Traditional Model Predictive Control Research Articles

A Variable Horizon Model Predictive Control for Magnetorheological Semi-Active Suspension with Air Springs

To improve the characteristics of traditional model predictive control (MPC) semi-active suspension that cannot achieve the optimal suspension control effect under different conditions, a variable horizon model predictive control (VHMPC) method is devised for magnetorheological semi-active suspension with air springs. Mathematical models are established for the magnetorheological dampers and air springs. Based on the improved hyperbolic tangent model, a forward model is established for the magnetorheological damper. The adaptive fuzzy neural network method is used to establish the inverse model of the magnetorheological damper. The relationship between different road excitation frequencies and the control effect of magnetorheological semi-active suspension with air springs is simulated, and the optimal prediction horizons under different conditions are obtained. The VHMPC method is designed to automatically switch the predictive horizon according to the road surface excitation frequency. The results demonstrate that under mixed conditions, compared with the traditional MPC, the VHMPC can improve the smoothness of the suspension by 2.614% and reduce the positive and negative peaks of the vertical vibration acceleration by 11.849% and 6.938%, respectively. Under variable speed road conditions, VHMPC improved the sprung mass acceleration, dynamic tire deformation, and suspension deflection by 7.191%, 7.936%, and 22.222%, respectively, compared to MPC.

A Fractional-Order Model Predictive Control Strategy with Takagi–Sugeno Fuzzy Optimization for Vehicle Active Suspension System

Aiming at the problem of system controller performance failure caused by improperly setting the value of each weighting coefficient of the model predictive control (MPC), a fractional-order MPC strategy with Takagi–Sugeno fuzzy optimization (T–SFO MPC) is proposed for a vehicle active suspension system. Firstly, the fractional-order model predictive control framework for active suspension systems is designed based on a 1/4 vehicle model. Then, we analyze the influence of different weighting coefficients on the suspension performance and introduce the Takagi–Sugeno fuzzy optimization theory to adaptively adjust the weighting coefficients of the fractional-order MPC controller. Finally, the system responses of the T–SFO MPC, traditional MPC, linear quadratic regulator (LQR), and passive suspension control are numerically analyzed under various road conditions. Simulation results show that suspension response with the T–SFO MPC is significantly improved compared with passive suspension control, traditional MPC control, and LQR control, and the weight coefficients of the T–SFO MPC can be adaptively adjusted according to the dynamic changes of suspension response. Compared with passive suspension, the root mean square (RMS) value of the vertical acceleration of the T–SFO MPC under various roads decreased by a maximum of 37.97%, and the RMS value of suspension dynamic deflection and tire dynamic load decreased by a maximum of 32.94% and 37.8%, respectively. These results validate that the proposed control method can achieve coordinated optimization of vehicle comfort and handling stability.

Research on an improved deadbeat model predictive current control of double three-phase open-winding permanent magnet motor

Model predictive current control has high control accuracy and good control performance, and has been widely applied in the control strategy of dual three-phase permanent magnet synchronous motors. This article proposes an improved deadbeat model predictive current control (DMPCC) method by analyzing the mathematical model of a dual three-phase open-winding permanent magnet synchronous motor. One inverter predicts and calculates the optimal voltage vector through the deadbeat model, while the other inverter calculates the optimal voltage vector through the value function rolling optimization. This method reduces the computational workload of the controller, avoids the delay problem of the traditional model predictive current control (MPCC) method, improves the system's response speed, effectively suppresses the current in the harmonic sub-plane, and reduces torque ripple. The simulation results have verified the accuracy and speed of the above control method.

Adaptive MPC path-tracking controller based on reinforcement learning and preview-based PID controller

Path-tracking control is a crucial process for autonomous vehicles, ensuring that the vehicle drives safely along the reference path, and the suitable controller parameters ensure the accuracy and stability of this process. To enhance the adaptability of traditional path-tracking controller parameters, this paper proposes an adaptive model predictive control (MPC) controller based on a preview-based PID controller and deep deterministic policy gradient (DDPG) algorithm to achieve adaptive tuning of the controller parameters. Starting with the design of the dynamics tracking error model of the vehicle and the MPC controller. Based on the actor-critic reinforcement learning architecture, the DDPG agent is designed to tune the prediction horizon and weight matrix of the MPC controller. A preview-based PID controller is proposed to improve the efficiency and stability of reinforcement learning and compensate for the error in vehicle modeling. The improved algorithm performance is verified through the simulation scenarios of high-speed lane changing and accelerated overtaking scenarios constructed by MATLAB/Simulink. The results show that the improved algorithm significantly improves the adaptive ability of the traditional MPC controller to time-varying conditions and achieves higher tracking accuracy and stability.

Lateral-Stability-Oriented Path-Tracking Control Design for Four-Wheel Independent Drive Autonomous Vehicles with Tire Dynamic Characteristics under Extreme Conditions

This paper proposes a lateral-stability-oriented path-tracking controller for four-wheel independent drive (4WID) autonomous vehicles. The proposed controller aims to maintain vehicle stability under extreme conditions while minimizing lateral deviation. Firstly, a tiered control framework comprising upper-level and lower-level controllers is introduced. The upper-level controller is a lateral stability path-tracking controller that incorporates tire dynamic characteristics, developed using model predictive control (MPC) theory. This controller dynamically updates the tire lateral force constraints in real time to account for variations in tire dynamics under extreme conditions. Additionally, it enhances lateral stability and reduces path-tracking errors by applying additional yaw torque based on minimum tire utilization. The lower-level controllers execute the required steering angles and yaw moments through the appropriate component equipment and torque distribution. The joint simulation results from CarSim and MATLAB/Simulink show that, compared to the traditional MPC controller with unstable sideslip, this controller can maintain vehicle lateral stability under extreme conditions. Compared to the MPC controller, which only considers lateral force constraints, this controller can significantly reduce lateral tracking errors, with an average yaw rate reduction of 31.62% and an average sideslip angle reduction of 40.21%.

Fixed Switching Frequency Model Predictive Control and Passivity Based Control for DC-DC Converter

The DC-DC converter represents a crucial component in the renewable energy sources. The stability and dynamic capability enhancement of the DC/DC converter have emerged as a significant research topic in the current era. Model predictive control (MPC) is particularly prevalent due to its high dynamic response speed, simplicity of the controller design, and capacity for multi-objective optimization. However, the traditional finite control set model predictive control (FCS-MPC) method is suffer to variable switching frequency and vast computing. To improve the dynamic performance of the converter, a novel nonlinear control strategy named fixed switching frequency MPC and passivity-based control (PBC), named FSFPBMPC, is proposed, which could achieve fixed switching frequency and enhance the system's dynamic response speed. Firstly, the Euler-Lagrange (EL) model of the boost converter is established. Secondly, the relationship between duty cycle and MPC is established. Ultimately, the output voltage of PBC is incorporated into the cost function of the FCS-MPC. The characteristics of PBC power shaping and damping injection can enhance the system's immunity to interference, improve the system's dynamic response speed, and thus reinforce the system's stability. Then, depending on MATLAB, the simulation results proved that the proposed strategy has the same effect as we expected.

Self-triggered MPC with adaptive prediction horizon for nano-satellite attitude control system

Nano-satellites are essential tools for various applications, including scientific experiments, deep space exploration and astronomical observation. Achieving precise model predictions is crucial for their successful operation. To address the intricate constraints of nano-satellites and enhance control performance, the Model Predictive Control (MPC) algorithm is an effective solution. However, implementing an MPC-based attitude control system in actual engineering scenarios presents significant challenges, primarily due to the substantial computational burden, especially given the limited onboard computing resources of nano-satellites. In this paper, we introduce a modified adaptive self-triggered model predictive control (ST-MPC) algorithm designed to stabilize the attitude of nano-satellites, while simultaneously reducing communication and computational overhead compared to traditional MPC methods. The proposed self-triggered mechanism dynamically determines the next trigger time according to the system state. Moreover, we incorporate considerations for the efficiency of actuators to address the constraints imposed by the magnetic torque characteristics within the modified self-triggered mechanism. Additionally, a strategy for adaptive prediction horizon is proposed to balance computation load and control accuracy. The results of our simulations demonstrate the effectiveness of the modified ST-MPC algorithm in comparison to both traditional MPC and standard ST-MPC approaches. This algorithm may have the potential to significantly impact attitude control applications for nano-satellites.

Vehicle platoon safety considering the vehicle cut-in: A coupled reinforcement learning and model predictive control approach

A longitudinal platoon control method based on Twin Delayed Deep Deterministic Policy Gradient (TD3) and Model Predictive Control (MPC) is proposed to solve the problems of low following efficiency and system instability in longitudinal platoon control. Firstly, Dynamic Bayesian Network (DBN) and Long Short-Term Memory (LSTM) network are introduced to identify the driving behavior of bystanders and derive the MPC objective constraint function containing three indicators of following, comfort and fuel consumption according to the platoon dynamics equation. Secondly, the system prediction model and cost function are introduced into the action-critic network of TD3 to solve the problem of no model training in the traditional TD3 algorithm and to speed up the training speed and accuracy of the network. On this basis, a Bellman equation is proposed to calculate the time-domain difference error and the expected loss function to solve the TD3 network overestimation problem. Finally, the joint simulation platform is built to simulate the platoon driving conditions and compare with the DDPG optimization algorithm and the traditional MPC algorithm respectively. The results show that the improved TD3-MPC algorithm satisfies the constraints and the spacing error is controlled within 0.3 m, and the vehicle speed changes more smoothly in the scenario of speed fluctuation in the front vehicle, and the ride comfort of the platoon is improved, and it has better robustness in the scenario of vehicle cut-in. The experimental results show that when the vehicle speeds are 20, 40, and 60 km/h, compared to MPC, the average spacing errors are reduced by 27.56%, 25.64%, and 28.04%, respectively, and compared to DDPG-MPC, the average spacing errors are reduced by 6.59%, 8.77%, and 7.86%, respectively.

Weightless Model Predictive Control for Permanent Magnet Synchronous Motors with Extended State Observer

Traditional model predictive torque control (MPTC) predicts the torque and flux values for the next time step and selects the voltage vector that minimizes the cost function as the optimal vector to apply to the inverter. This control approach is straightforward and allows for multi-objective control, but it has some issues in terms of the dynamic steady-state performance and parameter robustness. Therefore, this paper proposes a weightless model predictive control method based on an extended state observer (ESO). By designing an improved ESO to observe and compensate for motor parameter disturbances in real time, and employing a novel 2-D switching table and voltage vector sector selection diagram, the method evaluates three out of eight voltage vectors based on the torque and stator flux error signals. This reduces the computational load while increasing the number of candidate voltage vectors. Finally, a cost function without weighting factors is designed to lower the computational complexity. The simulation results show that the proposed new control method effectively reduces the torque and flux ripple and improves the current waveform compared to traditional MPTC.

A multi-layer predictive energy management strategy for intelligent hybrid electric trucks collaborated with eco-driving control

Nowadays, hybrid electric trucks (HETs) are also urgently expected to further enhance energy efficiency with the development of intelligent driving system. A multi-layer predictive energy management strategy is designed for intelligent parallel HET to enhance fuel economy and computational efficiency. Depending on intelligently implementation of traffic prediction with navigation data, an online smart battery SOC generation is proposed to obtain an approximately global optimal SOC reference trajectory in the upper layer. In the bottom controller, a novel method, the tolerant sequential model predictive control (MPC) collaborated with sampling strategy, could achieve eco-driving in consideration of both driving comfort and safety with less computation time in autonomous driving scenario. Moreover, to simultaneously accomplish fuel economy and decrease computational burden, the integrated equivalent consumption minimization strategy with dynamic programming (ECMS-DP) solver for MPC scheme is presented to frozen SOC state and jointly control torque distribution and gear action. Numerical simulations demonstrate that the proposed multi-layer strategy has improved over 20 % fuel economy and decreased almost 50 % computational burden relative to traditional MPC benchmark strategy, which could exhibit great effectiveness and potential for practical implementation in real driving routes.

Research on ground mobile robot trajectory tracking control based on MPC and ANFIS

This study focuses on the control strategy for a ground mobile robot (GMR) with independent three-axis six-wheel drive and four-wheel independent steering, performing double lane change trajectory tracking in complex scenarios. Initially, a dynamic model of the six-wheel independent drive and steering GMR was constructed. Utilizing Model Predictive Control (MPC) technology, the challenge of trajectory tracking at low speeds was effectively addressed. For high-speed conditions, by thoroughly analyzing the impact of the predictive time-domain, this study innovatively introduced an Adaptive Neuro-Fuzzy Inference System (ANFIS) to dynamically adjust the prediction horizon of the MPC. A novel trajectory tracking algorithm integrating MPC and ANFIS was developed, with the network structure being trained using backpropagation (BP) method and the least squares method. Compared to traditional MPC, this hybrid strategy significantly improves trajectory tracking accuracy and stability at high speeds, with computational efficiency increased by 48.65%. Additionally, the algorithm demonstrated excellent adaptability and control effectiveness in various rigorous tests, including different speed levels, complex steering paths, load changes, sudden obstacles, and variable terrain. A 70 km/h trajectory tracking experiment on a physical vehicle yielded a root mean square (RMS) error of 0.1904 m, verifying its superior tracking performance and practical reliability. This provides a pioneering solution for high-performance trajectory control of ground mobile robots.

Improved Model-Free Predictive Control of a Three-Phase Inverter

Model predictive control (MPC) performance depends on the accuracy of the system model. Moreover, the optimization algorithm of MPC requires numerous online computations. These inherent limitations of MPC hinder its application in power electronics systems. This paper proposes a two-part solution for these challenges for a three-phase inverter with an output LC filter. The first part of the control scheme is a linear and modified model-free approach based on the auto-regressive structure (ARX) with exogenous input. The second part is the computationally efficient optimization algorithm based on the active set method to solve the optimization problem of the MFPC. The objective of the control scheme is to regulate the output voltages of the inverter in the presence of constraints. The constraints are the maximum admissible filter current and optimal duty cycle to avoid any damage to the system. To validate the performance of the proposed control scheme, simulations and hardware-in-loop (HIL) real-time investigations have been performed, comparing the results of the proposed approach with the model-based predictive control. The results showcase the computational efficiency and effectiveness of the MFPC approach, demonstrating its potential for overcoming the limitations of traditional MPC in power electronics systems.

MPC-Based Asynchronous Attack Tolerant Control for Uncertain Markov Jump Cyber-Physical Systems.

The model predictive control (MPC)-based asynchronous attack tolerant control scheme is investigated in this article for uncertain Markov jump cyber-physical systems (MJCPSs) under the Denial-of-Service (DoS) attack. To tackle the problem of the system running mode may not be observed in the control center, an asynchronous model predictive controller is proposed. Specifically, a dynamic controller, which can tune the performance online, is designed besides a traditional state feedback one. Even though such a combination may cause possible degradation of system performance, it can expand the initial feasible region and relieve the online computation burden efficiently. In addition, a decision variable is introduced to alleviate limitations on the feasible region generated by the constraints in the traditional MPC method. A series of solvable optimal problems are further constructed to achieve the desired performances. Finally, an application of the proposed method is given to demonstrate its effectiveness.

Enhanced three-dimensional trajectory tracking control for AUVs in variable operating conditions using FMPC-FTTSMC

In addressing the variable operating conditions encountered in complex underwater tasks, an enhanced three-dimensional tracking control method is proposed for autonomous underwater vehicle (AUV) based on fuzzy model predictive control-finite time terminal sliding mode control (FMPC-FTTSMC). Firstly, to enhance adaptability to tasks and environments, fuzzy model predictive control method is designed to achieve precise three-dimensional trajectory tracking. Additionally, a fuzzy weight allocator is employed to enable AUV to autonomously adjust optimization strategies based on real-time states such as task type, speed, and distance from the seabed, thus better coping with changing conditions and improving the universality of the control method. Secondly, a dynamic controller is designed using the finite-time terminal sliding mode control method, combined with a finite-time radial basis function neural network (FTRBFNN) disturbance observer to accurately estimate disturbances. Finally, simulation results demonstrate that the proposed method effectively reduces optimization solving time compared to traditional model predictive control, achieves trajectory tracking control under various conditions, meets preset state constraints, and demonstrates excellent tracking accuracy and robustness.

Switching Current Predictive Control of a Permanent Magnet Synchronous Motor Based on the Exponential Moving Average Algorithm

To improve the dynamic and steady-state control performance of permanent magnet synchronous motors under the three-vector model predictive current control method, this study proposes a switching current predictive control method based on the exponential moving average algorithm, which evaluates the magnitude of the change of the q-axis current slope in real time to discriminate the motor’s operating conditions and selects the optimal control method for different operating conditions. Meanwhile, the traditional three-vector model predictive current control method is improved by introducing a comparison mechanism for the q-axis current slope to select the second effective voltage vector, avoiding the secondary optimization calculation of the value function and reducing the computational complexity of the traditional method. By comparing the proposed method with the traditional three-vector model predictive current control method, the experimental results prove that the proposed method improves the system’s dynamic response and steady-state performance.

A Wind Power Fluctuation Smoothing Control Strategy for Energy Storage Systems Considering the State of Charge

With the significant increase in the scale of energy storage configuration in wind farms, improving the smoothing capability and utilization of energy storage has become a key focus. Therefore, a wind power fluctuation smoothing control strategy is proposed for battery energy storage systems (BESSs), considering the state of charge (SOC). First, a BESS smoothing wind power fluctuation system model based on model predictive control (MPC) is constructed. The objective function aims to minimize the deviation of grid-connected power from the target power and the deviation of the BESS’s remaining capacity from the ideal value by comprehensively considering the smoothing effect and the SOC. Second, when the wind power’s grid-connected power exceeds the allowable fluctuation value, the weight coefficients in the objective function are adjusted in real time using the first layer of fuzzy control rules combined with SOC partitioning. This approach smooths wind power fluctuations while preventing overcharging and overdischarging of the BESS. When the grid-connected power is within the allowable fluctuation range, the charging and discharging power of the BESS is further refined using a second layer of fuzzy control rules. This enhances the BESS’s capability and utilization for smoothing future wind power fluctuations by preemptively charging and discharging. Finally, the proposed control strategy is simulated using MATLAB R2021b with actual operational data from a wind farm as a case study. Compared to the traditional MPC control method, the simulation results demonstrate that the proposed method effectively controls the SOC within a reasonable range, prevents the SOC from entering the dead zone, and enhances the BESS’s ability to smooth wind power fluctuations.

Neural network model predictive control of core power of Qinshan nuclear power plant based on reinforcement learning

The power change of Pressurized water reactors (PWRs) is a highly complex nonlinear coupling process, which requires the power controller to have a high nonlinear control capability. Since the traditional model predictive control (MPC) algorithm has the problems of insufficient robustness and adaptivity, this study proposes a neural network-based neural network model predictive control method based on model predictive control and optimizes its control parameters in real time by using the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm. The designed control method is validated on the simulation model of the Qinshan nuclear power plant (NPP). Simulation results show that the proposed control method can realize effective control of power under a variety of power changing conditions and dynamic adjustment of control parameters.

Trajectory tracking control of a flexible air-breathing hypersonic vehicle using Lyapunov-based model predictive control

Considering the constraints of inputs and angle of attack (AOA), the trajectory tracking control of a flexible air-breathing hypersonic vehicle (FAHV) is investigated. To solve the problem, the Lyapunov-based model predictive control (LMPC) is presented. Firstly, the virtual controller is designed by nonlinear backstepping control (BSC), and it is integrated into the Lyapunov contraction constraint in LMPC to ensure the stability of the closed-loop system. Secondly, LMPC law is obtained by optimizing the weighted summation performance index of the tracking error and the control. Within the LMPC framework, the input constraints and AOA constraints can be handled simply, and by designing the appropriate parameters of the virtual controller, closed-loop stability is achieved. The effectiveness and superiority of the proposed method are verified by comparing it with the BSC and traditional model predictive control.

Model predictive-based DNN control model for automated steering deployed on FPGA using an automatic IP generator tool

With the increase in the non-linearity and complexity of the driving system’s environment, developing and optimizing related applications is becoming more crucial and remains an open challenge for researchers and automotive companies alike. Model predictive control (MPC) is a well-known classic control strategy used to solve online optimization problems. MPC is computationally expensive and resource-consuming. Recently, machine learning has become an effective alternative to classical control systems. This paper provides a developed deep neural network (DNN)-based control strategy for automated steering deployed on FPGA. The DNN model was designed and trained based on the behavior of the traditional MPC controller. The performance of the DNN model is evaluated compared to the performance of the designed MPC which already proved its merit in automated driving task. A new automatic intellectual property generator based on the Xilinx system generator (XSG) has been developed, not only to perform the deployment but also to optimize it. The performance was evaluated based on the ability of the controllers to drive the lateral deviation and yaw angle of the vehicle to be as close as possible to zero. The DNN model was implemented on FPGA using two different data types, fixed-point and floating-point, in order to evaluate the efficiency in the terms of performance and resource consumption. The obtained results show that the suggested DNN model provided a satisfactory performance and successfully imitated the behavior of the traditional MPC with a very small root mean square error (RMSE = 0.011228 rad). Additionally, the results show that the deployments using fixed-point data greatly reduced resource consumption compared to the floating-point data type while maintaining satisfactory performance and meeting the safety conditions

Personalized driving behavior oriented autonomous vehicle control for typical traffic situations

autonomous driving systems not only provide services for human drivers, but also need to consider the personalized driving requirements of human beings. In current road traffic environments, the driving behaviors of drivers differ significantly. This suggests that the various needs of different drivers cannot be met by a single behavior mode in an autonomous driving decision-making system. This paper looks at the personalized characteristics of various drivers and considers the implications of their differences. First, a Proportional Integral Differential (PID) feedback channel is introduced in a traditional Model Predictive Control (MPC) to improve the performance of the controller, and comprehensively considering the collision risk, motion hysteresis and rule constraints, referring to the MPC idea, a collision avoidance method based on Q-ABSAS optimization is proposed. Then based on the Chance Constrained Programming, the control constraint is combined with driver personalization to reflect a variety of driving personality characteristics. Finally, the proposed method is tested using Hardware-in-the-loop (HIL) experiments. The experiment results demonstrate that the proposed method can successfully implement vehicle tracking control and make the vehicle's state of movement match the driver's expectations, which can increase driver comfort and driving safety.