1. Introduction
With the developments of power electronics and control theories, multiphase motor drives have become a competitive alternative to traditional three-phase drives due to their inherent merits, including lower torque pulsations, a higher power density, enhanced fault-tolerant capability, and a higher number of control degrees of freedom [
1,
2,
3].
Generally, the high-performance control strategies of multiphase motor drives are derived from traditional three-phase counterparts, e.g., field-oriented control [
4] and direct torque control [
5]. Meanwhile, finite control set-model predictive control (MPC) has been widely investigated in conjunction with motor drives [
6,
7,
8]. Model predictive current control and model predictive torque control are two typical manners of MPC. The former concentrates on the control of currents, and the latter focuses on the regulation of torque and stator flux. In contrast to the field-oriented control and direct torque control algorithms, a better balance between steady-state performance and dynamic response can be implemented by MPC. Furthermore, it is easier to deal with nonlinear constraints, such as reducing switching frequency and suppressing harmonic current. Nevertheless, since the number of switching states and subspaces increases in multiphase drives, MPC suffers from unsatisfactory steady-state performance, huge computational burden, and parameter uncertainties.
To improve steady-state performance and mitigate the influences of voltage vectors in the harmonic subspace, a concept of virtual voltage vector is proposed by means of voltage vector synthesis, and the duty cycle modulation is accordingly designed to generate pulses for dual three-phase permanent magnet synchronous motors (PMSMs) [
9,
10]. Later, the multivector MPC, combining two voltage vectors as outputs in each control cycle, is further developed to cope with the problem caused by the application of a single voltage vector [
11]. For computational burden reduction, a voltage preselection algorithm is proposed according to the location of the dead-beat voltage vector [
12] or the reference stator flux vector [
13].
To deal with the issues related to parameter dependence, model-free predictive control (MFPC) has become a promising alternative in the field of motor drives. Although the implementations and formulations are different, they share the common idea of making predictions free of a system model or at least less dependent on it. Existing methods are categorized into three main groups according to the extent to which they are model-free, namely, totally model-free, using an ultra-local model, and prediction correction [
14]. The first method is carried out by using the input and output information of systems without any model for prediction [
15,
16]. The second method uses a model with one or more uncertain terms that should be estimated continually via the input and output data of systems [
17,
18,
19,
20,
21,
22,
23]. The last type is devoted to the methods with an ideal model of the plant. However, by using the input, output, and previous prediction data of the system, some correction factors are estimated to compensate for the predictions [
24,
25,
26]. The totally model-free scheme generally faces the stagnation of the data updating, and prediction correction needs the nominal value of motor parameters. Comparatively, MFPC with an ultra-local model has attracted more attention.
The ultra-local model, derived from the mathematical model of motor drives, typically contains one or more uncertain terms that need to be identified. The estimation methods can be classified into two approaches. The first approach uses algebraic parameter identification techniques. The ultra-local model is usually studied in conjunction with model-free predictive current control (MFPCC). A nonlinear disturbance observer [
17], a linear extended state observer [
18], a sliding mode observer [
19], and a high-gain disturbance observer [
20] have been successively developed to estimate the known and unknown parts of the ultra-local model. Apart from the parameter-free predictive control, the steady-state performance enhancement is considered in [
21]; a discrete-space vector modulation is developed for induction motor drives. Noticeably, the stability of the MFPCC with observers should be considered. The improper gain tuning of observers may result in instability issues. The second approach investigates the inherent nature of the control-variable ripples to estimate uncertain parts of the ultra-local model instead of adopting observers. In contrast, the research on the second method is relatively rare. In [
22], the motor current time derivatives, which are expressed as functions of the phase angles of the basic voltage vectors, are predicted without motor parameters and are used for voltage vector optimization. The method lessens parameter dependence and eliminates the stagnation of data updating. In [
23], a current update mechanism based on the two most recent current variations to reconstruct the PMSM model is developed. The nonparametric predictive current control can effectively reduce torque ripple and enhance current performance.
Very recently, MFPC has also been applied in multi-phase motor drives. An ultra-local-based MFPCC in the natural coordinate system has been proposed for five-phase induction motors [
27], where the unknown terms of the ultra-local model are estimated by a linear extended state observer. Moreover, the MFPCC based on an ultra-local model and an extended state observer has been developed for an asymmetrical dual three-phase PMSM [
28]. The method was shown to provide superior current regulation when compared to the standard MPCC approach under uncertain parameter conditions. In [
29], a MFPCC method with an optimal modulation pattern was proposed for dual three-phase PMSMs. A novel nonlinear disturbance observer was designed to overcome the limitation of an extended state observer. This strategy can effectively compensate for voltage distortion caused by inverter characteristics and improve steady-state performance. Additionally, the MFPCC strategy has been investigated in the harmonic current control of multiple three-phase permanent magnet synchronous generators [
30]. The ultra-local model-based predictive current controller was designed to regulate the current component in the fifth-order multi-
dq coordinate. The uncertain parameter of the ultra-local model is estimated by the differential algebra method. However, the accuracy of estimation may be affected by the length of the gradient integral.
The abovementioned MFPC of multiphase drives mainly concentrates on ultra-local-based MFPC with observers, which would encounter the problems associated with gain tuning and system stability. In contrast, the ultra-local model using the output information of drives can avoid these drawbacks. To lessen the parameter dependence of current prediction, an ultra-local model-based MFPCC strategy is proposed for five-phase PMSM drives. The ultra-local model is constructed from the differential equation of current. The relation between the predictive current model and the ultra-local model is analyzed in detail. The unknowns of the ultra-local model are estimated by the current and voltage at different time instants without motor parameters. Moreover, space vector modulation (SVM) technology is employed to further reduce the voltage tracking error. The proposed methods not only theoretically eliminate the impact of machine parameters but also improve system performance. The contributions of this paper are summarized as follows:
An MFPCC strategy based on an ultra-local model and drive information is proposed for five-phase PMSM drives;
The unknown components of the ultra-local model are estimated with the current and voltage at different time instants without motor parameters or observers.
The organization of the rest of this paper is listed as follows. The conventional MPCC of a five-phase PMSM drive is presented in
Section 2. Then, the MFPCC is detailed based on the ultra-local model and SVM in
Section 3. In
Section 4, simulated and experimental results are demonstrated to verify the effectiveness of the proposed control schemes. Finally, conclusions are drawn in
Section 5.