Model Predictive Control Research Articles

Degradation Diagnosis and Control Strategy for a Diesel Hybrid Powertrain Considering State of Health

Hybrid electric vehicles (HEV) are a practical choice for energy saving in the transportation field. Degradation diagnosis (DD) is one of the main methods to guarantee system robustness. However, the classical DD methods cannot meet the requirements of HEV due to their system complexity. In this study, a novel Prognostics and Health Management (PHM) study was conducted to face these challenges. Firstly, a physical P2 HEV model with a rule-based controller was built, and its diesel engine sub-model was simplified by a neural network (NN) to ensure real-time performance of the degradation prognostics. Secondly, a degradation prognostics method based on gray relation analysis–principal component analysis (GRA-PCA) was illustrated, which could confirm degradation 2 s after the health index fell below the threshold. Finally, a degradation tolerance strategy based on long short term memory–model predictive control (LSTM-MPC) was performed to optimize vehicle speed tracing with minimal energy consumption and was validated by three cases. The result shows that the energy consumption stayed nearly unchanged for the engine degradation case. For the battery degradation case, the tracing error was reduced by 11.7% with 4.3% more energy consumption. For combined degradation, the strategy achieved a 12.3% tracing error reduction with 3.7% more energy consumption. The suggested PHM method guaranteed vehicle power performance under degradation situations.

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.

Optimization of Hybrid Energy Systems Based on MPC-LSTM-KAN: A Case Study of a High-Altitude Wind Energy Work Umbrella Control System

This paper presents an optimization method for hybrid energy systems based on Model Predictive Control (MPC), Long Short-Term Memory (LSTM) networks, and Kolmogorov–Arnold Networks (KANs). The proposed method is applied to a high-altitude wind energy work umbrella control system, where it aims to enhance the stability and efficiency of energy utilization. The work umbrella system integrates wind and solar energy sources, with energy stored in a battery and used to control the umbrella’s operations. The MPC framework is employed to optimize control actions by solving a finite-horizon optimization problem, ensuring the battery State of Charge (SOC) remains within an optimal range. The LSTM network provides accurate predictions of environmental conditions, including wind speed and solar irradiance, which are essential for MPC’s decision-making process. To address complex nonlinearities in the system, the KAN is utilized to model and approximate these dynamics, refining the LSTM predictions. The integration of these advanced control strategies enables the system to handle varying operational conditions and maintain optimal performance. The case study demonstrates the effectiveness of the MPC-LSTM-KAN approach, revealing improvements in the SOC stability, energy efficiency, and operational endurance of the high-altitude wind energy work umbrella system. The results indicate that this hybrid optimization method offers a robust solution for managing hybrid energy systems in dynamic environments.

Double-pancake superconducting coil integrated with DFIG-based wind power systems under voltage-dip events: Design and performance analysis study

The doubly fed induction generator (DFIG)-based wind turbine provides massive development in power generation. Uncertain power oscillations and voltage-dip events affect the stability of the DFIG. To mitigate the effect of voltage-dips in short period, superconducting magnetic energy storage (SMES), which possess rapid energy exchange and high power density, is integrated with large-scale renewable power systems. SMES is integrated at the DC link of the DFIG to ensure the power balance and fault ride-through (FRT) capability. During this operation, frequent current changes occur in the high-temperature superconducting (HTS) coil, which leads to an increase in AC losses. As a remedy, an additional power converter structure controlled with a model-predictive controller (MPC) is proposed. Firstly, a scale-down HTS double-pancake coil model is designed using a finite element model by which transport current loss and magnetic field formulation are studied. Additionally, the critical coil current is also verified through experimental studies. The effectiveness of the proposed MPC-based SMES integrated DFIG on DC link voltage and grid current under IEC-61000-4-11 standard, symmetrical and asymmetrical voltage-dip cases are investigated. The obtained results demonstrate that the proposed system effectively reduces transients in DC link voltage and improves the FRT capabilities of the grid.

Integrated automatic parking path planning and trajectory tracking optimization method

Current automatic parking systems often separate path planning and trajectory tracking, increasing complexity and failing to meet the parking needs of autonomous cars. Consequently, this study presents an approach based on Multi-stage Nonlinear Model Predictive Control (MSNMPC) for integrated autonomous parking path planning and trajectory tracking optimization. The method represents the evolution of uncertainty parameters over time through a scenario tree, and the MSNMPC controller with a predictive horizon P defines P + 1 phases, each with specific cost and constraint functions that depend only on the vehicle state and control inputs of that phase to satisfy the constraints of all phases of the parking process. In addition, the method integrates path planning and tracking control into one optimization problem, which is solved online to achieve integrated parking control. Simulation confirms that, in comparison to MPC with RRT* hierarchical control, the integrated parking scheme of MSNMPC has less lateral error and offers superior flexibility and tracking performance. To verify the generality of the scheme, it was validated in the diagonal parking scenario and the vertical parking scenario, respectively. The results show that, compared to the control experiments, the parking elapsed time has been reduced by 10.76% and 9.02%, respectively, enhancing parking efficiency. In addition, the parking error has decreased by 30.77% and 38.46%, respectively, thus improving parking accuracy. Moreover, the minimum safe distance in the control scheme for addressing uncertainty factors is 0.7 m greater than that of the control experiments, meeting the driving requirements for driverless vehicles in parking scenarios.

The role of automated surface water distribution systems in energy-saving agriculture: A case study from central Iran’s Arid Plateau

Study regionThe NekooAbad Irrigation District in central Iran faces challenges due to inefficient surface water distribution. 82 million m3 of groundwater is extracted annually from 15,000 tube-wells, leading to decreased groundwater levels and increased energy consumption of 234 million kWh per year. Study focusThis study explores implementing automation in surface water distribution to reduce groundwater extraction and conserve energy. A hydraulic simulation model and a centralized Model Predictive Control approach were used to analyze the existing system and propose a recovery plan. The potential impact of automated surface water distribution on reducing groundwater extraction and energy conservation was evaluated through spatial assessment in GIS. New hydrological insights for the regionThe results demonstrate that the introduction of automation can significantly improve surface water distribution and, accordingly, groundwater overexploitation and, consequently, energy conservation, particularly during water scarcity. Energy conservation increased by 42.3 %, 54.8 %, 56.2 %, and 57.7 % under normal conditions, with water shortages of less than 10 %, 10–15 %, and 15–20 %, respectively. However, as the surface water shortages intensified, the energy conservation rates decreased to 57.7 %, 43.7 %, 25.4 %, and 18.9 % for normal conditions, water shortages of 15–20 %, 20–30 %, 30–40 %, and over 40 %, respectively. The automation introduction effectively provided reliable surface water resources, prompting farmers to shut down pumping stations or reduce working hours. Even in extreme scenarios, the project achieved up to 18.9 % energy savings.

A Hybrid Multiobjective Control Strategy Based on Combination of Modulated Model Predictive Control and Phase‐Shifted Modulation for a Unidirectional Five‐Level Rectifier

ABSTRACTThe unidirectional multilevel rectifier has immense potential in high‐power medium‐voltage industrial applications. This paper proposes a multiobjective control method based on the combination of optimal‐vector‐pair modulated model predictive control (OVP‐M2PC) and a phase‐shifted modulation strategy for a unidirectional five‐level rectifier. This strategy takes both of the inductor current tracking and capacitor voltage balancing as the control objectives. First, an optimal vector pair is determined based on the AC‐side current variation rate, and then, through combining the calculated action duration of OVP with carrier phase‐shifted modulation, inductor current tracking is achieved. Second, capacitor voltage balancing control is carried out by compensating for the duty cycles which also decouples the input current tracking and output capacitor voltage balance control. Compared with traditional FCS‐MPC, under the proposed control strategy, complex cost function calculation and weighting factor tuning are not required, which much reduced computational burden. Multiobjective control is achieved with better performance in both steady‐state and dynamic conditions. The superiority of the proposed strategy over traditional FCS‐MPC are validated through simulations and hardware experiments.

Fast Nonlinear Model Predictive Control Combining Online Trajectory Optimization and Value Function Regression

ABSTRACTModel predictive control (MPC) is a well‐developed method capable of handling complex control tasks. Implementation of an MPC requires solution of a deterministic finite horizon nonlinear optimal control (OC) problem. OC problems can be solved globally, explicitly expressing the optimal policy (and value function) as a function of the present state, or, locally, using online trajectory optimization, generating a solution that is only valid for the present state. For nonlinear problems however, neither is possible analytically, and the latter, finding a local solution online, is usually preferred. The difficulty with online trajectory optimization is that the solution must be available within a single sampling period. The main parameter affecting the computational demand of MPC is the length of the prediction horizon. The goal in this work is to reduce the length of the prediction horizon of a model predictive controller (MPC) to reduce computation time whilst preserving optimality guarantees. To this end, we propose approximation of the trajectory optimization problem for MPC by learning a finite horizon value function. The approximated value function is inserted into a truncated trajectory optimization problem so that the MPC can be attained with a reduced prediction horizon, ergo reduced computational load. By sampling the value function in a goal oriented way, we show that an effective approximate value function can be found by including both the function value and the gradients of the value function. The result is an accurate approximate MPC which leverages learning methodologies to reduce computational cost while still accounting for constraints.

Fuel Efficiency Optimization in Adaptive Cruise Control: A Comparative Study of Model Predictive Control-Based Approaches

This work investigates the fuel efficiency potential of Adaptive Cruise Control (ACC) systems, focusing on two optimization-based control approaches for internal combustion engine (ICE) vehicles. In particular, this study compares two model predictive control (MPC) designs. In the first approach, a strictly quadratic cost is adopted, and fuel consumption is indirectly minimized by adjusting the weights assigned to state tracking and control effort. In the second approach, a fuel consumption map is explicitly included in the MPC cost function, aiming to directly minimize it. Both approaches are compared to a globally optimal benchmark obtained with dynamic programming. Although these methods have been discussed in the literature, no systematic comparison of their relative performance has been conducted, which is the primary contribution of this article. The results demonstrate that, with proper tuning, the simpler quadratic approach can achieve comparable fuel savings to the approach with explicit fuel consumption minimization, with a maximum variation of 0.5%. These results imply that the first alternative is more suitable for online implementation, due to the more favorable characteristics of the associated optimization problem.

Model-based workflow for sustainable production of high-quality spirits in packed column stills

This study addresses water scarcity in Chilean distilleries by developing a model-based engineering workflow. Prolonged droughts, likely driven by global warming, have intensified this problem. The primary challenge is maintaining high-quality spirits while reducing cooling water and energy use during batch distillation in packed columns. This process was modeled using mass and energy balances, resulting in a system of partial differential algebraic equations (PDAE). Our workflow includes mechanistic modeling, disturbance modeling, multiobjective optimization, model predictive control, and Monte Carlo simulations. Our findings show that cooling water consumption can be reduced by up to 35 % and energy consumption by up to 14.4 % while maintaining product quality. The proposed system is robust against operational disturbances and model mismatch, ensuring consistent distillate quality. This research demonstrates the integration of model-based optimization and control strategies in batch distillation processes, which can be replicated in other fruit wine distillation processes for improved sustainability.

Online Learning‐Based Event‐Triggered Model Predictive Control With Shrinking Prediction Horizon for Perturbed Nonlinear Systems

ABSTRACTThis article proposes an online learning‐based event‐triggered model predictive control (OLEMPC) scheme for constrained nonlinear systems with state‐dependent uncertainties. The scheme incorporates both the nominal and the learned models to ensure favorable theoretical properties during online learning. A composite measurement‐triggering strategy is devised to reduce the number of state measurements as well as solving the optimization problems. This strategy attenuates the conservatism in measurement and triggering through combining the event‐ and self‐triggering approaches. By implementing the algorithm, both state measurement and triggering frequency further decrease with the online refinement of the prediction model, and the prediction horizon adaptively shrinks as the state approaches the terminal region. It is shown that the feasibility of the optimization problem and stability of the closed‐loop system are guaranteed. Simulation results verify the effectiveness of this scheme in ensuring closed‐loop performance and alleviating computational burden.

Path tracking with switchable stability constraints for vehicle collision avoidance based on extended stability region

There is a certain conflict between vehicle stability and the performance of path-tracking under emergency conditions. In this paper, to make full use of the lateral capacity of vehicles, a path tracking method with switchable stability constraints is proposed. First, using the Lyapunov energy equation and Hurwitz’s theorem, the lateral stability region (SR) and the critical steering angle of steady steering at different longitudinal speeds are calculated. Based on this, the extended stability region (ESR) and the extended critical steering angle of the vehicle under the control of an additional yaw moment are obtained. Furthermore, the driving area during collision avoidance is divided into unsafe and safe areas, and based on the model predictive control strategy, a path-tracking controller with switchable stability constraints is established. In the unsafe area, the vehicle states are allowed to break through the SR temporarily, and to ensure path-tracking accuracy, the ESR is taken as the stability constraint. In the safe area, the stability constraint is switched to the SR, and to make the vehicle states quickly return to SR, a regain stability controller is established. Finally, a Simulink-CarSim simulation and a hardware-in-the-loop (HIL) experiment are conducted. The simulation results show that a balance between tracking effect and vehicle stability can be effectively achieved through the proposed path-tracking system under the investigated emergency conditions. The real-time performance of the proposed control strategy is validated through the HIL experiment.

Model predictive control for polytopic uncertain systems with persistent bounded disturbances under long-distance transmission: a cooperation protocol-based approach

Model predictive control for polytopic uncertain systems with persistent bounded disturbances under long-distance transmission: a cooperation protocol-based approach

Vehicle height control of air suspension based on speed adaptive double-zone model prediction

The electronically controlled air suspension (ECAS) system improves the ride comfort and stability of the vehicle by adjusting the vehicle height. Due to the compressibility of air and the inertia of suspension, the ECAS system has the problem of excessive adjustment in the process of vehicle height adjustment, so that the solenoid valve is repeatedly opened and closed. Aiming at this problem, this paper proposes a new vehicle height control method based on speed adaptive double-zone model prediction control (AD-MPC), which realizes the adjustment of vehicle height with less operation of solenoid valve. Firstly, the single-wheeled air suspension is selected as the characteristic model and the spatial state equation is established. Then, the seeker optimization algorithm for the double-zone selection problem is designed to quickly find the best double-zone to obtain a double-zone function that can adapt to the speed. And then, the predictive control method based on AD-MPC is designed. Finally, the effectiveness and feasibility of the method are verified by simulation and experiment.

NMPC‐Based Control of Underactuated Spacecraft: A Neighboring Extremal Approach Extended to SE(3)

ABSTRACTThe present work revolves around employing the benefits of neighboring extremal approach in the nonlinear model predictive control of mechanical systems evolving on SE(3). In the NMPC process, necessary conditions of optimality are extracted based on some discrete‐time version of the equations of motion referred as LGVI and the obtained TPBVP equations are solved using simplified sensitivity derivatives by means of an indirect shooting method. Taking into consideration that the repetitive optimization process of the NMPC is time consuming, making its implementation challenging, a method of neighboring extremal is proposed here for recalculating the responses of the systems in scenarios that face some unexpected changes in their parameters or are encountering some last‐minute re‐planning schemes. Based on the existing responses of the system to the first set of initial conditions, the reaction of the system to the altered set of initial conditions can be reconstructed without the need to solve the whole optimization process from scratch by utilizing the features of the NE method. A spacecraft model evolving on SE(3) with actuation constraints confirms the efficiency of the whole process in term of accuracy versus computation burden. Forasmuch as actuator failure is a probable yet important event in aerial/spatial missions, the performance of the control system in dealing with such situations is examined. The algorithm robustness and its capability to compensate the effects of the actuator loss is checked.

An Improved Vehicle Path-Tracking Model Based on Adaptive Nonlinear Model Predictive Control via Online Big Bang—Big Crunch Algorithm and Artificial Neural Network

<div>In this article, a novel tuning approach is proposed to obtain the best weights of the discrete-time adaptive nonlinear model predictive controller (AN-MPC) with consideration of improved path-following performance of a vehicle at different speeds in the NATO double lane change (DLC) maneuvers. The proposed approach combines artificial neural network (ANN) and Big Bang–Big Crunch (BB–BC) algorithm in two stages. Initially, ANN is used to tune all AN-MPC weights online. Vehicle speed, lateral position, and yaw angle outputs from many simulations, performed with different AN-MPC weights, are used to train the ANN structure. In addition, set-point signals are used as inputs to the ANN. Later, the BB–BC algorithm is implemented to enhance the path-tracking performance. ANN outputs are selected as the initial center of mass in the first iteration of the BB–BC algorithm. To prevent control signal fluctuations, control and prediction horizons are kept constant during the simulations. The results showed that all AN-MPC weights are successfully tuned online and updated during the maneuvers, and the path-following performance of the ego vehicle is improved at different NATO DLC speeds using the proposed ANN + BB–BC, compared to the method where ANN is used only.</div>

State and parameter estimation of a dynamic froth flotation model using industrial data

This paper investigates an observable dynamic model of froth flotation circuits aimed at online state and parameter estimation and model-based control. The aim is to estimate the model states and parameters online from industrial data. However, in light of limitations in the plant data, additional model analysis is conducted. It is shown that without online compositional measurements, only the states and parameters of a reduced model can be estimated online. The reduced model lumps all recovery mechanisms into a single empirical equation. The reduced model is used to develop a moving horizon estimator (MHE) which is implemented on the industrial data. The state and parameter estimates from the MHE are used to evaluate the model prediction accuracy over a receding control horizon as would be done in model predictive control (MPC). Given the uncertainty of the available data, unmeasured disturbances and missing online measurements, the estimation and prediction results are reasonably accurate, at least in a qualitative sense. If accurate and reliable online measurements are available for estimation, the reduced model shows potential to be used for long-term model-based supervisory control of a flotation circuit.

Multi-agent distributed control of integrated process networks using an adaptive community detection approach

This paper focuses on developing an adaptive system decomposition approach for multi-agent distributed model predictive control (DMPC) of integrated process networks. The proposed system decomposition employs a refined spectral community detection method to construct an optimal distributed control framework based on the weighted graph representation of the state space process model. The resulting distributed architecture assigns controlled outputs and manipulated inputs to controller agents and delineates their interactions. The decomposition evolves as the process network undergoes various operating conditions, enabling adjustments in the distributed architecture and DMPC design. This adaptive architecture enhances the closed-loop performance and robustness of DMPC systems. The effectiveness of the multi-agent distributed control approach is investigated for a benchmark benzene alkylation process under two distinct operating conditions characterized by medium and low recycle ratios. Simulation results demonstrate that adaptive decompositions derived through spectral community detection, utilizing weighted graph representations, outperform the commonly employed unweighted hierarchical community detection-based system decompositions in terms of closed-loop performance and computational efficiency.

Model Predictive Current Control for Six-Phase PMSM with Steady-State Performance Improvement

The application of finite control set model predictive control (FCS-MPC) in six-phase permanent magnet synchronous motors (PMSMs) often faces a trade-off between computational burden and accurate voltage vector selection, as well as challenges related to harmonic components and torque generation. This paper introduces an improved model predictive current control (MPCC) method to address these problems. Firstly, 12 virtual voltage vectors are synthesized to improve torque output performance while suppressing harmonic currents. Then, to generate symmetrical switching signals and reduce switching loss, the largest basic vector used to synthesize the virtual vector is replaced by two medium vectors. Secondly, to solve the problem of the increased computational burden caused by the increase in discrete virtual vectors, a two-step vector selection method is proposed. In this method, each part is divided into several parts according to N, and the traditional cost function is also replaced by two-step functions. Different control performances can be achieved according to different values of N. Experimental results show that the proposed control scheme not only achieves stable current quality but also significantly improves steady-state performance throughout the entire speed range.

Milling chatter suppression based on the model predictive optimal control with Kalman state estimation

Milling chatter suppression based on the model predictive optimal control with Kalman state estimation