Conventional Model Predictive Torque Control Research Articles

Model predictive control of induction motor based on amplitude–phase motion equation

Tedious adjustment of the weighting factor restricts the wide application of conventional model predictive torque control (MPTC) for induction motors (IMs) in practice. To solve this problem, this study introduces a new variable R (reactive torque) to control the flux of IM, which is the dual of torque T , with radial orientation and in relation to reactive power. Then, a novel MPTC strategy based on variable R and torque T is proposed and named RT-MPC. Compared with conventional MPTC, RT-MPC uses a pair of variables with the same dimensions and time scales instead of the torque and flux amplitude in MPTC. This approach eliminates the weighting factor of the cost function, unifies the time scales of control variables, and avoids prediction of rotor flux at the ( k + 2) instant. Simulation and experimental results show that RT-MPC can avoid the weighting factor, reduce switching frequency, and reduce control complexity. RT-MPC can also maintain excellent dynamic and steady-state performance similar to conventional MPTC. Hence, the proposed method is expected to be more practical.

Model Predictive Control for a Six-Phase PMSM Motor With a Reduced-Dimension Cost Function

This paper presents a model predictive control for a six-phase permanent magnet synchronous machine (PMSM) with a reduced-dimension cost function. Only the variables in the harmonic subspace are included into the cost function, while the energy conversion related variables are excluded. This is achieved by using the deadbeat direct torque and flux control method to obtain a reference voltage vector and then to track the torque and stator flux properly in the energy conversion related subspace. Then, according to the position of the reference vector, the appropriate prediction vectors can be determined. Subsequently, a reduced-dimension cost function including only the harmonic constraints is defined to evaluate the feasible prediction vectors. In this way, the predictive model and the cost function are simplified without redundant constraints. Meanwhile, the torque and flux can be regulated satisfactorily, and the harmonic currents are suppressed effectively. Finally, experimental results of the proposed method and the conventional model predictive torque control are presented in this paper to verify the validity of the proposed method.

A Simplified Model Predictive Control for a Dual Three-Phase PMSM With Reduced Harmonic Currents

The conventional model predictive control for dual three-phase motors only evaluates the largest voltage vectors to alleviate the computation burden, but at the costs of large current harmonics and torque ripple. This paper presents a simplified model predictive torque control (MPTC) for an asymmetrical dual three-phase permanent magnet synchronous motor (PMSM), which can significantly improve the machine performances. First, the 36 active voltage vectors in the outer three layers are considered with the proposed control method. In order to suppress the stator harmonic currents, the voltage vectors are preselected based on a switching table according to the flux position and torque deviation in the $\alpha \hbox{-} \beta, \text{x--}y$ subspace. Simultaneously, the number of prediction voltage vectors can also be reduced, thus effectively decreasing the computation time. In particular, with the proposed MPTC method, the harmonic currents can be effectively suppressed. Furthermore, the computational burden can be considerably alleviated. In the meantime, the merits of the conventional MPTC such as fast dynamic response and intuitive implementation are preserved. Finally, both simulation and experimental results are performed to verify the validation of the proposed MPTC methodology when comparing with the conventional MPTC for the dual three-phase PMSMs.

Double Vectors Model Predictive Torque Control Without Weighting Factor Based on Voltage Tracking Error

In order to reduce the computation burden and eliminate the weighting factor in conventional model predictive torque control (MPTC), this paper proposes an improved MPTC algorithm without the use of weighting factor. Based on the deadbeat direct torque and flux control, the reference voltage vector, which would be applied in the next period, is predicted to avoid testing all feasible voltage vectors, hence reducing the computation burden of conventional MPTC. Moreover, the torque and flux error-based cost function of conventional MPTC is replaced by the voltage vector tracking error-based cost function; thus, the weighting factor of stator flux in conventional MPTC, which is always necessary because of the different units between torque and flux, is eliminated. Furthermore, two voltage vectors, which include an active vector and a null vector, are applied during one control period to improve steady-state performance. The durations of the selected voltage vectors are determined based on the principle of voltage vector tracking error minimization. Moreover, to further improve the steady-state performance, a different vector selection way, in which the second voltage vector is not fixed as a null vector but selected in a border range, is introduced. The selection process of candidate voltage vectors is analyzed, and the duration is calculated. Simulation and experimental results both show the validity of the proposed control approach.

Model-Predictive Control of Induction Motor Drives: Torque Control Versus Flux Control

Recently, model-predictive torque control (MPTC) has been introduced as a powerful control method for induction motor drives. However, the weighting factor for stator flux must be tuned carefully to obtain satisfactory performance at different operation points. Unfortunately, so far the tuning of weighting factor in MPTC is mostly based on an empirical procedure. This paper solves this problem by proposing a model-predictive flux control (MPFC), which uses the stator flux vector as the control variable and eliminates the complicated prediction of stator current at $k+2$ instant. As a result, the weighting factor in conventional MPTC is eliminated, and the control complexity is significantly reduced. Both MPTC and MPFC are tested and compared in detail, including steady-state performance, dynamic response, and low-speed operation. The simulation and experimental results prove that the performance of conventional MPTC is dependent on the weighting factor, and the improper weighting factor would lead to significant performance deterioration. On the contrary, the proposed MPFC achieves similar or even better overall performance over a wide speed range with very low tuning work. Hence, it is concluded that the proposed MPFC is more practical than conventional MPTC.

Two-Vector-Based Model Predictive Torque Control Without Weighting Factors for Induction Motor Drives

Conventional model predictive torque control (MPTC) suffers from weighing factor tuning work and relatively high torque ripple, due to the different units of torque and stator flux and the limited number of voltage vectors. This paper proposes an improved MPTC without the use of weighting factor. The torque and flux magnitude references are converted into an equivalent reference vector of stator flux, hence eliminating the weighting factor of stator flux in conventional MPTC. Furthermore, two voltage vectors are applied during one control period to achieve better steady-state performance. Different from prior method using an active vector and a zero vector, the selected voltage vectors may be two nonzero vectors in the proposed method, which provides more opportunities to reduce both torque and flux ripples. The durations of the selected voltage vectors are determined based on the principle of stator flux error minimization. Both simulation and experimental results are presented to validate the effectiveness of the proposed method.

Model predictive torque control of induction motor drives with reduced torque ripple

Model predictive torque control (MPTC) is emerging as a high-performance control strategy for induction motor (IM) drives, due to its intuitive nature, flexibility to incorporate constraints and quick dynamic response. However, the implementation of MPTC requires high computational ability and the use of single voltage vector during one control period fails to reduce the torque ripple to the minimal value. This study proposes an improved MPTC for IM drives with reduced torque ripple and low complexity. On the basis of the relationship between stator current and stator flux, the complicated current prediction for each voltage vector is eliminated, reducing the control complexity significantly. Torque ripple reduction is achieved by allocating only a fraction of control period to the active vector selected from conventional MPTC, whereas the rest of time is allocated for a null vector. Two kinds of methods for optimising the duty ratio of the active vector are proposed and evaluated in detail. Presented experimental results prove that, compared with conventional MPTC, the proposed MPTC achieves better steady-state performance by reducing the torque ripple significantly. Meanwhile, the quick dynamic response of conventional MPTC is reserved.

Model-Predictive Flux Control of Induction Motor Drives With Switching Instant Optimization

Conventional model-predictive torque control (MPTC) requires tedious and time-consuming tuning work for stator flux weighting factor, and presents relatively high torque ripples. To solve these problems, this paper proposes a model-predictive flux control (MPFC) for two-level inverter-fed induction motor (IM) drives. The references of stator flux magnitude and torque in conventional MPTC are converted into an equivalent reference of stator flux vector in the proposed MPFC. As only the tracking error of stator flux vector is required in the cost function, the use of weighting factor is eliminated. The optimal voltage vector is selected based on the principle of stator flux error minimization and its switching instant is optimized rather than being in the beginning of each control period. The proposed MPFC with and without switching instant optimization are both implemented in a 32-bit floating digital signal processor, and they are compared in detail in terms of torque ripple, current harmonics, and average switching frequency. Both digital simulations and experimental tests were carried out on a two-level inverter-fed IM drive, and the obtained results validate the effectiveness of the proposed method.

Generalized Two-Vector-Based Model-Predictive Torque Control of Induction Motor Drives

Conventional single-vector-based model-predictive torque control (MPTC) has been widely studied owing to its intuitive concept and quick response. To improve the steady-state performance, recently, the concept of duty cycle control was introduced in MPTC by inserting a null vector along with an active vector during one control period. However, this still fails to reduce the torque error to a minimal value due to the imposed restriction on vector combination and the cascaded processing of vector selection and vector duration. This paper proposes a generalized two-vectors-based MPTC (GTV-MPTC) by relaxing the vector combination to two arbitrary voltage vectors. By evaluating the vector combination and their durations simultaneously in the predefined cost function, global minimization of torque error can be obtained in theory. However, the computational burden is also significantly increased. By choosing a proper method to determine the vector durations, the redundant vector combinations can be eliminated, which makes the proposed GTV-MPTC suitable for real-time implementation. Both simulation and experimental results were carried out to verify the effectiveness of the proposed method. The presented results show that, compared to prior MPTC with or without duty cycle control, the proposed GTV-MPTC achieves much better performance with lower sampling frequency over a wide speed range. Furthermore, the average switching frequency is even lower than that of conventional MPTC in the medium speed range.

Model Predictive Torque Control of Induction Motor Drives With Optimal Duty Cycle Control

Model predictive torque control (MPTC) is emerging as a powerful control scheme for high performance control of induction motor (IM) drives. Compared to direct torque control, MPTC is more effective and accurate in voltage vector selection by incorporating the system model directly with the finite switching states. However, for two-level inverter-fed IM drives, the sampling frequency of MPTC has to be high to achieve good performance due to the limited number of voltage vectors. Recently, the concept of duty cycle control was introduced in MPTC by inserting a null vector along with the selected active voltage vector to achieve torque ripple reduction. The active vector is first selected from conventional MPTC and then its duration is determined based on a certain principle. The cascaded processing of active vector and its duration leads to poor low-speed performance and the sampling frequency still has to be high. This paper proposes an improved MPTC with duty cycle control by optimizing the vector selection and its duration simultaneously when minimizing both torque and flux errors. As a result, better steady-state performance at both low and high speeds is achieved, even if the sampling frequency is reduced by half. The effectiveness of the proposed MPTC is verified by both simulation and experimental results.