Continuous Model Predictive Control Research Articles

Decoupled Continuous Control Set Model Predictive Control for T-Type Three-Phase Four-Leg Three-Level Inverters Driving Constant Power Loads

Decoupled Continuous Control Set Model Predictive Control for T-Type Three-Phase Four-Leg Three-Level Inverters Driving Constant Power Loads

Continuous adaptive nonlinear model predictive control using spiking neural networks and real-time learning

Model predictive control (MPC) is a prominent control paradigm providing accurate state prediction and subsequent control actions for intricate dynamical systems with applications ranging from autonomous driving to star tracking. However, there is an apparent discrepancy between the model’s mathematical description and its behavior in real-world conditions, affecting its performance in real-time. In this work, we propose a novel neuromorphic (brain-inspired) spiking neural network for continuous adaptive non-linear MPC. Utilizing real-time learning, our design significantly reduces dynamic error and augments model accuracy, while simultaneously addressing unforeseen situations. We evaluated our framework using real-world scenarios in autonomous driving, implemented in a physics-driven simulation. We tested our design with various vehicles (from a Tesla Model 3 to an Ambulance) experiencing malfunctioning and swift steering scenarios. We demonstrate significant improvements in dynamic error rate compared with traditional MPC implementation with up to 89.15% median prediction error reduction with 5 spiking neurons and up to 96.08% with 5,000 neurons. Our results may pave the way for novel applications in real-time control and stimulate further studies in the adaptive control realm with spiking neural networks.

Stability analysis for an ad-hoc model predictive control in DC/DC converters with a constant power load

This paper presents a stability analysis for a horizon-one continuous control set model predictive control (MPC) for DC/DC converters connected to a constant power loads (CPLs). Different MPC approaches have been previously presented, each tailored to a specific type of converter but without a formal stability proof, failing to ensure robust performance across various operating conditions. Unlike previous works in the scientific literature, our approach is general and applicable to any second-order DC/DC converter, including the Buck, Boost, Buck-Boost, and non-inverting Buck-Boost converters. A formal stability analysis was conducted using the proposed approach, initially for the open-loop system and subsequently for the closed-loop system. The trace-determinant or triangle criterion was employed for discrete-time systems in R2. Three analyses were conducted to evaluate the performance of the proposed MPC, showing the stability issues of DC/DC converters with CPLs in open loops. This work proposes solutions using the suggested technique. Numerical simulations utilizing the Boost and Buck-Boost converters demonstrate that, in open-loop operation, even minor perturbations in the CPL value can destabilize the behavior of electrical variables. In addition, simulations show that, for the Boost converter, the settling time was about 1.5ms. Meanwhile, in the Buck-Boost case, it was about 5ms. Standardized control indicators, such as the integral absolute error criterion (IAE), the integral of the time-multiplied absolute error criterion (ITAE), and the integral of the time-multiplied square error criterion (ITSE), confirm the effective performance of the proposed one-step MPC. The values range between 1.521×10−2 and 4.591×10−6 for the Boost converter, and between 6.607×10−3 and 3.366×10−6 for the Buck-Boost topology.

Continuous Control Set Model Predictive Control of a Hybrid Modular Multilevel Converter for Wind Energy Applications

Continuous Control Set Model Predictive Control of a Hybrid Modular Multilevel Converter for Wind Energy Applications

Noise Tolerance Strategy Based on Virtual Capacitor for DC-DC Converters with Continuous Control Set Model Predictive Control

Noise Tolerance Strategy Based on Virtual Capacitor for DC-DC Converters with Continuous Control Set Model Predictive Control

Dynamic Performance Improvement of Continuous Control Set Model Predictive Control for High-Frequency Link Matrix Converter

In this paper, a comprehensive control strategy of a high frequency link matrix converter (HFLMC) based on the interaction technology between electric vehicle and power grid is proposed to improve the dynamic performance of the system. The continuous control set model predictive control (CCS-MPC) is applied to the current loop to solve the problems of difficult selection of PI control parameters and slow dynamic response speed. In order to ensure that the grid-connected current can achieve better command tracking, a deviation suppression term is introduced into the cost function of CCS-MPC, and the online auto tuning method of weight factors of fast-tracking term and deviation suppression term is designed. On this basis, the PWM signals are generated by the coordinated modulation strategy of the HFLMC to obtain a constant switching frequency, which makes the harmonic of the grid connected current easier to be filtered out. Experimental results show the correctness and feasibility of the proposed control strategy.

Continuous Control Set Model Predictive Control of a Modular Multilevel Converter for Drive Applications

The Modular Multilevel Converter is a good alternative for high power, medium voltage drive applications due to its modularity and scalability. However, the control is complex and typically involves several highly-coupled circulating current feedback loops implemented using Single-Input Single-Output design tools. Additionally, each circulating current has many different frequency components and electrical sequences to increase the degrees of freedom in the controller. In this work, the use of Continuous Control Set Model Predictive Control is proposed in order to include cross-coupling and interactions between the state variables and consider the system constraints, such as maximum current and maximum output voltage. The controller is intended for drive applications and is designed to operate with good dynamic performance over the entire speed range of the machine. The control methodology proposed is experimentally validated using an 18-cell MMC prototype driving a cage machine. Additional experimental tests are performed using PLECS-RT HIL platforms.

Continuous Control Set Model Predictive Control for the optimal current control of Permanent Magnet Synchronous Motors

This paper proposes a Continuous Control Set Model Predictive Control (CCS-MPC) for controlling the internal loop of Permanent Magnet Synchronous Motors (PMSMs). The proposed controller has the ability to track the references with zero steady-state error and provides a fast dynamic response. The performance of the internal loop affects the motor currents and torque ripples. The obtained Total Harmonic Distortion (THD) with the same switching frequency is much lower than Finite Control Set Model Predictive Control (FCS-MPC), which is mostly used in controlling the internal loop.The control parameters are selected with a sensitivity analysis to provide a reasonable phase margin and gain margin. Furthermore, to overcome the nonlinearity of the model, the controller is designed beforehand for different speed setpoints, and the control law coefficients are saved in a look-up table. Then, in each sampling time, the speed is measured, the coefficient is interpolated, and the control law is updated.All the optimization of the proposed controller is performed offline and the output is some simple expressions thus the control law is not computationally expensive. In addition, the controller output is voltage in the continuous space that is applied to the inverter by a standard algorithm and works with a fixed switching frequency.The simulation and experimental results are presented to validate the proposed controller’s appealing features.

Dynamic performance improvement of induction motors used in rolling mill application: A two-loop model predictive control strategy

In this paper, a novel two-loop model predictive control (TLMPC) is proposed to enhance the dynamic performance of induction motors used in rolling mill applications. In such applications, two individual voltage source inverters feed induction motors which are connected to the grid in a back-to-back manner. The grid-side converter, responsible for controlling the DC-link voltage, plays a vital role in the dynamic performance of the induction motors. Its undesired performance deteriorates the speed control of induction motors, which is a crucial need in the rolling mill industry. The proposed TLMPC includes a short-horizon finite set model predictive control in the inner loop to control the power flow by finding the best switching state of the grid-side converter. Additionally, a long-horizon continuous set model predictive control is developed in the outer loop for adjusting the set point value of the inner loop by predicting the DC-link voltage in a limited time horizon. An identification approach is exploited to approximate the non-linear model of the grid-side converter in order to use it in the outer loop. The mathematical proof of the robust stability of the proposed TLMPC is provided and its real-time execution is also certified. Finally, the capability of the proposed approach is evaluated using MATLAB/Simulink. A sensitivity analysis to evaluate the effect of the model’s inaccuracy and uncertainties on the performance of the proposed strategy is also provided.

A Novel Continuous Control Set Model Predictive Control for LC-Filtered Three-Phase Four-Wire Three-Level Voltage-Source Inverter

In this article, a novel continuous control set model predictive control (CCS–MPC) is proposed for an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> -filtered three-phase three-level four-wire voltage-source inverter (3P-4W-3L-VSI). The proposed MPC algorithm provides independent control of each phase of the 3P-4W-3L-VSI under various unbalanced load conditions, which shows superior performance under unbalanced loads. Furthermore, different from conventional MPC methods, the CCS–MPC achieves fixed switching frequency, hence simplifying the design of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> filters. In addition, dc offsets are introduced to the proposed modulation to effectively balance the neutral-point voltage of the 3P-4W-3L-VSI. Experimental results are presented to verify the effectiveness of the proposed MPC algorithm.

Adaptive Model Predictive Current Control for PMLSM Drive System

This article proposes an adaptive model predictive current control (AM-MPCC) for surface-mounted permanent magnet linear synchronous motor systems to simultaneously enhance the robustness against permanent magnet flux, inductance, and resistance mismatches. First, the conventional continuous control set model predictive control is analyzed, illustrating that parameter variations will inevitably deteriorate the current regulation performance. Then, an adaptive predictive model, which involves a disturbance term and an optimized current change rate coefficient, is proposed. The optimal coefficient is estimated using a steady-state incremental model and the steepest descent method at each control period. A discrete-time sliding mode disturbance observer is devised based on the adaptive model with updated coefficients to achieve the disturbance term. Finally, an exponential reaching law-based-reference trajectory is defined for the cost function of AM-MPCC to adjust the current approach trajectory. Experimental results verify the excellent robustness performances of the proposed method.

A Novel Modulation Method Based on Model Prediction Control With Significantly Reduced Switching Loss and Current Zero-Crossing Distortion for Vienna Rectifier

Finite control set model predictive control (FCS-MPC) is widely used in rectifiers due to its fast response. When there are multiple control objectives, the optimal switching sequence is selected by minimizing the cost function with weighting factors. However, the reduction of current ripple caused by output error and switching loss is in conflict to a certain extent for FCS-MPC. In addition, when multiple objectives are controlled, the selection of weighting factor is a serious challenge. Therefore, a modulation method based on continuous control set model predictive control is proposed in this article. Two phases are clamped and one phase is modulated, which not only can significantly reduce the switching loss without increasing the computational burden, but also can control the neutral point voltage without using weighting factors. In addition, when the proposed method is adopted, current zero-crossing distortion can be suppressed over the full range of modulation index. The effectiveness of the proposed method is verified by simulation and experimental results.

Robust Continuous Control Set Model Predictive Control in Synchronous Reference Frame for Grid-Tied Inverters

This article proposes a continuous control set model predictive control (CCS-MPC) for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> -based grid-tied inverters. The proposed controller has inherent robustness against <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> resonance and does not need an active damping loop. The controller is designed in the synchronous reference frame where the variables are dc quantified. Otherwise, it can generate a steady-state offset in the stationary frame. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> model, which is needed for the CCS-MPC design, shows a strong cross-coupling between the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> axes, and the order of the model is high. To deal with the cross-coupling, a multi-input multioutput CCS-MPC is designed, and to reduce the order, system identification is used to build the process model. The optimization of CCS-MPC is performed offline, and a low real-time computation is needed. Moreover, the controller’s output is applied by a modulator, and it operates with a fixed switching frequency. To guarantee the closed-loop stability, the controller parameters are selected by a sensitivity analysis. The simulation and experimental results are presented to validate the proposed controller’s appealing features.

Implementation of Continuous Control Set Model Predictive Control Method for PMSM on FPGA

The generalized predictive control (GPC-MPC) algorithm adopts an optimal control strategy, which requires online matrix inversion operation and is difficult to be applied to real-time control systems. Therefore, the permanent magnet synchronous motor (PMSM) drive experiments, using the GPC-MPC algorithm with constraints, are primarily performed in a simulation environment. This paper proposes a new matrix inversion and its circuit design method to complete the above experiments in an embedded environment. By using the calculation steps of matrix block decomposition and reinversion, the parallelism of matrix calculation and the regularity of storage address are improved, and the speed of matrix inversion is accelerated. Also, the model-based design (MBD) method is used to complete the design and verification of the rest of the algorithm, which speeds up the implementation and deployment of the algorithm. Finally, the GPC-MPC algorithm control experiments with current constraints are implemented on the Field programmable gate array (FPGA) experimental board. The experimental results show that the proposed design method has a good control effect and computational efficiency.

Low-Ripple Continuous Control Set Model Predictive Torque Control for Switched Reluctance Machines Based on Equivalent Linear SRM Model

In this article, a low-ripple continuous control set (CCS) model predictive torque control (MPTC) method for switched reluctance machines (SRMs) is proposed. The inherent high nonlinearity of the SRMs makes it difficult to solve the optimization problem in the CCS MPTC algorithm analytically. To address this issue, an equivalent linear SRM model is adopted, and the cost function is also properly modified. Then, with the torque boundary values provided by executing the voltage vectors of an improved switching table, the optimization problem in the CCS MPTC method becomes simple and analytically solvable. The Lagrange multiplier method is employed to solve this optimization problem analytically and generate the optimum torque reference values for the active phases. Based on the estimated torque variation rates, the duty cycles for each phase are calculated. Extensive simulation and experimental tests are carried out in a four-phase 8/6 SRM setup. These testing results reveal that the proposed CCS MPTC method shows much lower torque ripples and current ripples in a wide speed range with a low computational burden than the existing finite control set MPTC methods.

Continuous Model Predictive Control for the Direct Torque Control of a PM Synchronous Motor

This paper presents the application of the continuous model predictive control (C-MPC) for the direct torque control (DTC) of a permanent magnet synchronous motor (PMSM). The C-MPC is designed for the direct regulation of the components of the stator flux and the electromagnetic torque of the PMSM. A linear state-space model based on a feedback linearization of the PMSM is used to formulate the controller. The control signals are applied to the PMSM via a power inverter through a pulse width modulator (PWM). The proposed controller is formulated as a constrained optimization problem, where the voltage applied to the motor is selected as the control input and restricted to the power inverter's linear region. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

Optimal Tracking and Resonance Damping Design of Cascaded Modular Model Predictive Control for a Common-Mode Stabilized Grid-Tied $LCL$ Inverter

A cascaded modular model predictive control (MMPC) method is designed for a modified nonisolated <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$LCL$</tex-math></inline-formula> grid-connected inverters to provide resonance damping, improved dynamic performance, and leakage current attenuation capabilities. The continuous control set model predictive control strategy is applied for the proposed method. The active damping function of the inner loop MMPC is analyzed in detail to illustrate the mechanism of improving the system dynamic performance. The cascaded MMPC method is compared with the conventional proportional-integral (PI) control methods with/without a notch filter to show the merits in resonance damping and dynamic response. The optimal control parameters design procedure is elucidated with the tuning mechanism of the MMPC weighing factor and PI gain. With the proposed optimal MMPC design method, the dynamic performance of rising time and overshoot are improved compared to the conventional PI control methods with/without the notch filter. The simulation and experimental results verified the proposed control design method.

Continuous Set Model Predictive Control for Energy Management of Modular Multilevel Matrix Converters

The modular multilevel matrix converter (M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> C) is an ac to ac power converter composed of 9 arms and is proposed for high power applications such as motor drive and wind energy conversion systems. Energy Control of the M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> C is achieved using four circulating currents, and is frequently divided into the different frequency mode (DFM) and equal frequency mode (EFM). EFM is more challenging, because of the larger capacitor voltage oscillations that can be produced. The control schemes are typically different for EFM/DFM operation and this further increases the complexity. In this article, a continuous-control-set model predictive control for energy management of the M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> C is proposed. The control scheme is based on solving an equality constrained quadratic programming problem, where the optimal solution is analytically obtained. The result is a single and simple control law to obtain the circulating current references, where good performance is achieved for both EFM and DFM. The proposed strategy is experimentally validated using a scaled-down M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> C prototype composed of 27 power cells.

Fast Solver for Implicit Continuous Set Model Predictive Control of Electric Drives

This paper proposes a fast and accurate solver for implicit Continuous Set Model Predictive Control for the current control loop of synchronous motor drives with input constraints, allowing for reaching the maximum voltage feasible set. The related control problem requires an iterative solver to find the optimal solution. The real-time certification of the algorithm is of paramount importance to move the technology toward industrial-scale applications. A relevant feature of the proposed solver is that the total number of operations can be computed in the worst-case scenario. Thus, the maximum computational time is known a priori. The solver is deeply illustrated, showing its feasibility for real-time applications in the microseconds range by means of experimental tests. The proposed method outperforms general-purpose algorithms in terms of computation time, while keeping the same accuracy.

Robust Continuous Model Predictive Speed and Current Control for PMSM With Adaptive Integral Sliding-Mode Approach

Model predictive control has been considered as a potential alternative method in electrical drives. High reliable predictive model design is a research hotspot. To further improve the performance, a robust continuous model predictive speed and current control for PMSM with an adaptive integral sliding-mode approach are put forward. The prediction model is directly derived from the integral slinging-mode surface. By using the self-regulation method control and the amplitude of the sliding-mode function, an adaptive integral sliding-mode predictive control (AISMPC) is designed. The proposed strategy solves the chattering problem of sliding-mode control and improves the dynamics of the system. AISMPC has been carried out on a digital signal processing hardware system. The experimental results validate the excellent tracking performance of the proposed strategy.