Model Predictive Control Method Research Articles

Time-delay-aware power coordinated control approach for series hybrid electric vehicles

Series hybrid electric vehicles (S-HEVs) have attracted extensive attention thanks to the simple structure and excellent efficiency, which power transfer rely on high-voltage microgrids consisting of engine-generator set, battery, motor, and other actuators. However, with possible communication time delays (CTDs), the interaction between the actuators and control unit in terms of state and control command is desynchronize, resulting in the unstable operation of S-HEVs, such as engine stalls and bus voltage jitter. This presents a great challenge to the power coordinated control approach (PCCA) design that controls different actuators. Motivated by the mentioned above, this paper presents a time-delay-aware PCCA to achieve the stable driving of S-HEVs. First, an integrated powertrain control-oriented model that incorporates communication is built. Second, an increment model predictive control method (MPC) is designed. And then by leveraging the Lyapunov-Razumikhin stability theorem, a stability condition is derived by defining a parameterization weight matrix and known upper bound of CTDs, reducing the complexity of parameter designing. Additionally, an adaptive mechanism is designed to extend application of the proposed approach in unknown CTDs condition. Finally, the hardware-in-the-loop experiment is performed, and the results demonstrate that the presented approach in the mean and root mean square of the engine speed error and DC-bus voltage error decrease 39.87%, 43.85%, 44.67%, and 79.94% than nominal MPC in one period CTDs condition, respectively. And for the larger CTDs condition, the proposed method also shows efficient robustness. These substantiate that the proposed control method effectively improves vehicle running stability when encountering CTDs.

Optimization Method of Multi-Mode Model Predictive Control for Wind Farm Reactive Power

This paper presents a novel approach for optimizing wind farm control through the utilization of a combined model predictive control method. In contrast to conventional methods of controlling active and reactive power in wind farms, the suggested approach integrates a wind power prediction model driven by a neural network and a state-space model for wind turbines. This combination facilitates a more precise forecast of active power, thereby enabling the dynamic prediction of the range of reactive power output from the wind turbines. When combined with the equation of state in wind farm space, it is possible to accurately optimize the reactive power of a wind farm. Furthermore, the impact of active power on voltage fluctuations in the wind farm collector system was examined. The utilization of model predictive control enhances voltage regulation, optimizes system redundancy, and increases the reactive capacity. Sensitivity coefficients were calculated using analytical methods to enhance computational efficiency and to resolve issues related to convergence. In order to validate the proposed methodology and control scheme, a wind farm simulation model comprising 20 turbines was developed to assess the feasibility of the scheme.

An optimal solutions-guided deep reinforcement learning approach for online energy storage control

As renewable energy becomes more prevalent in the power grid, energy storage systems (ESSs) are playing an ever-increasingly crucial role in mitigating short-term supply–demand imbalances. However, the operation and control of ESS are not straightforward, given the ever-changing electricity prices in the market environment and the stochastic and intermittent nature of renewable energy generations, which respond to real-time load variations. In this paper, we propose a deep reinforcement learning (DRL) approach to address the electricity arbitrage problem associated with optimal ESS management. First, we analyze the structure of the optimal offline ESS control problem using the mixed-integer linear programming (MILP) formulation. This formulation identifies optimal control actions to absorb excess renewable energy and perform price arbitrage strategies. To tackle the uncertainties inherent in the prediction data, we then recast the online ESS control problem into a Markov Decision Process (MDP) framework and develop the DRL approach, which involves integrating the optimal offline control solution obtained from the training data into the training process and introducing noise to the state transitions. Unlike typical offline DRL training over a long time interval, we employ the Deep Deterministic Policy Gradient (DDPG) and Proximal Policy Optimization (PPO) algorithms with smaller neural networks training over a short time interval. Numerical studies demonstrate the promising potential of the proposed DRL-enabled approach for achieving better online control performance than the model predictive control (MPC) method under different price errors. This highlights the sample efficiency and robustness of our DRL approaches in managing ESS for electricity arbitrage.

Yaw Stability Control of Unmanned Emergency Supplies Transportation Vehicle Considering Two-Layer Model Predictive Control

The transportation of emergency supplies is characterized by real-time, urgent, and non-contact, which constitute the basic guarantee for emergency rescue and disposal. To improve the yaw stability of the four-wheel-drive unmanned emergency supplies transportation vehicle (ESTV) during operation, a two-layer model predictive controller (MPC) method based on a Kalman filter is proposed in this paper. Firstly, the dynamics model of the ESTV is established. Secondly, the improved Sage–Husa adaptive extended Kalman filter (SHAEKF) is used to decrease the impact of noise on the ESTV system. Thirdly, a two-layer MPC is designed for the yaw stability control of the ESTV. The upper-layer controller solves the yaw moment and the front wheel steering angle of the ESTV. The lower-layer controller optimizes the torque distribution of the four tires of the ESTV to ensure the self-stabilization of the ESTV operation. Finally, analysis and verification are carried out. The simulation results have verified that the improved SHAEKF can decrease the state estimation error by more than 78% and achieve the noise reduction of the ESTV state. Under extreme conditions of high velocity and low adhesion, the average relative error is within 6.77%. The proposed control method can effectively prevent the instability of the ESTV and maintain good yaw stability.

Dynamic safety control of offshore wind turbine based on model predictive control

Offshore wind power is a clean energy source with excellent development prospects that are conducive to realising China's goal of carbon neutrality. However, offshore wind turbines (WTs) are prone to failure and damage owing to their long-term operation in marine environments with high humidity, high wind speeds, and frequent extreme weather. To ensure the safe operation of offshore WTs, a modified dynamic model predictive control (MPC) method was proposed in this study. First, a dynamic model of an offshore WT was established and its nonlinear state-space equations were obtained. These state-space equations were subsequently linearised and discretised, then fast trajectory tracking of the state variables was performed according to the conventional MPC principle. Finally, a control strategy was designed to realise the safe operational control of offshore WT using the safety index as a constraint condition in the MPC. Simulation results confirmed that the proposed MPC strategy using the safety index-based constraint exhibited superior tracking of the set trajectory and achieved the minimum energy loss under varying wind speeds.

Automation of superconducting cavity cooldown process using two-layer surrogate model and model predictive control method

Superconducting cavity is the key equipment of the superconducting accelerator, which provides higher acceleration voltage and higher frequency power per unit length, and saves equipment space. Superconducting cavities need to be gradually cooled from ambient temperature (300 K) to the superconducting temperature (4.2 K or below) during the test and operation. The temperature difference on the cavity must be strictly limited during the cooldown process to prevent excessive thermal stress on the surface of the superconducting cavity. Since this cooldown process for the superconducting cavity is a typical large hysteresis, non-linear process that is difficult to control automatically using decoupled proportion integral derivative (PID) methods directly, a less efficient manual control scheme is normally adopted. In this paper, 3D numerical simulation, 1D pipe and 0D tank model with artificial neural network (ANN) were combined to generate a two-layer surrogate model that can balance computational accuracy and speed, to improve the automation and cooling efficiency of the superconducting cavity cooldown process. In order to achieve automatic control of the cooling procedure for the superconducting cavity, a model predictive control (MPC) approach was also built on the basis of this two-layer surrogate model. According to the results of the experiment test, the improved method could realize a quick and smooth cooldown process of the superconducting cavity, during which the temperature difference on the cavity could satisfy the requirements. Additionally, the improved automatic cooldown method was more adaptable and saved 29 % more time than the original manual control method. The foundation for a more intelligent automated control of future large cryogenic systems or other system with the large hysteresis, non-linear properties, was laid.

An Angle-Based Virtual Vector Model Predictive Current Control for IPMSM Considering Overmodulation

The conventional model predictive control method suffers from large current and torque harmonics due to the limited voltage vectors. To increase the control performance, in many papers, the methods of extending the predictive control set by adding virtual vectors are proposed. However, constructing virtual vectors will bring extra computational burden for vector optimization. To solve this problem, this paper proposes an angle-based virtual vector model predictive current control (ABVV-MPCC) method for interior permanent magnet synchronous motor (IPMSM). In this method, a hexagonal coordinate system is introduced to define the virtual vectors. After obtaining the composite relationship between the reference voltage vector and the adjacent basic vector, the vector optimization range is reduced from six voltage sectors to one voltage sector. And the optimal voltage vector is directly obtained by searching for the closest candidate voltage vector. After adopting the proposed method, the exhaustive optimization is avoided and the calculation burden is independent from the virtual voltage vectors number. Therefore, virtual voltage vectors number can be set arbitrarily, which greatly reduces current harmonics. Besides, a simple overmodulation dealing method by finding the optimal reachable voltage vector is proposed. And the dynamic performance under overmodulation is increased without adding additional control module.

Event-Triggered Deep Learning Control of Quadrotors for Trajectory Tracking

This paper proposes an event-triggered deep learning control strategy to achieve real-time trajectory tracking control for quadrotors. In the training data collection phase, the event-triggered model predictive control (MPC) method is applied to the quadrotor in the simulation environment to generate training data. Then, a deep neural network (DNN) controller is trained to approximate the optimal control policy of the event-triggered MPC. To further save computing resources of on-board processor, the event-triggered mechanism is incorporated with the DNN controller, and the dual-mode approach is employed in it. Finally, simulation and experimental results show that the proposed controller can ensure almost similar trajectory tracking performance to the event-triggered MPC controller while requiring a lower control computation cost.

Koopman-Based MPC With Learned Dynamics: Hierarchical Neural Network Approach.

This article presents a data-driven control strategy for nonlinear dynamical systems, enabling the construction of a Koopman-based linear system associated with nonlinear dynamics. The primary idea is to apply the deep learning technique to the Koopman framework for globally linearizing nonlinear dynamics and impose a Koopman-based model predictive control (MPC) approach to stabilize the nonlinear dynamical systems. In this work, we first generalize the Koopman framework to nonlinear control systems, enabling comprehensive linear analysis and control methods to be effective for nonlinear systems. We next present a hierarchical neural network (HNN) approach to deal with the crucial challenge of the finite-dimensional Koopman representation approximation. In particular, a scale-invariant constrained network in the HNN includes four modules, in which a predictor module and a linear module can accurately approximate the finite Koopman eigenfunctions and Koopman operator, respectively, thus forming the lifted linear system. Then, we design the Koopman-based MPC scheme for controlling nonlinear systems with constraints by adopting the modified MPC with a saturation-like function on the lifted linear system. Importantly, the Koopman-based MPC enjoys higher computational efficiency compared to the classical linear MPC and nonlinear MPC methods. Finally, a physical experiment on an overhead crane system is provided to demonstrate the effectiveness of the proposed data-driven control framework.

Inertia load reduction for loadoff during floating offshore wind turbine installation: Release decision and ballast control

High offshore installation costs are a significant factor limiting the competitiveness of offshore wind energy. One efficient installation approach for floating offshore wind turbines is to preassemble the tower, nacelle, and rotor onshore and perform a single lifting operation to mate the superstructure with the floating foundation at the installation site. It is heavy lifting, due to the weighty payload. At the end of the mating process, a loadoff operation is conducted to transfer the preassembly to the floating foundation. It results in a sudden change in total force acting on the vessel and causes substantial acceleration and potential damage to the mechanism in the onboard nacelles. The magnitude of acceleration of the onboard nacelles can vary greatly at different release instants. In this research, a simplified two-degrees-of-freedom (DOF) (heave and pitch) model is also proposed to account for the heavy lifting process and variable ballast tanks. The sudden payload transfer is approximated using a hyperbolic tangent function to guarantee continuity and differentiability. The loadoff operation consists of the decision-making and vessel-stabilizing phases. Based on the nonlinear model predictive control method, a payload-transfer time selector and anti-pitch ballast controller have been developed to achieve optimal release time decisions and stabilize the vessel after payload release, respectively. Six-DOF simulation results show that the proposed algorithms are capable to a satisfying level of robustness of deciding the optimal payload release time instant, as well as limiting the peak and mean acceleration magnitudes of the onboard nacelles after payload release. The decision-making and control strategies may promote the sustainable energy transformation by extending the operation window and reduce the installation costs.

Superiority of model predictive control with robust and stable approach for sliding wheeled mobile systems in the presence of obstacles

AbstractIn this paper, we present two distinct linear Model Predictive Control (MPC) methods for controlling mobile robots in the presence of obstacles while considering the wheel slip. Predictability of the controller enables the robot to automatically choose an alternative path to avoid obstacles. However, environmental conditions and disturbances, including slip, may impact the system model. Therefore, to accurately represent the system, slip angle and slip ratio are factored into the modeling process. Then the kinematic model is linearized using the successive method to reduce computational cost. Next, both Stable MPC (SMPC) and Robust MPC have been designed and implemented on the linearized time‐variant model to control the robot. The superiority of the robust predictive control method over the stable method has been discussed in terms of safety and optimal performance considering wheel slip. Finally, based on experimental tests, it has been found that the robust predictive controller is more effective than stable control when the surface is slippery and there is an obstacle in front of the robot. However, in a case where the wheel slip is neglectable, SMPC can be a better choice in presence of obstacles due to the lower computational cost.

Adaptive distributed MPC based load frequency control with dynamic virtual inertia of offshore wind farms

AbstractThe penetration of offshore wind farms (OWFs) in city‐close power systems is rapidly increasing. System inertia will be further reduced. Active frequency support of wind power is essential to solve the load frequency control (LFC) problem. Here, the dynamic virtual inertia control (VIC) method is employed to enhance frequency stability within the permitted operating states of OWFs. An adaptive distributed model predictive control (DMPC) method is proposed and applied to an interconnected power system. The dynamic VIC‐based LFC model is derived and used to construct the predictive model of DMPC. To expand the adaptation of the analytical linearized model of OWFs in different operating points, the adaptive law is further designed to dynamically adjust the parameters of DMPC. The simulation results demonstrate the effectiveness of the proposed control method. The frequency fluctuations can be well‐restrained under different disturbances.

Enhanced Model Predictive Control for Induction Motor Drives in Marine Electric Power Propulsion System

Marine electric propulsion is an important topic in the research of modern ships and underwater vehicles. The propulsion motor drives based on model predictive control (MPC) are becoming increasingly popular in marine propulsion systems as an emerging technology. However, the multi-objective optimization in conventional MPC requires cumbersome weighting factor tuning. The relatively large computational cost is also detrimental to the industrial application of MPC. Aiming at reducing the computational complexity of multi-objective optimization without weighting factors, this paper proposes an enhanced ranking-based MPC method for induction motor drives in marine electric power propulsion. The presented control set pre-optimization aims to reduce the computational complexity of enumeration and ranking. Based on the sign of torque prediction deviation, the proposed method avoids enumerating all fundamental voltage vectors. Consequently, the number of candidate elements in the initial control set are reduced to four without excessively excluding feasible solutions. By converting predicted numerical errors into ranking results, the proposed MPC seeks the optimal solution among the candidates through improved ranking evaluation. Considering the situation of simultaneous optimal ranking, the normalization error judgment is developed to further optimize the optimal solution selection process. The simulation and experimental results confirm that the proposed MPC is simple and effective. Without the involvement of tuning the weighting factors, the proposed method achieves good performance.

Model predictive control for three-axle trucks during tire blowout on expressway based on equivalent chassis

Unexpected tire blowout on expressway is one of the most dangerous scenarios for heavy load multi-axle trucks, especially under the inexperienced driver’s improper intervention. To this end, this paper proposes an autonomous tire blowout controller for three-axle trucks based on model predictive control (MPC) method. First of all, aiming at balancing the computing load and the path-tracking accuracy, an equivalent chassis is transformed based on the stable two-dimensional vehicle dynamic model. Second, a tire blowout–oriented vehicle high-fidelity dynamic model is established based on the equivalent chassis, in which the vehicle lateral, yaw, and roll motions are all considered at the same time. Then, an MPC-based dynamic control strategy is proposed to achieve effective tire blowout suppression with the consideration of vehicle rollover stability. Afterward, a transient vertical tire force shock is employed to simulate the real tire blowout behavior, on which two typical scenarios are constructed based on the TruckSim–Simulink co-simulation platform. The simulation results illustrate the feasibility and effectiveness of the proposed method. In two different dangerous tire blowout conditions, the lateral load transfer rate (LTR) value of the vehicle is reduced by 3.45% and 40.87%, respectively, while the trajectory tracking error is reduced at the same time.

Practical Applications of Model Predictive Control and Other Advanced Control Methods in the Built Environment: An Overview of the Special Issue

This paper summarizes the results of a Special Issue focusing on the practical applications of model predictive control and other advanced control methods in the built environment. This Special Issue contains eleven publications and deals with various topics such as the virtual sensing of indoor air pollutants and prediction models for indoor air temperature and building heating and cooling loads, as well as local and supervisory control strategies. The last three publications tackle the predictive maintenance of chilled water systems. Most of these publications are field demonstrations of advanced control solutions or promising methodologies to facilitate the adoption of such control strategies, and they deal with existing buildings. The Special Issue also contains two review papers that provide a comprehensive overview of practical challenges, opportunities, and solutions to improve building operations. This article concludes with a discussion of the perspectives of advanced controls in the built environment and the increasing importance of data-driven solutions.

An anti-disturbance lane-changing trajectory tracking control method combining extended Kalman filter and robust tube-based model predictive control

This paper proposes a trajectory tracking control method combining extended Kalman filter (EKF) and robust tube-based model predictive control (RTMPC) methods to improve the anti-disturbance capability during lane-changing maneuver of automated vehicles. A time-based quintic polynomial function is introduced for the implementation of trajectory planning to obtain the desired reference trajectory. The planned trajectory is input to the nominal system-oriented model predictive controller (MPC) in RTMPC for optimization to obtain the optimal control of the nominal system. The EKF collects the state measurements of the current instant and the optimal state estimates of the previous instant, and performs filtering to obtain the optimal state estimates of the current instant. The optimal estimate of the current state and the current state of the nominal system are input into the auxiliary control law of RTMPC to obtain the control of the actual system. Comparative numerical simulation experiments are conducted to analyze robustness and sensitivity of the proposed method. The results show that the control method combining EKF and RTMPC can optimize the trajectory tracking performance of the vehicle system, especially in the lateral displacement and the yaw-rate control. When the amplitude of measurement noise reaches the maximum, the optimization effect of lateral control is most significant in experiments. And the optimization effect in the control of lateral displacement and yaw angle continues to enhance with the increase of measurement disturbance. Therefore, this study can provide a reference for the anti-interference lane change trajectory tracking strategy of automated vehicles in the future.

Enhancing fuel cell performance through a dual MPC strategy for coordinated temperature management

Ensuring the optimal operating temperature is imperative for achieving efficient performance in proton exchange membrane fuel cells. Consequently, this study introduces a dual-model predictive control strategy to regulate the water pump and cooling fan in a cooling system. Initially, we establish an electrochemical and thermal model for fuel cell stacks and validate the model’s accuracy through experimental data. The system model is linearized, and the model predictive control (MPC) controller is formulated using the MATLAB/Simulink toolbox. Subsequently, it is collaboratively simulated with the electrochemical model of the fuel cell stack and the temperature model. To evaluate the effectiveness of the MPC controller, we conducted a comparative analysis with the traditional proportional–integral–derivative (PID) control and water pump MPC under step load, uniform load increase, and variable target scenarios. The findings indicate that in contrast to the PID control, the MPC controller significantly decreases the stack temperature difference fluctuation by more than 50%, maintaining the stack temperature within ±0.6 K of the set value. Furthermore, we independently assessed the performance of the MPC controller under varying ambient temperatures. The findings illustrate that the dual MPC method proficiently adapts cooling parameters across different ambient temperature ranges (288.15 K–308.15 K), ensuring the stable performance of the fuel cell. The model is linearized, and the simulation work is explained mainly on the MATLAB/Simulink platform. In order to compare the effectiveness of the MPC controller, the comparison with the MPC controller strategy of the water pump is added, which can better reflect the effectiveness of the proposed collaborative MPC controller strategy.

An Optimized Model Predictive Control Method With Fixed Switching Frequency for Eliminating Common-Mode Voltage of Five-Level Converters

In this paper, an optimized model predictive control (MPC) method with fixed switching frequency (FSF) is proposed to eliminate the common-mode voltage (CMV) and balance the capacitor voltage. Firstly, the zero CMV vector diagram is divided by finite control set MPC (FCS-MPC) to obtain the candidate vectors effectively. Then, in order to control the capacitor voltage and avoid the great computational burden originated from the redundant switching combinations, a piecewise control scheme is proposed to determine the required ones directly. The sequence generated by the selected vectors is further optimized for the purpose of saving switching transitions according to the internal and external parts of the vector diagram. Finally, the duty ratios are evaluated based on the results of the FCS-MPC in dividing sectors so as to avoid any extra complex calculation. The experimental evaluation has been carried out to validate the feasibility and effectiveness of the proposed method.

A Control Architecture for Regulating Voltage and Power Flows in a Networked Microgrid System

This paper presents a unique control system to regulate power exchanges and load bus voltage in a networked microgrid (NMG) system comprising AC and DC microgrids. During the islanding of a microgrid in this NMG system, load voltage and power balance can get disturbed. A control system and associated converter and inverter control methods are presented to rectify these issues. An efficient model predictive control (MPC) method, which gives a tracking error of 50% lower than a conventional proportional-integral (PI) controller, is used to control multiple inverters in the NMG system. Simulation studies are conducted to test the NMG in islanding and load change scenarios. With the help of these studies, it is verified that the MPC-controlled inverters can provide better tracking accuracy in achieving desired power flows in the NMG system.

Observer‐based event‐triggered distributed model predictive control for a class of nonlinear interconnected systems

AbstractIn this paper, an observer‐based event‐triggered distributed model predictive control method is proposed for a class of nonlinear interconnected systems with bounded disturbances, considering unmeasurable states. First of all, the state observer is constructed. It is proved that the observation error is bounded. Second, distributed model predictive controller is designed by using observed value. Meanwhile, the event‐triggered mechanism is set by using the error between the actual output and the predicted output. The setting of event‐triggered mechanism not only ensures the error between the actual output and the predicted output within a certain range, but also reduces the calculation amounts of solving the optimization problem. The states of each subsystem enter the terminal invariant set by distributed model predictive control, and then are stabilized in the invariant set under the action of output feedback control law. In addition, sufficient conditions are given to ensure the feasibility of the algorithm and the stability of the closed‐loop system. Finally, the numerical example is given, and the simulation results verify the effectiveness of the proposed algorithm.