Nonlinear Model Predictive Control Research Articles

Nonlinear model predictive controller of hydrogenation of dimethyl oxalate for ethylene glycol production

Abstract Ethylene glycol (EG) is a valuable commodity organic intermediate that is produced using the catalyzed gas-phase hydrogenation process of dimethyl oxalate (DMO) from syngas. The reactor process is challenging to control because of its nonlinearity and multivariable condition. Thus, this study proposes the application of Neural Wiener model predictive control (NWMPC) for DMO hydrogenation reactor control. The application of empirical-based MPC, such as NWMPC, is still new in DMO hydrogenation reactor control. In order to simulate the process, the DMO hydrogenation reactor is modeled using Aspen Plus and Aspen Dynamic software. The Neural Wiener (NW) model is developed based on state space and neural network modeling using a Linear-Nonlinear (L-N) identification approach. A validation test is also performed to verify the accuracy of the NW model. Based on the test, the model accuracy is acceptable with the coefficient of determination (R2) of 0.965 for EG output mole fraction (first output) and R2 of 0.936 for product temperature (second output). The NWMPC capability is evaluated with a PID controller to handle a setpoint change in EG output mole fraction and reject disturbance in the feed stream flow rate. The control performance results have demonstrated the superior ability of the NWMPC to handle such scenarios better than PID in terms of controller action speed and profile.

Health-aware battery fast charging technique with zonal battery model using pulsed amplitude-width modulation and multi-step constant current constant voltage

ABSTRACT This article presents an innovative method for rapidly charging batteries while considering health factors. The strategy utilizes a closed-loop control approach based on a mathematical model. Initially, an intricate thermo-electric aging cell model (TEACM) was constructed based on electrochemical aging study. The model’s parameters are continuously updated in real-time by pulling data from the battery pack while it is being charged. The TEACM algorithm analyzes the parameter values and calculates different battery statuses. These estimations are then used to improve the charging process. The charge optimization phase optimizes the precharging and boosts charging processes individually. Several pulse precharging approaches have been analyzed, and by calculating the diffusion coefficient, the most effective precharging method has been identified. The use of multistage constant current technique is utilized to optimize the battery charging process. The optimization is accomplished by implementing the non-linear model predictive controller. Ultimately, the two refined charging methods are combined and sent to the charger. The hypothesis was validated using a cell cycling test bench. The acquired findings were compared with other recognized benchmark charging techniques, demonstrating that the suggested approach charges the cell in half the time compared to the 1C-CCCV charging methodology while also increasing the cycle life by 6.67%.

Ecological cooperative merging control of heterogeneous electric vehicle platoons.

Vehicle platooning improves energy savings via vehicle-to-vehicle (V2V) communication. Ecological cooperative adaptive cruise control (Eco-CACC) is implemented in platoons for merging task by using regrouped platoon models. The merging positions are selected in the middle and tail of an original platoon with a two-vehicle sub-platoon. The distributed nonlinear model predictive controller based on signal temporal logic (DNMPC-STL) approach is developed to model the Eco-CACC merging strategy. The performance of the Eco-CACC merging strategy is modeled by objective control for a predecessor-leader following (PLF) topology. The results demonstrate that merging positions located in the tail exhibit superior performance and can be used to improve stability, tracking performance, energy consumption efficiency and SOC of battery.

CNN-LSTM-Based Nonlinear Model Predictive Controller for Temperature Trajectory Tracking in a Batch Reactor

CNN-LSTM-Based Nonlinear Model Predictive Controller for Temperature Trajectory Tracking in a Batch Reactor

Bifurcation Analysis and Multiobjective Nonlinear Model Predictive Control of Sustainable Ecosystems

<i>Objective: </i>All optimal control work involving ecological models involves single objective optimization. In this work, we perform multiobjective nonlinear model predictive control (MNLMPC) in conjunction with bifurcation analysis on an ecosystem model. <i>Methods: </i>Bifurcation analysis was performed using the MATLAB software MATCONT while the multi-objective nonlinear model predictive control was performed by using the optimization language PYOMO. <i>Results: </i>Rigorous proof showing the existence of bifurcation (branch) points is presented along with computational validation. It is also demonstrated (both numerically and analytically) that the presence of the branch points was instrumental in obtaining the Utopia solution when the multiobjective nonlinear model prediction calculations were performed. <i>Conclusions: </i>The main conclusions of this work are that one can attain the utopia point in MNLMPC calculations because of the branch points that occur in the ecosystem model and the presence of the branch point can be proved analytically. The use of rigorous mathematics to enhance sustainability will be a significant step in encouraging sustainable development. The main practical implication of this work is that the strategies developed here can be used by all researchers involved in maximizing sustainability The future work will involve using these mathematical strategies to other ecosystem models and food chain models which will be a huge step in developing strategies to address problems involving nutrition.

Optimized multi-stage constant current fast charging protocol suppressing lithium plating for lithium-ion batteries using reduced order electrochemical-thermal-life model

Multi-stage Constant Current (MCC) is a state-of-the-art fast-charging protocol considering battery aging. It divides the charging process into multiple stages, each with a different current amplitude based on specific transition criteria, significantly influencing battery performance, such as charging time, degradation rate, and thermal effects. A key challenge in designing MCC protocols is addressing the lithium plating (LiP), which can accelerate degradation and pose a severe risk of thermal runaway. Since the LiP onset conditions vary between fresh and aged cells, this paper proposes an optimized MCC (O-MCC) charging protocol suppressing LiP based on the battery's state of health. To accurately simulate LiP conditions, different platforms of reduced-order electrochemical-thermal-life models are designed, compared, and optimized for speed and accuracy using a genetic algorithm, resulting in a 36.4 % reduction in computational time while maintaining the accuracy of the Pseudo Two-Dimensional model. The Nonlinear Model Predictive Control algorithm is then used to optimize the MCC protocol, minimizing charging time while preventing LiP throughout life. Experimental results show that O-MCC reduces charging time by 11.7 % and capacity loss by 59.4 %, enhancing battery safety. Additionally, O-MCCs with varying constraints are developed to meet specific demands and simulated at the battery pack level.

A NEW HYBRID OPTIMIZATION METHOD USED IN PREDICTIVE CONTROL OF A NONLINEAR FRACTIONAL MODEL BASED ON FRACTIONAL HAMMERSTEIN STRUCTURE

Fractional Hammerstein models represent various nonlinear processes, such as thermal and mechanical. Their major drawback is the non-convex optimization problem in a nonlinear model predictive control scheme due to its static nonlinearity. Indeed, an efficient optimization algorithm is needed. This work proposes a hybrid optimization algorithm combining the Nelder Mead optimization method and the Honey Badger one to synthesize a predictive control algorithm based on fractional Hammerstein models. As illustrated through simulation results, the proposed method offers clear improvements in convergence and tracking performances.

Attitude Control System for Quadrotor Using Robust Monte Carlo Model Predictive Control

Monte Carlo Model Predictive Control (MCMPC) is a kind of non-linear Model Predictive Control (MPC) that determines control inputs using the Monte Carlo method. The Monte Carlo method used in MCMPC can handle discontinuous phenomena, and there have been reports of its application in control systems for quadrotors, where the objective is to maintain the stability of the attitude during collisions. However, as with conventional MPC, concerns remain about control performance degradation due to modeling errors and external disturbances such as unexpected wind gusts. In this study, we propose a novel Robust Monte Carlo Model Predictive Control (RMCMPC), which improves the robustness of MCMPC by considering the hypersurface known from the Sliding Mode Control (SMC) theory. The proposed RMCMPC is applied to a quadrotor attitude control system, and its effectiveness is validated through numerical simulations.

Design of the predictive management and control system for combined propulsion complex

The object of this researching is the process of maneuvering a sea-based vehicle under compressed conditions, which requires one hundred percent reserve of thrusters (THRs) of various modifications and locations. The main problem is the provision of energy-efficient control over the ship's motion at low speed in the horizontal plane using a high-level predictive controller. The hierarchy of the motion control system (MCS) is usually divided into several levels with the help of a high-level motion controller and the THR motor control distribution algorithm. This allows for a modular software structure where a high-level controller (HLC) can be designed without using comprehensive information about the THR motors. However, for a certain reference of THR configurations, such a decoupling can lead to reduced control performance due to the limitations of HLC regarding the physical constraints of the vessel and the behavior of MCS. The main results of the researching are methods to improve control performance using a nonlinear model predictive control (MPC) as a basis for the designed motion controllers due to its optimized solution and ability to consider constraints. A decoupled system was implemented for two simple motor tasks showing dissociation problems. The shortcomings were eliminated through the development of a nonlinear MPC controller, which combines the motion controller and the distribution of control over THR motors. To preserve the discrete modularity of the control system and achieve adequate performance, a nonlinear MPC controller with time-varying constraints was designed. This has made it possible to take into account the current limitations of the THR control system, increase the accuracy of control, and reduce the response time of the system by 10 %.

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.

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>

A Design Method for Road Vehicles with Autonomous Driving Control

The past three decades have witnessed extensive studies on motion-planning and tracking-control for autonomous vehicles (AVs). There is, however, a lack of studies on effective design methods for AVs, which consist of the subsystems of the mechanical vehicle, tracking-control, motion-planning, etc. To tackle this problem, this paper proposes a design approach for AVs. The proposed method features a design framework with two layers: at the upper layer, a particle swarm optimization (PSO) algorithm serves as a solver to a multi-objective optimization problem for desired AV trajectory-tracking performance; at the lower layer, a coupled dynamic analysis is conducted among the three subsystems, i.e., a nonlinear model for the mechanical vehicle, a motion-planning module, and a controller based on nonlinear model predictive control (NLMPC) for direction control. The simulation results demonstrate that the proposed method can effectively determine the desired design variables for the NLMPC controller and the mechanical vehicle to achieve optimal trajectory-tracking performance. The research findings from this work provide guidelines for designing AVs.

Efficient Nonlinear Model Predictive Path Tracking Control for Autonomous Vehicle: Investigating the Effects of Vehicle Dynamics Stiffness

Motion control is one of the three core modules of autonomous driving, and nonlinear model predictive control (NMPC) has recently attracted widespread attention in the field of motion control. Vehicle dynamics equations, as a widely used model, have a significant impact on the solution efficiency of NMPC due to their stiffness. This paper first theoretically analyzes the limitations on the discretized time step caused by the stiffness of the vehicle dynamics model equations when using existing common numerical methods to solve NMPC, thereby revealing the reasons for the low computational efficiency of NMPC. Then, an A-stable controller based on the finite element orthogonal collocation method is proposed, which greatly expands the stable domain range of the numerical solution process of NMPC, thus achieving the purpose of relaxing the discretized time step restrictions and improving the real-time performance of NMPC. Finally, through CarSim 8.0/Simulink 2021a co-simulation, it is verified that the vehicle dynamics model equations are with great stiffness when the vehicle speed is low, and the proposed controller can enhance the real-time performance of NMPC. As the vehicle speed increases, the stiffness of the vehicle dynamics model equation decreases. In addition to the superior capability in addressing the integration stability issues arising from the stiffness nature of the vehicle dynamics equations, the proposed NMPC controller also demonstrates higher accuracy across a broad range of vehicle speeds.

Landing Guidance Control Combining Powered Descending with Nonlinear Optimization and Vertical Descending with Model Prediction

In this study, we propose a landing guidance control method for the Moon using two control methods. The landing of a spacecraft on the Moon is divided into two phases: the powered descending phase and the vertical descending phase. The powered descending phase aims to optimize the entire trajectory to satisfy the termination constraint, instead of allowing for a relatively long control period. This phase performs feedback control using trajectory updates via nonlinear optimization. The vertical-descending phase aims to achieve accurate control over a short control period. This phase applies nonlinear model predictive control for fast optimization on finite time intervals. First, the landing of a spacecraft on the Moon is modeled as a two-body problem of the Moon and spacecraft, and equations of motion are derived. Subsequently, we formulated an optimization problem for each phase and developed the proposed landing guidance method by combining the two control methods. Furthermore, numerical simulations based on the derived equations of motion were performed to confirm the effectiveness of the proposed method and to compare its performance with another optimization method, the successive convexification (SCvx) algorithm.

Real-time robust nonlinear model predictive control with monotonically increasing weight for quadruped locomotion

Real-time robust nonlinear model predictive control with monotonically increasing weight for quadruped locomotion

Non-Periodic Quantized Model Predictive Control Method for Underwater Dynamic Docking

This study proposed an event-triggered quantized model predictive control (ETQMPC) method for the dynamic docking of unmanned underwater vehicles (UUVs) and human-occupied vehicles (HOVs). The proposed strategy employed a non-periodic control approach that initiated the non-linear model predictive control (NMPC) optimization and state sampling based on tracking errors and deviations from the predicted optimal state, thereby enhancing computing performance and system efficiency without compromising the control quality. To further conserve communication resources and improve information transfer efficiency, a quantitative feedback mechanism was employed for sampling and state quantification. The simulation experiments were performed to verify the effectiveness of the method, demonstrating excellent docking trajectory tracking performance, robustness against bounded current interference, and significant reductions in computational and communication burdens. The experimental results demonstrated that the method outperformed in the docking trajectory tracking control performance significantly improved the computational and communication performance, and comprehensively improved the system efficiency.

A nonlinear model predictive control for air suspension of hub motor electric vehicle based on hybrid H2/H∞ state estimation

To alleviate the vibration from the road irregularities and the unbalanced electromagnetic forces (UEFs), deteriorating the dynamic performance of hub motor electric vehicles (HM-EVs), a novel nonlinear model predictive control (NMPC) is proposed based on a hybrid H2/H ∞ filtering algorithm for the HM-EVs with air suspension (HM-AS). The dynamic HM-AS model involves the electric vehicle’s longitudinal, lateral, and vertical motion. The air suspension system between the body and the hub motor enhances ride quality and insulates the oscillation delivered to the vehicle body. Then, the dynamic HM-AS model is validated by the actual vehicle test, and the proposed filter is developed to obtain the vehicle states. Besides, the NMPC controller guarantees the dynamic performance of HM-AS by intervening in vehicle attitude, road-holding stability, motor safety, and ride comfort. Finally, compared with the application of PID and MPC, the efficiency of the proposed method is demonstrated based on several random road scenarios. The results indicate the proposed algorithm can alleviate the dynamic performance of HM-AS and reduce motor vibration.

Nonlinear Model Predictive Control of Heaving Wave Energy Converter with Nonlinear Froude–Krylov Forces

Wave energy holds significant promise as a renewable energy source due to the consistent and predictable nature of ocean waves. However, optimizing wave energy devices is essential for achieving competitive viability in the energy market. This paper presents the application of a nonlinear model predictive controller (MPC) to enhance the energy extraction of a heaving point absorber. The wave energy converter (WEC) model accounts for the nonlinear dynamics and static Froude–Krylov forces, which are essential in accurately representing the system’s behavior. The nonlinear MPC is tested under irregular wave conditions within the power production region, where constraints on displacement and the power take-off (PTO) force are enforced to ensure the WEC’s safety while maximizing energy absorption. A comparison is made with a linear MPC, which uses a linear approximation of the Froude–Krylov forces. The study comprehensively compares power performance and computational costs between the linear and nonlinear MPC approaches. Both MPC variants determine the optimal PTO force to maximize energy absorption, utilizing (1) a linear WEC model (LMPC) for state predictions and (2) a nonlinear model (NLMPC) incorporating exact Froude–Krylov forces. Additionally, the study analyzes four controller configurations, varying the MPC prediction horizon and re-optimization time. The results indicate that, in general, the NLMPC achieves higher energy absorption than the LMPC. The nonlinear model also better adheres to system constraints, with the linear model showing some displacement violations. This paper further discusses the computational load and power generation implications of adjusting the prediction horizon and re-optimization time parameters in the NLMPC.

Model predictive control for autonomous vehicle path tracking through optimized kinematics

Tracking performance and stability of path tracking is crucial for unmanned vehicles' navigational tasks. Researches on vehicle path tracking controllers primarily rely on dynamic models. In contrast, there are less designs and researches that focus on path tracking controller based on kinematic model. This scarcity may stem from the perceived inadequacy in the accuracy of vehicle kinematic models. This research introduces a novel method for modifying the traditional vehicle kinematic model by incorporating a front wheel steering angle modification function to enhance tracking performance of path tracking controllers based on kinematic models. In terms of control strategy selection, the study opted for nonlinear model predictive control with terminal cost. A controller which is founded on the modified model was used on a simulated vehicle on CarSim-Simulink platform to assess the tracking performance. The simulation was designed with a double-shift line reference trajectory and the initial speeds of the simulated vehicle are 5 m/s and 10 m/s, respectively. The results of the simulations indicate that employing a controller based on the modified model could reduce the peak tracking error by 76.45 % and 43.06 %, and the root mean square of the tracking error was reduced by 73.29 % and 36.06 %, respectively.