Finite Set Model Predictive Control Research Articles

Comparative Study of BLDC Motor Drives with Different Approaches: FCS-Model Predictive Control and Hysteresis Current Control

The control techniques of the brushless DC (BLDC) motor have gained a large amount of interest in recent years, with their use being implemented in order to achieve a high-performance drive, including quick transient response and high-quality waveforms at the steady state. This paper provides a comparative study between three control schemes of BLDC motors: the direct power control scheme using a finite control set model predictive control (FCS-MPC) approach, the stator current controlled scheme using an FCS-MPC approach, and the stator current controlled scheme using ON–OFF hysteresis current controllers. The three systems were studied and investigated under the same operating conditions. The comparative study included investigating the performance of the BLDC drive in both steady state and transient operations. Qualitative and quantitative analyses were performed on the results obtained with each control scheme. The obtained results demonstrate the validity and effectiveness of the three investigated schemes in controlling the motor speed to the desired value under sudden load changes and achieving satisfactory quick transient responses. However, the results indicate the superiority of the direct power control scheme using an FCS-MPC approach over the others in terms of its minimum torque ripple, lowest torque and speed pulsations, minimum active and reactive power ripples, and high-quality waveforms of the stator currents drawn by the motor with minimum THD.

Performance improvement of hydraulic turbine generation system using subdivided finite set model predictive current control

Performance improvement of hydraulic turbine generation system using subdivided finite set model predictive current control

Hierarchical search approach based online model predictive control of three‐level converter fed PMSM driving systems

The finite-control-set model predictive control (FCS-MPC) can achieve a high output and fast control response. However, the size of the candidate vector set of FCS-MPC must be very huge to achieve a satisfactory steady-state control performance. Although some studies suggest that the candidate vector set can be expanded by increasing the number of vectors in one period or directly defining new virtual vectors, there is a tricky contradiction between improving the steady-state control performance and reducing the computational burden. It makes the online realization difficult. This study presents a hierarchical search approach based FCS-MPC of three-level converter fed permanent magnet synchronous motor (PMSM) driving systems. The optimal vector is obtained by continuously shrinking the vector space, so that only 30 prediction calculations are needed to evaluate more than 20,000 candidate vectors. Consequently, the proposed method can achieve the excellent steady-and transient-state control performance online. Moreover, since the optimal vector is chosen directly from the vector set, the linear-and over-modulation are unified. No special treatment is necessary for over-modulation driving systems, because the reference voltage is decided naturally by the cost function of FCS-MPC. Some experimental results are shown finally to prove the correctness and feasibility of the proposed method.

Virtual Voltage Vector Based Model Predictive Control for a Nine-Phase Open-End Winding PMSM With a Common DC Bus

Finite control set model predictive control (FCS-MPC) is a control strategy with fast response and a simple and flexible structure. However, when the control plant is complicated such as a multiphase electric machine, the application of FCS-MPC faces clear challenges. This article for the first time investigates the FCS-MPC for a nine-phase open-end winding (OW) permanent magnet synchronous machine, which is powered by nine H-bridge inverters with a common dc bus. First, in order to solve the challenge of substantial iterations in the conventional FCS-MPC, the number of control sets is simplified by reconfiguring the high level in switching states. Then, to eliminate the zero-sequence current caused by the common dc bus, the zero common-mode voltage (CMV) vector is selected. Subsequently, duty-ratio optimization is used to further reduce the available vectors. By the abovementioned measures, the number of iterations is reduced from 19 171 to 18. In order to suppress the harmonic current, the virtual voltage vectors (VVs) are designed. Each VV is synthesized by two zero CMV vectors, which can eliminate all the third and fifth harmonics in the output voltage. In addition, to achieve symmetrical pulsewidth modulation pulse sequences, a general pulse generation method for OW drive systems is proposed. Finally, the control performance of different control sets and harmonic weighting factors are evaluated and compared, and the experimental results have verified the effectiveness of the proposed methods.

Integral Sliding Mode Observer-Based Ultralocal Model for Finite-Set Model Predictive Current Control of Induction Motor

The ultralocal model of a plant expresses the behavior of the output variable in relation to the input without requiring any specific information about the plant. Replacing the conventional model of the system with an ultralocal model can effectively improve the robustness of the model predictive control (MPC) because all types of uncertainties that correlate with the system modeling are removed in the ultralocal model. This article proposes an integral sliding mode observer (ISMO)-based ultralocal model for the finite-set model predictive current control (FS-MPCC) of an induction motor (IM). The ISMO is constructed based on the Lyapunov theory to guarantee the stability of the proposed control method. Moreover, an analytical comparison is made between the proposed ISMO and the conventional extended state observer (ESO) in the application of the ultralocal model. This comparison shows that the stability of ESO depends on the unknown term of the ultralocal model. In contrast, the stability of the proposed ISMO does not rely on any terms of the ultralocal model. Experimental tests confirm that the proposed FS-MPCC method is practically applicable to the IM drive system. Also, it improves the robustness of the predictive method against model uncertainty.

Weighting Factor Free Model Predictive Control for a Flying Capacitor Converter in a DC Microgrid

This paper presents a single-objective model predictive control for a bidirectional DC-DC flying capacitor (FC) converter, which integrates a battery to the microgrid. The presence of multiple FCs facilitates the converter to interface a low-voltage battery to a high-voltage DC bus at reduced voltage stress on its power switches. However, such converter requires a controller that fulfils multiple objectives, namely DC bus and FC voltage regulations, and bidirectional power flow. The key feature of the proposed controller is that it utilizes a model predictive control with a single-objective cost function based on battery current and a redundant state selection scheme to attain these multiple objectives. Adopting such a strategy not only reduces computational burden but also eliminates the need for weighting factors and requirement of complex numerical models for its estimation. Another notable aspect is that the controller employs an improved dynamic reference model to generate appropriate battery current reference for the DC bus voltage regulation, without necessitating a secondary control loop and additional current sensors. Finally, experimental results of the proposed system for a step-response of the DC bus voltage, varying PV power, and loads are validated and compared against finite control set model predictive control.

A Desired Voltage Vector Based MPTC Strategy for PMSM With Optimized Switching Pattern

The main challenges for Finite Set-model Predictive Torque and Flux Control (MPTC) include huge calculation amount, large torque ripple, and the selection of weighting factor. To deal with these challenges and achieve the fastest torque response, a novel MPTC strategy with virtual voltage vector-based pattern is proposed in this paper. In each control period, a desired voltage vector is computed based on the maximum torque variation rate. The virtual desired voltage vector is combined by using basic voltage vectors with the minimum switching times. The switching pattern between two adjacent control periods is optimized by using a cost function in realtime. Compared with the traditional MPTC approach, the novel strategy has multifaceted improved performances: faster torque response, less calculation amount, lower switching frequency, reduced torque ripple, higher efficiency and no weighting factor. The proposed method is contrasted with traditional MPTC method and a well-known generalized multiple-vector-based MPC method via experiments.

Robust adaptive direct speed control of PMSG-based airborne wind energy system using FCS-MPC method

Electricity generation using airborne wind energy system (AWES) tends to be more efficient than that of conventional wind turbines due to their ability at extracting higher speeds from wind at higher altitudes by the tethered kite generator system (TKGS). The speed regulation of a permanent synchronous machine (PMSM) attached to a kite to maximize harvested power from wind is the topic of the present research. To track the optimal speed produced by TKGS, a finite-control-set model predictive control (FCS-MPC) with a new cost function is directly employed to generate appropriate gate signals for a 3-level neutral point clamped (3-L NPC) inverter that drives a PMSM. A novel adaptive algorithm is also provided for adjusting the weight coefficients of the cost function to improve the system’s performance across a wider range of change in the operating conditions. Moreover, a terminal sliding mode disturbance observer (TSMDO) is designed to estimate the load torque. A terminal sliding mode speed controller (TSMSC) is also used to produce the current reference for the optimizing algorithm in FCS-MPC. The proposed control scheme eliminates the need for a cascade structure while significantly reduces current deformation and torque oscillations. Additionally, the controller operates as fast as a traditional direct speed controller without the use of a cascade structure and is more robust against parameter uncertainties. To illustrate the success of the suggested controller, the results of simulations are presented in MATLAB/SIMULINK® software. The performance of the proposed technique is evaluated in three situations which simulates a grid-connected PMSM fed by a back to back 3-L NPC. In the first scenario, it is demonstrated that the suggested technique performs well when the system’s operational conditions vary. The performance of the adaptive tuning mechanism of the cost function weight factors is investigated in the second scenario, which takes into account model parameter uncertainty. The impacts of the disturbance observer (DO) on the system performance are explored in the final scenario, and it is discovered that the disturbance observer may increase the speed response and DC link voltage tracking performance. All of the simulation results show that the new technique outperformed the traditional FSC-MPC.

A Low-Complexity Gradient Descent Solution With Backtracking Iteration Approach for Finite Control Set Predictive Current Control

Finite control set model predictive control (FCS-MPC) has been widely recognized in the field of electrical drive control during the past decades, due to its merits of quick dynamic response and low switching frequency. However, it is inherently penalized by high tracking deviations in the steady-state as well as exhaustive search among the switching sequences. To cope with this issue, a low-complexity gradient descent-based finite control set predictive current control (GD-FCSPCC) combined with a backtracking iteration approach is proposed in this article, aiming to improve the control performance by effectively tracking the reference value. First, FCS-PCC is reformulated as a quadratic programming (QP) problem from a geometric perspective. Consequently, the convexity of QP problem is proved to underlying the gradient descent, which minimizes the tracking deviations in an effective manner. Thus, the optimal solutions are selected by optimizing the reformulated objective functions. To reduce the number of the searched control inputs, a two-layer generalized decision-tree is employed. The procedures are repeated in several iteration periods optimized via a backtracking method, until the stopping criterion is satisfied. The effectiveness of the proposed GD-FCSPCC is experimentally validated on a 2.2 kW induction machine testbench.

Weighting Factor-Less Sequential Predictive Control of LC-Filtered Voltage Source Inverters

To eliminate the weighting factor tuning effort of typical finite-set model predictive control (FS-MPC), this paper proposes a weighting factor-less sequential model predictive control (SMPC) scheme for LC-filtered voltage source inverters. Two independent cost functions for minimizing capacitor-voltage and inductor-current tracking errors are deployed in a cascaded structure, eliminating the weighting factor. First, the optimal cascade order of the cost function is selected by the internal relationship of two control variables. Then, a graphical method is proposed to determine the optimal number of candidate voltage vectors selected from the first cost function. Moreover, to realize the strict current limitation, the current-constraint term is proved to be included in the voltage-related cost function. Another attractive feature of the proposed SMPC is that a smoother inductor-current starting response can be obtained compared to typical FS-MPC. Simulation and experimental results verify the feasibility of the presented approach.

Neural Predictor-Based Low Switching Frequency FCS-MPC for MMC With Online Weighting Factors Tuning

In this article, we propose a novel predictive control framework for modular multilevel converter, which makes use of neural predictor-based low switching frequency finite control-set model predictive control methodology with respect to online weighting factors tuning subject to robustness characteristics. The main objectives of this article are to maintain a low switching frequency operation and to enhance the system robustness. First, a modified cost function together with an online weighting factors auto-tuning technique, which has good potential to fulfill the low frequency operation, is presented under different operating conditions. Next, we provide a framework to explicitly address parameter mismatches and unknown nonlinear system dynamics in this proposal by introducing the neural network predictor control technique. The novelty of contribution of this article lies not only in incorporating the proposed cost function with a predictor-based neural network design solution for satisfying the requirement of the low switching frequency and robustness but also in the utilization of the auto-tuning technique for online determining the suitable weighting factors. Finally, we demonstrate the applicability of the proposed predictive control framework in comparison with the state-of-the-art finite control-set model predictive control approaches under various operating conditions.

Multirate Finite-Control-Set Model Predictive Control for High Switching Frequency Power Converters

Due to the modulator free structure, the finite-control-setmodel predictive control (FCS-MPC) needs a high sampling frequency/interrupt frequency (20–50 kHz) for power converters application, while the typical converter switching frequency is around 20–25% of the sampling frequency. To obtain a high switching frequency, it is not always practical to increase the sampling rate by considering the computational burden in a digital processor. Therefore, increasing the switching frequency without using a high sampling frequency is a critical task for FCS-MPC, particularly applied to silicon carbide and gallium nitride-based high switching frequency power converters. To solve this problem, this article proposes the multirate FCS-MPC (MRFCS-MPC), where the control frequency is allowed to be higher than the sampling frequency. Consequently, the switching frequency can be significantly increased without changing the sampling frequency. The proposed scheme inherits the ability to handle complex control objectives from the traditional FCS-MPC. The lifting model is built to predict the fast rate information of state variables based on the low sampling output. Then, the fast rate control inputs within one sampling interval are solved efficiently with a good tradeoff between computational burden and optimized system performance. The experimental motor drive system tests are carried out to verify the effectiveness of the proposed MRFCS-MPC.

Single-Stage Grid-Connected PV System With Finite Control Set Model Predictive Control and an Improved Maximum Power Point Tracking

The single-stage grid-connected photovoltaic (PV) topology has recently drawn attention as it can reduce overall losses and installation costs. This paper presents a new control approach for single-stage grid-connected PV systems. The proposed controller is a combination of a finite control set model predictive control (FCS-MPC) and a maximum power point tracking (MPPT) algorithm, which ensures the extraction of maximum power from the PV panels and good transient performance for the output voltage and current. The disadvantages of classical MPPT algorithms in tracking the global maximum power point under fluctuating environmental conditions are avoided by including additional constraints in the cost function of the FCS-MPC. Further, the controller is tested for partial shading in PV. The performance of the proposed controller is compared with the two-stage and single-stage PV configuration with different controls and MPPT algorithms. The simulation results show that the single-stage PV system with the proposed control can effectively extract the maximum power from the PV system and maintain a stable output signal for the transient condition. Finally, experimental results according to a control hardware-in-the-loop (C-HIL) approach are presented to validate the effectiveness of the proposed algorithm.

Hybrid Decision Based on DNN and DTC for Model Predictive Torque Control of PMSM

To address the issue of poor real-time performance caused by the heavy computational burden of the finite control set model predictive torque control (MPTC) of a permanent magnet synchronous motor (PMSM), a data-driven control method using a deep neural network (DNN) is proposed in this paper. The DNN can learn the MPTC’s selective laws from its operation data by training offline and then substitute them for voltage vector selection online. Aiming to address the data-driven runaway problems caused by the asymmetry between the dynamic and static training data, a hybrid decision control strategy based on DNN and DTC (direct torque control) is further proposed, which can realize four-quadrant operation with a control effect basically equivalent to MPTC. The proposed strategy has great application potential for use in multi-level inverter and matrix converter driving with multiple candidate voltage vectors or multi-step prediction.

A Two-Step Horizon Optimum Switching Vector-Model Predictive Control with a Novel Shunt Active Filter Reference Current Extraction

Shunt active filters (SAFs) can be used for harmonic mitigation, reactive power compensation and power factor control in electrical distribution networks. Model predictive controller (MPC) can be used to give optimum performance for SAF’s due to its inherent cost function optimization. The SAF’s reference current extraction technique in finite control set-MPC (FCS-MPC) plays a vital role in the effectiveness of the SAF’s operation. The advantage of FCS-MPC is that it closely tracks the reference and injects the required compensating currents by optimizing the SAF’s switching vector and it does not require an external modulator for pulse generation. FCS-MPC can be implemented as either an optimal switching vector MPC (OSV-MPC) or an optimal switching sequence MPC (OSS-MPC) technique. The OSV-MPC technique is simple and efficient for SAF applications. In this paper, a novel reference current extraction technique, the inverse matrix average pq-synchronous reference frame (SRF) (IMApq-SRF) technique, is proposed along with the OSV-MPC technique. Practically a two-step delay compensation is essential in the implementation of the technique for the control of an SAF. Hence in this paper a two-step horizon OSV-MPC technique is proposed along with an IMApq-SRF reference current extraction technique to improve the power quality in distribution networks. The presented results show that the proposed methodology gives optimum SAF performance under a large range of supply and load conditions.

Model predictive control of solar photovoltaic‐based microgrid with composite energy storage

SummaryThe renewable energy (e.g., solar photovoltaic)‐based grid‐connected microgrid (MG) with composite energy storage system (CESS) is feasible to ensure sustainable and quality power to the commercial and domestic load demands. Effective control systems provide the dynamic performance of such deployed MGs. This paper investigates the application of the finite control‐set model predictive controller (FCS‐MPC) for solar photovoltaic‐based grid‐connected MGs with composite energy storage. FCS‐MPC considers the discrete nature of interfacing (DC–AC and DC–DC) converters into the control algorithm to predict the optimal control command for reference current tracking. Compared to classical control approaches, FCS‐MPC provides a fast‐dynamic response, discards the modulation stage, and effectively handles the effects of dynamic source and load variations and nonlinear loads. The control system encapsulates a proportional–integral (PI) controller, low‐pass filter (LPF), power management algorithm (PMA) unit, and followed by the FCS‐MPC approach. The CESS unit consists of a battery and supercapacitor storage system. The efficacy of the FCS‐MPC approach is verified through the MATLAB/Simulink results. Solar photovoltaic variation due to irradiance, utility grid availability, electricity pricing, and dynamic load variations are considered in the implementation. Furthermore, real‐time simulation of the proposed method is validated using OPAL‐RT OP4510 real‐time simulator.

Efficient Fixed-Switching Modulated Finite Control Set-Model Predictive Control Based on Artificial Neural Networks

The disadvantage of finite control set-model predictive control (FCS-MPC) is that the switching frequency is variable and relies on the sampling time and operating point. This paper describes how to implement a new algorithm to achieve a fixed-switching frequency functionality for the FCS-MPC. The used approach combines the FCS-MPC with the SVPWM, resulting in the calculation of dwell times and the selection of the best two active vectors for the next sample interval. These dwell times have a significant impact on FCS-MPC performance during transient and steady-state conditions, and their values are determined using various mathematical models. To solve the problem of the fixed-switching frequency with lower harmonics distortion compared to the conventional modulated MPC (M2PC), an ANN-based trained network is proposed to calculate the duty-cycle of the applied vectors and thus the dwell time in the next sampling interval. The ANN network receives the cost functions of the two active vectors and the zero vector from the M2PC control algorithm and determines the optimal duty-cycle for each vector based on a proper tuning. In this way, three goals are achieved, the first goal is that the algorithm explicitly obtains a fixed-switching frequency, and secondly, the cost is as simple as the conventional M2PC. Finally, the feature of including objectives and non-linearity is still applicable. The paper’s case study used the two level voltage source inverter (2L-VSI) for uninterruptible power supply (UPS) applications. The results based on MATLAB/Simulink revealed that the ANN-M2PC has retained all FCS-MPC features in addition to operating at a fixed-switching frequency, while the power quality is significantly enhanced.

Modulated Predictive Control to Improve the Steady-State Performance of NSI-Based Electrification Systems

This paper presents a modulated model predictive control (M2PC) strategy for a nine-switch inverter (NSI) based electrification system to improve the steady-state performance. The model predictive control method has gained significant interest due to its straightforward structure. However, the traditional finite control set model predictive control (FCS-MPC) imposes a high computational burden that is problematic in practical applications. This prevents reaching the high sampling frequencies due to an excessive increase in algorithm run-time. Selecting a low sampling frequency causes an unpleasant distortion in the control variable or poor power quality. An M2PC method for the NSI is proposed in this work to remove this trade-off. One zero vector and two active vectors are selected by evaluating a cost function for each allowed switching state of the NSI. The duty cycles of these vectors are calculated by assessing the cost function employing current error terms. An optimized sequence of these vectors is applied to the system that operates with the fixed-modulation frequency. Thus, an improvement in power quality (reduced harmonics with a better spectral content) with a lower sampling frequency is achieved. The computational burden rate (CBR) on the processor is reduced. These enhancements were proved by simulation and experimental studies. The comparison work was conducted to highlight the advantages of the proposed method over the other techniques reported in the literature. The proposed M2PC method was verified on a lab-scale NSI prototype driving two induction machines. The machine torques and speeds are well regulated, and the quality of the stator current is improved.

A Finite Control Set Model Predictive Control for Five-Phase PMSMs With Improved DC-Link Utilization

Finite control set model predictive control (FCS-MPC) based on virtual voltage vectors (V3s) is widely studied and applied in five-phase permanent magnet synchronous motor (PMSM) drives. The synthesized V3s can inherently eliminate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">xy</i> -axes voltages and reduce the number of candidate vectors, which can significantly reduce the computation burden. However, the dc-link utilization is reduced due to the usage of V3s. To address this issue, an FCS-MPC method with improved dc-link utilization is proposed in this article. First, only large vectors are selected to predict the system evolution. The large vector that minimizes cost function is selected, and rescaled using the duty ratio estimation. Then, in order to control the third harmonic currents, three adjacent large vectors are applied to replace the selected vector, and the duty ratios are reassigned. Additionally, zero vectors are replaced with two opposite large vectors to reduce common-mode voltage (CMV). Finally, the proposed FCS-MPC is compared with conventional methods in experiments. Experimental results have verified that the proposed method can improve the dc-link utilization, and keep the superiorities of low CMV and low computation burden.

Decoupled Predictive Current Control With Duty-Cycle Optimization of a Grid-Tied Nine-Switch Converter Applied to an Induction Generator

The nine-switch converter (NSC) was developed aiming at the reduction in the number of power converter switches in multiport systems, such as variable-speed drives for power generation. Among the possible control techniques for the NSC, finite-control-set model-predictive control (FCS-MPC) stands out due to its fast dynamics and easy incorporation of system restrictions. However, converters with many switching possibilities and control goals increase the computational burden and the cost function complexity. Moreover, FCS-MPC can present high ripple values in the system outputs. This article proposes a decoupled predictive current control with duty-cycle optimization (PCC-DD) for the NSC, which decouples the control of an induction generator from the grid control. The separation between grid and generator controls decreases the enumeration of voltage vectors to be performed, reducing computational burden. Then, duty-cycle calculations are responsible for reducing torque and active power ripples. Experimental results show that PCC-DD provides lower ripple factors for the desired variables when compared to the approach with a concentrated cost function. The main contribution is a better steady-state performance with a lower computational burden. Therefore, PCC-DD is a suitable low-ripple technique for NSC control and for application to power generation with variable-speed generators.