Proposed Model Predictive Control Method Research Articles

Model Predictive Control for Three-Phase, Four-Leg Dynamic Voltage Restorer

Dynamic voltage restores (DVRs) are usually used to mitigate the effect of voltage sag and guarantee sufficient power supply for sensitive loads. However, three-phase voltage cannot be compensated to the desired balance voltage under unbalanced three-phase loads by traditional DVRs with a three-phase, three-leg inverter. To address this problem, a three-phase, four-leg inverter-based DVR is first introduced in this paper, and then the state space model in its continuous form and discrete form are established, respectively. A two-step predictive method is proposed for the prediction of the output voltage in each switching state by the established voltage prediction model. Finite-control-set model predictive control (MPC) is developed to be used in the three-phase, four-leg inverter-based DVR. Its dynamic response is effectively improved by the proposed MPC method under various voltage sag conditions. The proposed DVR control strategy is validated via MATLAB/Simulink-R2022b simulations, which demonstrate its effectiveness in voltage compensation under various sag conditions.

A Comparative Study on Autonomous Vehicle Local Path Planning Through Model Predictive Control and Frenet Frame Method

<div>In recent years, autonomous vehicles (AVs) have been receiving increasing attention from investors, automakers, and academia due to the envisioned potentials of AVs in enhancing safety, reducing emissions, and improving comfort. The crucial task in AV development boils down to perception and navigation. The research is underway, in both academia and industry, to improve AV’s perception and navigation and reduce the underlying computation and costs. This article proposes a model predictive control (MPC)-based local path-planning method in the Cartesian framework to overcome the long computation time and lack of smoothness of the Frenet method. A new equation is proposed in the MPC cost function to improve the safety in path planning. In this regard, an AV is built based on a 2015 Nissan Leaf S by modifying the drive-by-wire function and installing environment perception sensors and computation units. The custom-made AV then collected data in Norman, Oklahoma, and assisted in the performance evaluation of the two control algorithms in this work. Both straight roads and curved roads are considered in the evaluation. For the purpose of saving costs and raising real-world implementation potential, the vision-only solution is applied in object detection and bird’s-eye-view coordinate data generation. MPC and Frenet coordinate system approaches are independently employed to generate a safe and smooth path for the AV using the collected data. The two methods are compared in terms of smoothness, safety, and computation time. Compared with the Frenet-based method, the proposed MPC method reduces the computation time by 80%, and the path smoothness is significantly improved.</div>

A Data-Driven Predictive Control Method for Modeling Doubly-Fed Variable-Speed Pumped Storage Units

In this study, a data-driven model predictive control (MPC) method is proposed for the optimal control of a doubly-fed variable-speed pumped storage unit. This method combines modern control theory with the dynamic characteristics of the pumped storage unit to establish an accurate dynamic model based on actual operating data. In each control cycle, the MPC uses the system model to predict future system behavior and determines the optimal control input sequence by solving the constrained optimization problem, thereby effectively dealing with the nonlinearity, time-varying characteristics, and multivariable coupling problems of the system. When compared with a traditional PID control, this method significantly improves control accuracy, response speed, and system stability. The simulation results show that the proposed MPC method exhibits better steady-state error, overshoot, adjustment time, and control energy under various operating conditions, demonstrating its advantages in complex multivariable systems. This study provides an innovative solution for the efficient control of doubly-fed variable-speed pumped storage units and lays a solid foundation for the efficient utilization of new energy sources.

Low Computational Burden Model Predictive Control for Single-Phase Cascaded H-Bridge Converters Without Weighting Factor

In this article, a low computational burden model predictive control (MPC) strategy without weighting factor is proposed for the single-phase cascaded H-bridge CHB converters. To reduce the switching state candidates, a hierarchy control algorithm is proposed. The grid current is controlled by selecting a subregion from the designed 2-D control plane, instead of the entire area. Two vectors are chosen in one sampling period for more accurate tracking. Then, the voltage balancing is achieved by selecting the optimal switching state from the subregion candidates to form the above two vectors. The cost function can be constructed of one variable: load voltage. Therefore, the weighting factor can be eliminated. No tuning or retuning processes are required in the proposed method. To reduce the computational time further, the principle of eliminating the switching state candidates operating the same voltage balancing performance is proposed. Conventional and proposed MPC methods are verified by experimental tests via a laboratory setup of a three-cell connected CHB converter. Steady-state and transient operations demonstrate that the proposed method guarantees less distortion grid current and shorter execution time (reduced from 15 to 3 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu s$</tex-math></inline-formula> ). Fast response speed to variations in voltage reference and load resistance can be achieved t.

Pseudo-spectral optimization and model predictive control of vehicle shift process with dual clutch transmission

To improve the shift quality of dual clutch transmission (DCT) vehicles and reduce the jerk and sliding friction in the shift process, a real-time planning of clutch optimal engagement trajectory and control method in the shift process is proposed. This method combines pseudo-spectral optimization, machine learning, and model predictive control. First, considering the jerk, sliding friction work, and shift time as the optimization indices, the adaptive pseudo-spectral method is employed to optimize the engagement trajectory of the clutch during the shift process. Based on the optimal trajectory data set, a gradient boosting decision tree-based real-time planning method for the clutch target engagement trajectory is proposed. Second, a model predictive control strategy for the shift process is proposed based on the DCT system model to track the optimal target trajectory in real-time. Simulations and experiments reveal that the proposed target engagement trajectory planning method can plan the clutch target engagement trajectory for various accelerator pedal openings and initial clutch speed states in real-time, and the proposed model predictive control method can accurately track the target trajectory. Compared with the original vehicle strategy, under 35% and 65% accelerator pedal opening, the maximum absolute value of jerk produced by the proposed strategy was reduced by 31.06% and 31.46%, respectively, and the sliding friction work was reduced by 22.87% and 23.24%, respectively. The shift times of the proposed strategy under 35% and 65% accelerator pedal openings were 19.12% and 20.69% lower than that of the original vehicle strategy, respectively.

Autonomous cooperative formation control of underactuated USVs based on improved MPC in complex ocean environment

A dual model predictive control (DMPC) method based on virtual trajectory is proposed in this paper, in order to achieve autonomous cooperative formation control of underactuated unmanned surface vehicles (USVs) in complex ocean environment. Firstly, the formation tracking error model of the USVs is designed, and considering the large initial state tracking error of USVs, a virtual transition trajectory is put forward to guide the design of tracking controller. To solve the mutation problem caused by misalignment of the follower USV's desired trajectory in the early stage, an improved differential tracker is introduced into virtual leader USV to smooth the desired trajectory of the follower USV. In addition, a dual mode switching strategy is designed to decide when and how to quit the transition of the virtual USV. A nonlinear disturbance observer is introduced to compensate the complex marine environment interference. Finally, by introducing terminal penalty function and linear state feedback controller, the Lyapunov function is constructed to prove the control stability of the proposed model predictive control method in finite time domain, and the effectiveness and reliability of the proposed method are verified by simulation experiments.

A novel adaptive model predictive frequency control using unscented Kalman filter

This paper proposes a novel adaptive load frequency control (LFC) method based on model predictive control (MPC) using an unscented Kalman filter (UKF). The objective is to develop a robust LFC controller against the change in frequency characteristics of a power system. An adaptive MPC (AMPC) control is realized by updating the prediction model on-line to capture the frequency characteristics of a target system. A simplified prediction model is identified in the preliminary examination of the closed-loop performance of the target system, and then the system parameters are estimated in real-time circumstances. The estimated parameters include equivalent inertia of the target system. An interconnected three-area test system is used in the simulations to confirm the effectiveness of the proposed approach. The simulation results verify that the proposed MPC method can work successfully and efficiently handle the disturbances of the power system. The successful results also confirm that the proposed control scheme can be applied to a microgrid (MG) project, which is being promoted by the authors.

Integrated Propulsion and Cabin-Cooling Management for Electric Vehicles

This paper presents two nonlinear model predictive control (MPC) methods for the integrated propulsion and cabin-cooling management of electric vehicles. An air-conditioning (AC) model, which has previously been validated on a real system, is used to accomplish system-level optimization. To investigate the optimal solution for the integrated optimal control problem (OCP), we first build an MPC, referred to as a joint MPC, in which the goal is to minimize battery energy consumption while maintaining cabin-cooling comfort. Second, we divide the integrated OCP into two small-scale problems and devise a co-optimization MPC (co-MPC), where speed planning on hilly roads and cabin-cooling management with propulsion power information are addressed successively. Our proposed MPC methods are then validated through two case studies. The results show that both the joint MPC and co-MPC can produce significant energy benefits while maintaining driving and thermal comfort. Compared to regular constant-speed cruise control that is equipped with a proportion integral (PI)-based AC controller, the benefits to the battery energy earned by the joint MPC and co-MPC range from 2.09% to 2.72%. Furthermore, compared with the joint MPC, the co-MPC method can achieve comparable performance in energy consumption and temperature regulation but with reduced computation time.

Computationally Efficient Model Predictive Control With Fixed Switching Frequency of Five-Level ANPC Converters

This article proposes a fixed switching frequency (FSF)-based improved model predictive control (MPC) for a five-level active neutral-point clamped (5L-ANPC) converter. Compared to the conventional MPC for 5L-ANPC converter, the proposed MPC significantly reduces the computational burden while ensuring the balance of dc-link and flying capacitor voltages. The proposed MPC optimally selects the control voltage vectors to reduce common mode voltage (CMV), leading to a small CMV of the converter. Using three voltage vectors action per control cycle in MPC, FSF is achieved. Steady-state and dynamic performances of the proposed MPC have been evaluated by experiments. The results verify the feasibility and effectiveness of the proposed MPC method.

Dynamic Characteristic Improvement of Integrated On-Board Charger Using a Model Predictive Control

This paper proposes a dynamic characteristic improvement of an integrated on-board charger (OBC) using a model predictive control (MPC) method. The integrated OBC performs both battery charging and starter generator (SG) driving for engine starting in plug-in hybrid electric vehicles (PHEVs). If it performs battery charging, battery-side voltage and battery-side current are control objects which are usually controlled by using a proportional-integral (PI) controller. However, it has the disadvantage of undesirable dynamic characteristics, and gain tuning of the PI controller is necessary to properly control the voltage and current. Therefore, this paper proposes the MPC method for the dynamic characteristic improvement of integrated OBC. It can achieve not only dynamic characteristic improvement, but also robustness from the abrupt change of load impedance. By using the proposed MPC method for integrated OBC, the settling time to control the output voltage is decreased by 50% in the transient state compared to that by using the PI controller. The effectiveness of the proposed MPC method is verified by simulation and experimental results.

Modeling and Finite-Horizon MPC for a Boiler-Turbine System Using Minimal Realization State-Space Model

This paper aims to address a finite-horizon model predictive control (MPC) for non-linear drum-type boiler-turbine system using a system-identification method. Considering that the strong state coupling of a non-linear mechanism model, the subspace identification method is first utilized to obtain a linear state-space model, and transformed into an input–output model. By taking the inputs and outputs of the input–output model as system states, an augmented non-minimal state-space (NMSS) model of state measurable is constructed. In order to reduce the computation burden, the augmented NMSS model is further transformed into a canonical formulation by adopting a Kalman decomposition. Based on the minimal realization state-space model, the MPC controller is parameterized as a finite-horizon optimization problem. Finally, simulations are performed and evaluated the performance of the proposed method, and the simulation results show that: the linear model approximate the non-linear system accurately; the proposed MPC method can achieve a satisfactory stable control performance; and the computation time 18.388 s for the overall optimization problem also illustrates the real-time performance effectively.

Predictive Control for a Wave-Energy Converter Array Based on an Interconnected Model

This paper proposes a model predictive control (MPC) method based on an interconnected model to maximize the ocean wave energy extracted by a wave-energy converter (WEC) array. In the proposed method, a formally uniform interconnected model is applied to represent the dynamics of an array consisting of an arbitrary quantity of WECs, simultaneously considering the hydrodynamic interaction among all the WEC devices. First, the WEC devices and their hydrodynamic interaction are represented in an interconnected model that describes the networked dynamics of a variety of WEC arrays with distinct spatial geometry layout of the WEC devices deployed in the sea field. Second, based on the presented model, an MPC method is applied to achieve the coordinated control of the WEC array to improve its energy conversion efficiency under the constraints of buoy position and control force. Third, a hardware-in-the-loop (HIL) platform is developed to simulate the WEC array’s physical operating conditions, and the proposed method is implemented on the platform to test its performance. The test results show that the proposed MPC method using the interconnected model has a higher energy harvesting efficiency than the classic MPC method.

A computationally efficient hybrid optimization‐based model predictive control for inductive power transfer systems

Model predictive control (MPC) has been actively researched in recent years for power electronics applications due to its intuitive concept, flexibility, and superior dynamic performance. However, current research on MPC for inductive power transfer (IPT) systems is rather limited. Several emerging applications such as dynamic electric vehicle charging, vehicle-to-grid services, and ad hoc power transfer between mobile devices require IPT systems to possess fast dynamic response characteristic. Here, a new MPC method based on computationally efficient hybrid optimization scheme is proposed to meet the needs of these applications. The proposed MPC method adaptively selects the moving discretized control set-based optimization or the newly proposed group-based optimization under different system's states to minimize the number of iterations required for determining the optimum control variable, thus offering the advantage of low computational burden. The paper also proposes a new prediction error compensation scheme that effectively improves the control accuracy of the proposed MPC method. All the proposed works are experimentally verified on a laboratory prototype.

Angle stability enhancement of off-grid microgrids based on model predictive control

To compensate for the lack of inertia and damping, virtual synchronous generator (VSG) control which mimic the synchronous generator (SG) is applied to converters of distributed generation. The synchronous operation of SG and multi-VSG are more likely not be maintained after a large disturbance due to the difference of frequency regulation for the VSG and SG. The rotor motion equations of SG and VSG combination as well as multi-VSG combination are established based on the VSG common reference frame. On this basis, the angle stability of an off-grid microgrid is analyzed and the impact of the controlled current source model of energy storage system (ESS) on transient stability is investigated. A model predictive control (MPC) method using ESS is proposed to enhance the angle stability of the off-gird microgrid. By establishing the prediction model of angle difference, angular frequency difference, and ESS output power and designing the cost function to minimize angle and angular frequency difference and variations of reference power as control variables, the reference active and reactive power can be optimized and then transmit to ESS. The simulation results validate the effectiveness of the proposed MPC method using ESS to enhance the angle stability of off-grid microgrid after large disturbances in the system.

Real-time optimization for train regulation and stop-skipping adjustment strategy of urban rail transit lines

This paper addresses the real-time train regulation problem by taking the stop-skipping strategy into account in high-frequency urban rail transit lines. During rush hours, if the train regulation is not adopted properly and rapidly to deal with the frequent disturbances, the delays may further spread and result in a large number of passengers stranded in the stations. The purpose of this paper is to explore the possibility of dynamic train regulation and stop-skipping adjustment strategy to cope with the disturbance management in a real-time manner. By considering the impact of dynamic passenger flows, a nonlinear programming model for train regulation problem is proposed with the objective of minimizing the total train deviation and enhancing the passenger service quality, which is further converted into a mixed-integer quadratic programming model for ease to solve. In addition, the constraints related to the train rolling-stock plan are taken into account to provide a feasible scheme. Based on a customized model predictive control (MPC) method, the proposed model can be solved in a real-time manner, laying a theoretical groundwork for implementation of the train regulation strategy. Computational results based on the real-world data of Beijing Yizhuang metro line illustrate the superiority of the train regulation strategy in comparison with the practical strategy. The robustness of the method is examined through various scenarios of uncertain passenger demands, and the adjustment performance with different prediction horizons is explored to illustrate the added value brought by the updated information of the proposed MPC method.

Model predictive based frequency control of power system incorporating air-conditioning loads with communication delay

The variability of renewable energy sources (RESs) introduces more frequency fluctuations, and the reserve capacity of generation side needs to be sharply enlarged to maintain frequency stability, which inevitably increases the cost. In this paper, massive inverter air conditioners (IACs) as flexible regulation resources are aggregated to provide capacity support in frequency regulation. This paper establishes the state-space dynamic model and then presents a coordinated optimal control strategy by using model predictive control (MPC). However, the communication delay during the control signal transmission to IACs is one of the main obstacles that degrades the system performance in frequency regulation. To handle this issue, a predictive compensation method (PCM) based on MPC is applied to the control loop of IACs to compensate for the communication delay. Moreover, the robustness of the proposed MPC method with PCM against variations of system delay and parameters in the frequency response process is investigated in comparison to the proportional–integral (PI) controller. The simulation results are conducted to validate the superiority of the proposed method to the PI control method in virtue of the dynamic response and the performance indices, which demonstrates faster response, robustness, fewer fluctuations.

A Machine Learning-Based Model Predictive Control Method for Pumped Storage Systems

Integrated systems required for renewable energy use are under development. These systems impose more stringent control requirements. It is quite challenging to control a pumped storage system (PSS), which is a key component of such power systems. Because of the S-characteristic area of the PSS pump turbine, traditional proportional-integral-derivative (PID) control induces considerable speed oscillation under medium and low water heads. PSSs are difficult to model because of their nonlinear characteristics. Therefore, we propose a machine learning (ML)-based model predictive control (MPC) method. The ML algorithm is based on Koopman theory and experimental data that includes PSS state variables, and is used to establish linear relationships between the variables in high-dimensional space. Subsequently, a simple, accurate mathematical PSS model is obtained. This mathematical model is used via the MPC method to obtain the predicted control quantity value quickly and accurately. The feasibility and effectiveness of this method are simulated and tested under various operating conditions. The results demonstrate that the proposed MPC method is feasible. The MPC method can reduce the speed oscillation amplitude and improve the system response speed more effectively than PID control.

Model Predictive Current Control With Low Complexity for Single-Phase Four-Level Hybrid-Clamped Converters

This article presents a simplified model predictive control (MPC) method for single-phase four-level hybrid-clamped converters (1P-4L-HCCs), achieving high-quality current control and strong capacitor voltage balancing. Different from a conventional MPC, the proposed method aims to dramatically reduce switching states (control voltage vectors) in the cost function optimization of MPC. It utilizes only 16 switching states, compared to 64 in conventional methods, resulting in reduced execution time and significantly increased control bandwidth. Steady-state and dynamic performances are evaluated by simulated and experimental test, and the main results are provided to verify the effectiveness of the proposed MPC method.

Improved nonlinear MPC for aircraft gas turbine engine based on semi-alternative optimization strategy

The development of advanced control systems is motivated to achieve the complicated aircraft engine control, so a novel semi-alternative optimization strategy based model predictive control is proposed. In this proposed controller, a nonlinear state-space model is generated as the predictive model on the basis of a baseline engine model that estimates the current operating state of engine with an extended Kalman filter every sampling instant, and a quadratic constrained problem rather than a higher order nonlinear problem is constructed based on this model. Moreover, a novel control sequence to be optimized based on semi-alternative optimization strategy is proposed, which includes two parts. The first part represents that all the control variables of the engine are optimized for the current sampling instant while the second part represents that different control variables are optimized alternatively for different future sampling instants over the control horizon. The proposed model predictive control method is implemented to a twin-spool turbofan engine. Simulation results demonstrate not only that the proposed method can achieve a smaller control error than the standard model predictive control algorithm does, but also that the proposed controller is more time-saving than the standard model predictive control, which can save up to about 61% optimization time when control horizon increases to nine.

Feedback linearization-based MIMO model predictive control with defined pseudo-reference for hydrogen regulation of automotive fuel cells

Proton exchange membrane fuel cells (PEMFCs) possess the benefits of high conversion efficiency, low operation noise and no pollution which are considered as potential power solutions for the automotive application. The supply and recirculation of hydrogen determines the output performance of PEMFC that is required to be well regulated. The hydrogen excess ratio (HER) is asked to locate at appropriate operating points and the pressure difference between anode and cathode should be limited within a reasonable range. In this paper, a pseudo-reference-based multiple-input multiple-output (MIMO) model predictive control (MPC) integrated with the feedback linearization is proposed for the HER regulation and the pressure balance of electrodes. The nonlinear hydrogen delivery system model is developed which consists of two actuators: flow control valve and hydrogen circulating pump. To address the high nonlinearity of the hydrogen delivery system, the feedback linearization is formulated. The MIMO MPC is then developed based on the feedback linearized model with the defined pseudo-reference which can effectively reduce the overshoot of HER. Comparing with the normal MPC based on one working-point first-order Taylor expansion, the more accurate hydrogen regulation performance of the proposed MPC can be achieved. The proposed MPC can effectively reduce the HER overshoot by 59.25% at the initial response phase with nearly same convergence time. Under the New European Driving Cycle (NEDC) simulation condition, the average overshoot reduction of anode pressure and HER can reach to 47.45% and 77.34% that demonstrates a well application prospect of the proposed MPC in the automotive PEMFC hydrogen regulation. A hardware in loop (HIL) experiment was finally conducted to show the real-time capacity of the proposed MPC method.