error to nil. Figure 7 shows the basic block diagram of this procedure. The intent is to accomplish a zero error in the forthcoming sampling period, which results in y(k +1) equating to Γ*. Thus, the model's representation can be described as In (6), the ideal input sequence û(k + j) ensures that the output y(k + j) = y(û (k + j)) = Γ*. Within the motor system, this reference sequence is normalized based on the DC link voltage Vdc to determine the duty cycle. This duty cycle is then relayed to the modulation phase. At this stage, the PWM signal is dispatched to the motor driver, guaranteeing an operation with a consistent switching frequency.

Model Predictive Control
MPC stands out as the most prominent predictive control approach in contemporary research. In the review, the MPC methodology entails using a predictive model to anticipate the output y(k + j) and a cost function to determine the best input sequence u(k +1) for the upcoming sampling interval. Figure 8 depicts the block diagram of the MPC approach. Typically, there are two versions of MPC, one using a continuous control set and the other using a finite control

Model Predictive Control
MPC stands out as the most prominent predictive control approach in contemporary research. In the review, the MPC methodology entails using a predictive model to anticipate the output y(k + j) and a cost function to determine the best input sequence u(k +1) for the upcoming sampling interval. Figure 8 depicts the block diagram of the MPC approach. Typically, there are two versions of MPC, one using a continuous control set and the other using a finite control set. Both of these MPC methods utilize the predictive model to estimate the future trajectory of the output y(k + j) using the input u(k). set. Both of these MPC methods utilize the predictive model to estimate the future trajectory of the output y(k + j) using the input u(k). CCS-MPC utilizes mathematical tools to optimize the value function and obtain the optimal control amount, which acts on the system through pulse width modulation (PWM), while FCS-MPC takes advantage of the discreteness and finiteness of the converter to select voltage vectors. The voltage vector that minimizes the value function is the optimal control amount, which is directly applied to the system. The result with the least error is chosen, and the related switching state is executed. This choice omits the need for a modulator and leads to a variable switching frequency, which is only constrained by the sampling frequency [Error! Reference source not found.]. Although there is a variable switching frequency, it is offset by an enhanced dynamic response [89].

Predictive Current Control
SRM operates with a cascaded control structure, akin to the field-oriented control (FOC) seen in regular AC drives. The outer loop monitors the reference torque, usually acting as a speed controller. Meanwhile, the inner loop oversees the reference current derived from the torque loop. This part delves into the issue of current tracking and the application of predictive control to resolve it.
Owing to the nonlinear nature of the phase inductance profiles, managing the current in SRM becomes quite a task [90]. As pointed out in the second section, factors such as variable reluctance and saturation features result in flux linkage, dependent on the elec- CCS-MPC utilizes mathematical tools to optimize the value function and obtain the optimal control amount, which acts on the system through pulse width modulation (PWM), while FCS-MPC takes advantage of the discreteness and finiteness of the converter to select voltage vectors. The voltage vector that minimizes the value function is the optimal control amount, which is directly applied to the system. The result with the least error is chosen, and the related switching state is executed. This choice omits the need for a modulator and leads to a variable switching frequency, which is only constrained by the sampling frequency [66]. Although there is a variable switching frequency, it is offset by an enhanced dynamic response [89].

Predictive Current Control
SRM operates with a cascaded control structure, akin to the field-oriented control (FOC) seen in regular AC drives. The outer loop monitors the reference torque, usually acting as a speed controller. Meanwhile, the inner loop oversees the reference current derived from the torque loop. This part delves into the issue of current tracking and the application of predictive control to resolve it.
Owing to the nonlinear nature of the phase inductance profiles, managing the current in SRM becomes quite a task [90]. As pointed out in the second section, factors such as variable reluctance and saturation features result in flux linkage, dependent on the electrical angle and phase current. Not being able to follow the reference current might enhance torque fluctuations and potentially increase noise due to significant current ripples [8]. This section describes the work of applying predictive current control.

Predictive Model
For the precise tracking of both transient and steady-state responses in predictive current control, an accurate model is essential. Intuitively, a current-based approach would be most suitable. Yet, given the nonlinear inductance of the SRM, directly estimating the current requires first addressing its nonlinearity. One way to tackle this challenge is the predictive current control method using the lookup table technique [91,92].
Another approach is the online estimation and learning of the inductance surface [93], used a stochastic MPC scheme for switched reluctance motor current control. The comprehensive layout of the suggested inductance table and its learning mechanism can be seen in Figure 9a, while Figure 9b illustrates the complete control structure. The system incorporates a state estimator, crafted as a recursive linear quadratic regulator. Furthermore, a dynamic learning system is designed to adapt the motor's inductance curve in real-time, updating both the MPC and the Kalman filter parameters accordingly. This advanced control approach is adept at managing uncertainties and disturbances found in the machine's nonlinear inductance landscape.  In a similar vein, an unconstrained model predictive controller, known as the finite horizon linear quadratic regulator, is employed for the current control of SRM [83]. State estimation is achieved through Kalman filtering, and an adaptive controller facilitates dynamic tweaking and updates of both MPC and Kalman models. In [94], a novel current control technique for dual stator switched reluctance motor (DSSRM) drives is introduced. This recommended current control strategy hinges on the MPC approach and incorporates an adaptive estimator to monitor inductance variations in the DSSRM. In a similar vein, an unconstrained model predictive controller, known as the finite horizon linear quadratic regulator, is employed for the current control of SRM [83]. State estimation is achieved through Kalman filtering, and an adaptive controller facilitates dynamic tweaking and updates of both MPC and Kalman models. In [94], a novel current control technique for dual stator switched reluctance motor (DSSRM) drives is introduced. This recommended current control strategy hinges on the MPC approach and incorporates an adaptive estimator to monitor inductance variations in the DSSRM.
The online estimation of the magnetization surface is another approach on predictive models. The magnetization surface can be obtained through offline testing. However, its drawbacks are that it requires tuning time and specialized mechanical equipment. Additionally, the magnetization surface changes with variations in rotor and stator temperatures. In [95], a recognition method is proposed to run parallel with a model predictive current control system that utilizes a magnetization diagram. The discrepancy between the reference current and the actual current is utilized to adjust the reference points on the two-dimensional grid that depicts the magnetization surface.
In [96], a method of modifying the starting point for model prediction is used to mitigate errors stemming from communication delays between sensors and controllers. This effectively improves the tracking performance of delay and packet loss in transmission. An algorithm is introduced to analyze current, leveraging a semi-numerical model of the switched reluctance motor in [97], which is implemented in conjunction with a high precision look-up table based on the semi-digital machine model. The algorithm's development considers both torque ripple and controller bandwidth requirements, enabling speed and performance improvements for low-ripple torque control over extended speed range.
The model of SRM is nonlinear and varies based on both the current intensity and the position of the rotor. Using a lookup table is a solution, but it requires a complete understanding of the motor and can be affected by temperature and operating variables. To address these issues and enhance the tracking performance of the control system, scholars proposed model-less predictive current control [98]. The predictive algorithm that does not rely on a specific model is crafted by updating the next time period for the subsequent step of predictive control. A novel method for parameter estimation is introduced, designed to discern the parameters of the model of SRM while conserving computational resources. With a real-time grasp on these parameters, the optimal voltage vector is employed for each cycle, and the ideal duration for each of these cycles is determined. As a result, the recommended current controller operates with minimal prior knowledge of the particular motor in use. Figure 10 illustrates this proposed model-free MPC. In contrast to conventional MPC, the lookup table is supplanted by the newly introduced algorithm. Speed becomes redundant as a variable, and the inputs to the estimation module are the observed current and the predicted current for the k + 1 cycle. The estimation procedure is twofold: the initial phase determines if the prediction error stems from discrepancies in gain or offset parameters. The subsequent phase is a recursive procedure tailored to diminish the error pinpointed in the initial phase. To address these issues and enhance the tracking performance of the control system, scholars proposed model-less predictive current control [98]. The predictive algorithm that does not rely on a specific model is crafted by updating the next time period for the subsequent step of predictive control. A novel method for parameter estimation is introduced, designed to discern the parameters of the model of SRM while conserving computational resources. With a real-time grasp on these parameters, the optimal voltage vector is employed for each cycle, and the ideal duration for each of these cycles is determined. As a result, the recommended current controller operates with minimal prior knowledge of the particular motor in use. Figure 10 illustrates this proposed model-free MPC. In contrast to conventional MPC, the lookup table is supplanted by the newly introduced algorithm. Speed becomes redundant as a variable, and the inputs to the estimation module are the observed current and the predicted current for the k + 1 cycle. The estimation procedure is twofold: the initial phase determines if the prediction error stems from discrepancies in gain or offset parameters. The subsequent phase is a recursive procedure tailored to diminish the error pinpointed in the initial phase. In [99], a unique indirect predictive control technique was introduced with the objective of minimizing torque ripple in switched reluctance motor drives, particularly when employed in electric vehicle contexts. Figure 11 outlines the procedural flowchart of this indirect predictive control approach. * represents the reference value. In [99], a unique indirect predictive control technique was introduced with the objective of minimizing torque ripple in switched reluctance motor drives, particularly when employed in electric vehicle contexts. Figure 11 outlines the procedural flowchart of this indirect predictive control approach. * represents the reference value. In [99], a unique indirect predictive control technique was introduced with the objective of minimizing torque ripple in switched reluctance motor drives, particularly when employed in electric vehicle contexts. Figure 11 outlines the procedural flowchart of this indirect predictive control approach. * represents the reference value.  The newly introduced indirect predictive control algorithm is bifurcated into the following two main sections: the torque inverse model and the robust predictive current controller. The torque inverse model employs the strategy of incorporating a torque error compensator to a rudimentary linear model. This aids in accurate mapping from torque to current. This approach also lightens the computational load traditionally associated with torque inverse models. The robust predictive current controller, on the other hand, screens all possible switch states and selects the state that minimizes the designated cost function as the optimal choice for output. Furthermore, various inconsistencies, such as modeling mistakes, variations in parameters, and sampling errors, are collectively treated as an aggregate disturbance. To bolster the robustness of the predictive control, these disturbances are countered by the suggested disturbance observer. The essence of the proposed control strategy is that it indirectly accomplishes real-time torque management via precise current tracking. This method is straightforward to put into practice and is aptly suited for propelling electric vehicles.
A novel characterization scheme for SRM, based on constant current injection, and the required new predictive current controller, which can operate without a machine model, are proposed in [100]. Contrary to conventional characterization methods where the rotor remains static at a set position, the method based on current injection maintains a steady phase current while the machine operates at a consistent speed. In [101], a predictive phase current control strategy for a switched reluctance motor, which leans on a local linear phase voltage model, is put forward. A linear model is crafted to provide a close approximation of the relationship between the shifts in voltage and current over a brief span. The control of the current is achieved by modulating the average voltage using PWM, which maintains a constant switching frequency. The intercept and gradient of this model are identified in real-time based on the voltage and current fluctuations from the preceding control period. During this last control period, the phase voltage transitions from zero to either a positive or negative DC bus voltage. Subsequently, the model that has been identified is used to anticipate the average voltage required by the current in the upcoming PWM cycle to ensure it closely follows its reference value. When juxtaposed with hysteresis control operating at an identical sampling rate, this proposed control approach can markedly diminish both current and torque ripples. Furthermore, this predictive current control design does not necessitate pre-acquiring motor traits. It also displays minimal sensitivity to variations in characteristic parameters due to motor wear and tear. This makes the system especially apt for applications that necessitate the precise tracking of a given current trajectory. In [102], the choice is made to estimate the back electromotive force signal in MPC, thus obtaining an accurate model for estimating the future behavior of the current, resulting in very low current estimation errors within the MPC framework.

Switching Behavior
Controlling switching behavior is also an effective method in predictive torque control [103]. The non-linear characteristics of the SRM and system operation result in high DC bus current ripple on the input side, which requires higher DC bus capacitance. An interleaved fixed switching frequency predictive current control method is proposed in [104] to reduce the number of DC link capacitors in SRM drives. The introduced interleaving method has the capability to diminish the primary harmonic component present in the DC bus current, which predominantly revolves around double the switching frequency. As a result, this alleviates the need for a high number of DC bus capacitors. The control scheme can also reduce the switching frequency of the converter to achieve higher system efficiency while maintaining extremely low DC bus capacitor requirements. Furthermore, the proposed method does not require phase current shaping, ensuring that there is no additional current stress on the inverter switches and motor phase windings.
In [103], a new fixed-switching-frequency PTC technique for SRM is introduced. Utilizing a deadbeat predictive current controller, it can precisely forecast the necessary on-time duration of the PWM pulse based on a specified reference current. The width of this pulse is influenced by machine specifics, rotor position, and operational circumstances. To make an accurate voltage prediction, the controller harnesses the machine's inductance profile, which varies with both current and rotor position.
By combining the space vector modulation strategy with the beatless predictive control technique in [105], a reduced set of switching states is employed, which can decrease the computational workload. This control method selects the best state from the reduced switching state group and applies it to the neutral point clamped active front-end rectifier of the switched reluctance motor drive system. At the same time, the proposed strategy can avoid using well-known modulation methods, thereby improving dynamic performance. Compared with traditional methods, the allowed number of switching states in this scheme is significantly reduced, saving execution time for model predictive direct power control and DC control.

Other Predictive Current Control
Researchers have investigated a virtual flux FCS-MPC strategy for SRM [106]. The phase current is indirectly controlled using a flux tracking algorithm. This algorithm is based on the estimated virtual flux obtained from the static characteristics of the machine.
A predictive delta current regulator (PDCR) algorithm for SRM is proposed in [107]. This control method combines the advantages of the traditional delta modulation current regulator, which is structurally simple and does not require any motor parameters, with PCC. The PCC uses sampled data of the previous moment to estimate the error signal of the current for the upcoming sampling interval.
In [108], the efficacy of the SRM in electric vehicles is bolstered through the application of MPC. This control strategy is implemented on the SRM's power converter. By pinpointing the optimal switching state, it ensures that the current closely follows the reference signal, achieving the least amount of current ripple. This reduces the torque ripple in the motor. The proposed controller is put to the test under various load scenarios and is compared with other methods, such as hysteresis current control (HCC), proving that the proposed control method can effectively drive the SRM.
In [109], a fusion of the PCC method with TSF is introduced. When measured against the traditional hysteresis current control, this suggested technique enhances the current tracking prowess and curtails the torque ripple inherent in the switched reluctance motor. Notably, these improvements are achieved without ramping up the switching frequency or modifying the hysteresis band.
A model predictive control method reducing the integration step size is introduced in [110] to utilize pulse-width modulation for precise torque stability. Active thermal control is also developed to enhance the continuous output power of the driver. The study in [111] proposed a rotor position and speed estimator for the SRM operating under CCS-MPC. It realizes the phase-locked loop fed by the error between the reference current and its actual value. This estimator is examined using a simulation model and provides fast, accurate tracking of speed and position.
In [112], there is a detailed comparative study between two current control techniques for SRM drive systems: the conventional PI control and DPC. Different performance indicators of the controllers are evaluated and compared, including command tracking behavior, disturbance suppression ability, noise transmission characteristics, and resilience towards modeling inaccuracies, particularly errors in parameter estimation. This analytical approach significantly streamlines the decision-making process when choosing the bestsuited current control method for application with particular performance criteria.
A robust control based on GPC is proposed in [113] for the current control loop of SRM drives. This proposed controller possesses two degrees of freedom, enabling it to separate set-point tracking from the suppression of load disturbances under standard conditions.

Predictive Torque Control
Predictive torque control (PTC), alongside PCC, has also been a central area of research for many scholars in the field [114][115][116][117]. A method for suppressing torque ripple based on MPC is proposed in [118]. Following the basic principles of model predictive control, a nonlinear model for SRM is established. Real-time acquisition of phase current and rotor position signals, as well as bus voltage, is undertaken. According to the established mathematical model, the electromagnetic torque at the next moment is predicted. Then, an objective function based on torque ripple is established. By determining candidate sequences for the working states of upper and lower tubes of the power converter, and combining these with the objective function, the optimal control sequence is obtained. This control sequence's corresponding state values are used for the SRM predictive control system, thereby achieving the suppression of motor torque ripple. Similarly, [119] also employs MPC for suppressing torque ripple in SRM.

Torque Distribution
Reducing the torque ripple in SRM can be effectively achieved using the torque sharing method [120,121], especially when it is combined with PTC [122]. By segmenting the torque range to define the torque distribution configurations, the attenuation of torque ripple is simplified [123]. In [124], a PTC strategy incorporating TSF is introduced, merging TSF with MPC. Through the TSF, the reference torque is assigned to each phase offline. Then, the SRM's discrete model predicts the torque for the subsequent cycle. The optimal control variable needed to follow the reference torque is then determined using the cost function. When compared to the conventional current chopping control approach that relies on TSF, this novel control strategy eradicates current hysteresis, leading to enhanced control precision. In [125], a force sharing function is derived based on the torque-sharing function and is combined with model predictive control. Through the online fine-tuning of the turn-on angle to optimize the sharing function, the method effectively achieves the concurrent suppression of both torque and force ripples. The instantaneous torque control of SRM of any pole number is introduced in [126]. A new torque-sharing strategy is proposed, which is used for predicting the pulse width modulation direct instantaneous torque control with a low-loss commutation strategy. This strategy can minimize the ohmic loss during two-phase commutation without relying on precomputed current or torque trajectories.
A novel TSF that combines torque sharing methods with predictive control methods is proposed in [127]. The torque reference value is divided into three phases by a sinusoidal profile. The PTC technique is utilized to follow the reference value of phase torque. An FCS-MPDTC strategy is introduced in [128] to diminish the torque fluctuations in SSRM during its operation at low speeds. A predictive dynamic model is established, and by observing the phase current and rotor position signals, the phase torque is forecasted. Details about the functioning of the power converter and the choice of voltage vectors are presented. Taking into account the objectives of minimizing torque ripple and curtailing copper losses, a comprehensive cost function is crafted. This constructed function plays a crucial role in determining the best voltage vector to manage the power converter. The TSF is then employed to allocate the overall torque to individual phase torques, leading to a further reduction in torque pulsation.
In [129], a new control strategy, grounded in both MPC and TSF, is put forward to mitigate the torque ripple of the SRM. Figure 12 illustrates the flowchart of this suggested approach. * represents the reference value. The model of the SRM, derived from the flux linkage characteristic curve garnered from a locked-rotor test, is capable of forecasting the future operating state of the SRM drive system. The enhanced TSF curve adopts a genetic algorithm to fine-tune the TSF parameters, aiming to diminish torque ripple during the commutation phase. Furthermore, within the TSF control setup, MPC is seamlessly incorporated, replacing the conventional HC. To improve the mechanical safety of aero-engine starters/generators, a multi-objective optimization control approach for SRM is introduced in [130]. For model predictive control, the immediate phase torque is deduced from the magnetic linkage characteristics through the Hermite interpolation method, and the reference phase torque is then derived from TSF. The new TSF efficiently bridges the gap between the estimated momentary torque and the real-time torque.

Predictive Model
The efficacy of predictive control is largely contingent on the precision of the predicted variables and the model [131,132]. When compared to the current control, the modeling for SRM torque control is intricate since it necessitates the functioning of two models: the flux linkage and torque traits, both of which exhibit significant nonlinearity [133].
The model predictive torque control (MPTC) method based on the look-up table (LUT) presents the issue of occupying a large amount of storage space. To alleviate this problem, a simplified linear model of SRM is used in [134], which addresses the differences between linear and non-linear models of SRM. Additionally, an MPTC approach is implemented, which greatly shortens the execution time and reduces the occupation of storage space. Similarly, [135] also adopts an equivalent linear SRM model and makes appropriate modifications to the cost function.
Some scholars propose to first use a torque balance measurement technique to capture part of the flux linkage features. Subsequently, a mathematical framework is put forth to portray the full spectrum of torque and flux linkage traits [136,137]. Alternatively, a discrete-time model is formulated to foresee the upcoming state of the system, based on precise analytical methods [138].
Since flux can be easily estimated by integrating phase voltage, a new torque control approach is introduced in [139] to reduce torque pulsation using model prediction, which can minimize torque pulsation over an extensive speed spectrum, resulting in a highly efficient drive.

Candidate Voltage Vector Optimization
Candidate voltage vector (CVV) optimization is a method that can be combined with various control schemes and can effectively suppress torque ripple. In [140], an MPTC To improve the mechanical safety of aero-engine starters/generators, a multi-objective optimization control approach for SRM is introduced in [130]. For model predictive control, the immediate phase torque is deduced from the magnetic linkage characteristics through the Hermite interpolation method, and the reference phase torque is then derived from TSF. The new TSF efficiently bridges the gap between the estimated momentary torque and the real-time torque.

Predictive Model
The efficacy of predictive control is largely contingent on the precision of the predicted variables and the model [131,132]. When compared to the current control, the modeling for SRM torque control is intricate since it necessitates the functioning of two models: the flux linkage and torque traits, both of which exhibit significant nonlinearity [133].
The model predictive torque control (MPTC) method based on the look-up table (LUT) presents the issue of occupying a large amount of storage space. To alleviate this problem, a simplified linear model of SRM is used in [134], which addresses the differences between linear and non-linear models of SRM. Additionally, an MPTC approach is implemented, which greatly shortens the execution time and reduces the occupation of storage space. Similarly, [135] also adopts an equivalent linear SRM model and makes appropriate modifications to the cost function.
Some scholars propose to first use a torque balance measurement technique to capture part of the flux linkage features. Subsequently, a mathematical framework is put forth to portray the full spectrum of torque and flux linkage traits [136,137]. Alternatively, a discrete-time model is formulated to foresee the upcoming state of the system, based on precise analytical methods [138].
Since flux can be easily estimated by integrating phase voltage, a new torque control approach is introduced in [139] to reduce torque pulsation using model prediction, which can minimize torque pulsation over an extensive speed spectrum, resulting in a highly efficient drive.

Candidate Voltage Vector Optimization
Candidate voltage vector (CVV) optimization is a method that can be combined with various control schemes and can effectively suppress torque ripple. In [140], an MPTC approach for SRM drives is put forward, emphasizing the optimization of CVV and eliminating the need for flux linkage computations. The electrical cycle period of SRM is segmented into six parts, grounded on the torque distribution curve. The proposed method avoids a large amount of useless calculation and no longer relies on the hysteresis control loop.
An innovative MPC technique is introduced in [141], emphasizing the selection of CVV across varied regions to diminish the torque pulsation of the SRM and enhance its power factor. The electrical cycle of SRM is segmented into six regions. CVVs for every sector are chosen based on the phase torque characteristics. The constraint function aims to pinpoint the best voltage vector among the CVVs, thereby minimizing torque ripple. This contemporary control strategy sidesteps a large amount of unnecessary computation and steers clear of depending on hysteresis signals.
In [142], the torque of the SRM is managed using discrete space vector modulation (DSVM) combined with virtual state vectors for controlling the torque of SRM. Good closedloop control performance is achieved within a wide speed range and short prediction range, minimizing torque ripple to the greatest extent. Similarly, a method for predictive torque control based on DSVM is proposed in [143]. By estimating the torque output for k + 1 times, the torque reference value for k + 1 times is outputted. The optimal solution of the cost function for each sampling period is solved, thereby determining the required output control signal. This allows the SRM torque to follow the given torque, reducing torque ripple.

Error Compensation
Researchers have investigated error compensation in predictive torque control. One primary drawback of traditional FCS-MPC is the steady-state tracking error. Such errors might arise because of parameter inconsistencies. In traditional MPTC, the control action is derived through a multi-objective cost function. This function aims to align with the reference torque whilst curtailing the phase current throughout the prediction window. The best switching state that trims down the cost function is chosen and instituted at each switch instance. In [144], a compensatory term is integrated with the reference torque for every sampling interval, aiming to curtail the torque tracking discrepancy. This compensatory term is deduced from the anticipated average torque tracking error from the preceding sampling duration. The proposed method shows good results compared to traditional FCS-MPC.
With enhanced prediction ability through delay compensation, an improved predictive torque control strategy based on the look-up table is proposed in [145]. The table or static graph contains the machine's flux-linkage and torque characteristics, providing superior predictive precision relative to the approximate analytical model. The delay compensation is further refined by using a Kalman filter phase. Compared to traditional methods, the torque sharing capability is improved.

Other Predictive Control Applications
Apart from PCC and PTC, predictive flux control (PFC) is also recognized as an effective control method. In [146], a new control strategy related to flux linkage and MPFC is introduced, with the aim of reducing torque ripple in SRM.
In [147], an innovative model prediction technique is introduced to simultaneously suppress the torque ripple and source current ripple. Leveraging the data, the machine's torque and inverter current under all conceivable switch states are predicted, culminating in the formulation of a cost function. The operation state that registers the smallest cost function is deemed the prime switching signal. By deploying this signal to regulate the power converter, the dual objective of reducing both the torque pulsation and source current pulsation is effectively achieved.
Due to the inherent high thermal capacity of motors, they can be overloaded in a short period of time [148]. A model predictive overload control strategy for a water-cooled automotive switched reluctance motor is proposed in [149]. It predicts the maximum allowable torque based on real-time hotspot temperature estimates, ensuring full utilization of the machine's thermal capacity.
A multi-objective MPC method is proposed in [150] for three-phase isolated converterfed SRM integrated battery chargers in electric vehicle (EV) applications. The proposed control, based on the finite control set model predictive control, is apt for real-time prediction over a singular prediction horizon. With the custom multi-objective cost function, the proposed MPC achieves a unit input power factor while balancing the battery's state of charge (SoC) by the conclusion of its charging phase, regardless of its initial SoC.
To address the problem of large torque pulsations in SRMs, a novel control approach rooted in MPFC is introduced in [151]. Utilizing the discrete-time model of SRMs, the flux for the ensuing period is determined. The voltage vector that best minimizes flux is identified and then applied to the system. The proposed method is suitable for the nonlinear magnetic characteristics of SRMs. In [152], a robust control scheme based on GPC was proposed. The architecture of this proposed controller hinges on filter design, which allows for fast response, disturbance suppression, noise attenuation, and robustness, and it has a low computational cost.
For SRMs with high dynamic speed control, a four-quadrant operation strategy is proposed in [153]. The core of this is an online adaptive phase excitation predictive control technique based on PWM. The PC method consists of MPC and DPC. The MPC is employed within the commutation zone, whereas the DPC is utilized to determine the control signal. Through the deployment of this advanced control method, the usable range of PC spans into the braking torque area, facilitating a full four-quadrant operation of SRM in high dynamic speed regulation applications.
Traditionally, an asymmetrical half-bridge converter (AHBC) fed by a diode bridge rectifier is used to drive the SRM, resulting in poor power quality on the grid side [154]. In the system proposed in [155], a system topology that comprises a voltage source converter and an AHBC is introduced to power the high-speed SRM. The SRM's stable operation is ensured by controlling the active power directed to the motor. Based on this, the power quality on the grid side sees improvement through the direct adjustment of the input reactive power. A DPC paired with a disturbance observer is employed to accurately follow the power reference.
Scholars have also proposed a new scheme for SRM nonlinear predictive control [156] based on the target state equation (TSE). Considering the nonlinear model of SRM, nonlinear control theory is employed to define the offset of SRM's torque and angular velocity as TSE. Based on TSE and predictive control theory, a nonlinear predictive control of the SRM control system is designed. Using torque and angular velocity as feedback variables, the nonlinear predictive control law is obtained. Table 2 lists some limitations and advantages of the predictive control strategy of SRMs and some development directions of predictive control strategy of SRM with these limitations and advantages.

Rated Power and Topology of SRM
Predictive control for SRM is typically confined to low-power, low-voltage setups. A few instances explore high-power systems through simulated scenarios. There remains potential for PC in high-power machines [157], which often feature a greater number of pole pairs.
Additionally, so far, only traditional SRMs have been analyzed. Further study is needed for other topologies such as segmented rotor SRM, dual stator SRM (DSSRM), or mutually coupled SRM (MCSRM). Employing new predictive control techniques could hasten their commercial appeal.

Application in Electrified Powertrain
Even though SRMs cannot provide smooth torque and lower levels of NVH, their capability to function under malfunction and high-speed scenarios, combined with their efficient DC link utilization, significantly outperforms traditional AC drives. This makes them fitting for electrified power systems [158]. Developing a unified controller that can manage these varied conditions presents a fitting challenge for PC functions.
SRMs excel in post-fault operations due to their independently controlled phases. Since torque is reliant on individual phase contributions, the machine can still function with decreased torque if a phase goes missing. Furthermore, unused stages can serve other purposes, such as sensor-less control, bolstering the drive's robustness. These different operations and structural nuances require several adjustments to control tactics, which predictive control can streamline.

Control Strategies
Low inductance near unaligned positions leads to rapid current response; thus, precise current tracking can be achieved. This can be advantageously used during high-speed operation to allow the phase current to reach the reference current in a short excitation time when inductance is low [159].
There are multiple variants of power converters for SRMs. The converter's design, when integrated with current control, can introduce added features, such as self-tuning drives [100] or battery charging in electric vehicles [150].

Conclusions
Predictive control is currently drawing attention due to its enhanced AC drive control performance, particularly in improving dynamic response. It stands out in its ability to deal with non-linearities and the complex objectives of intricate systems. Given the highly nonlinear behavior of SRM drives, such features make PC approaches applicable to SRM drives. This overview introduced the composition and nonlinear model of the SRM drive system and the basics and classification of predictive control technology. The research situation of predictive control in the SRM drive system was discussed, mainly divided into PCC, PTC, and other PC applications. Finally, we discussed and summarized the direction of development of predictive control in the SRM drive system.
Given the distinct control objectives and challenges of SRMs, coupled with the potential solutions provided by recent advancements in PC, the future market prospects for SRMs appear bright. If the nonlinear behavior of the motor is addressed, the major shortcomings of this machine can be overcome. This behavior restricts the employment of preset control laws, thus promoting the use of algorithms that ascertain optimal laws in real-time. Model predictive control has showcased its prowess as a dependable, high-performance multiobjective control approach across numerous drives and power electronic systems. The main challenge lies in defining accurate predictive models based on control requirements.