Closed-loop Model Predictive Control Research Articles

Performance analysis of different control models for smart demand–supply energy management system

Several features of innovative grid technologies can be deployed to improve the overall performance of the power system environment. This can be seen from the generation to the consumption of energy. The two-way communication of smart metering introduces the novel functionalities of the energy management system. This paper presents a practical implementation of using the intelligent metering system. It consists of implementing a nanogrid that optimally coordinates the energy from the solar panel, battery storage and utility grid to supply the end user. The developed model is validated with an optimal value of the state of charge of the distributed energy storage to maximise energy from the solar panel and battery storage while minimising the power received from the utility grid. A demand response scheme is employed to formulate the performance index of the energy management system using three optimal control models: adaptive open-loop control, adaptive closed-loop control and model predictive control schemes. The formulation of the performance index of each approach is a function of the energy flow from different resources depending on the power consumption. The three models have given different insights into the performance of the smart nanogrid, which may be used to the advantage of the grid owner or end user. Through the performance of the optimal strategies, it can be observed that energy management is ensured, and real-time monitoring of the entire system is guaranteed. The performance models facilitate the minimisation of the power from the utility, resulting in savings between 23.7% and 39.240% of the total energy demand from the end user. Besides, the system design is validated by an electrical system to form a real-world innovative nanogrid application in residential environments.

Closed loop model predictive control of a hybrid battery-hydrogen energy storage system using mixed-integer linear programming

The derivation of an efficient operational strategy for storing intermittent renewable energies using a hybrid battery-hydrogen energy storage system is a difficult task. One approach for deriving an efficient operational strategy is using mathematical optimization in the context of model predictive control. However, mathematical optimization derives an operational strategy based on a non-exact mathematical system representation for a specified prediction horizon to optimize a specified target. Thus, the resulting operational strategies can vary depending on the optimization settings.This work focuses on evaluating potential improvements in the operational strategy for a hybrid battery-hydrogen energy storage system using mathematical optimization. To investigate the operation, a simulation model of a hybrid energy storage system and a tailor-made mixed integer linear programming optimization model of this specific system are utilized in the context of a model predictive control framework. The resulting operational strategies for different settings of the model predictive control framework are compared to a rule-based controller to show the potential benefits of model predictive control compared to a conventional approach. Furthermore, an in-depth analysis of different factors that impact the effectiveness of the model predictive controller is done. Therefore, a sensitivity analysis of the effect of different electricity demands and resource sizes on the performance relative to a rule-based controller is conducted. The model predictive controller reduced the energy consumption by at least 3.9 % and up to 17.9% compared to a rule-based controller. Finally, Pareto fronts for multi-objective optimizations with different prediction and control horizons are derived and compared to the results of a rule-based controller. A cost reduction of up to 47 % is achieved by a model predictive controller with a prediction horizon of 7 days and perfect foresight.

Fast Nonlinear Predictive Control Using Classical and Parallel Wiener Models: A Comparison for a Neutralization Reactor Process

The Wiener model, composed of a linear dynamical block and a nonlinear static one connected in series, is frequently used for prediction in Model Predictive Control (MPC) algorithms. The parallel structure is an extension of the classical Wiener model; it is expected to offer better modeling accuracy and increase the MPC control quality. This work discusses the benefits of using the parallel Wiener model in MPC. It has three objectives. Firstly, it describes a fast MPC algorithm in which parallel Wiener models are used for online prediction. In the presented approach, sophisticated trajectory linearization is performed online, which leads to computationally fast quadratic optimization. The second objective of this work is to study the influence of the model structure on modeling accuracy. The well-known neutralization benchmark process is considered. It is shown that the parallel Wiener models in the open-loop mode generate significantly fewer errors than the classical structure. This work’s third objective is to validate the efficiency of parallel Wiener models in closed-loop MPC. For the neutralization process, it is demonstrated that parallel models demonstrate better control quality using various indicators, but the difference between the classical and parallel models is not significant.

Distributed Dual Closed-Loop Model Predictive Formation Control for Collision-Free Multi-AUV System Subject to Compound Disturbances

This paper focuses on the collision-free formation tracking of autonomous underwater vehicles (AUVs) with compound disturbances in complex ocean environments. We propose a novel finite-time extended state observer (FTESO)-based distributed dual closed-loop model predictive control scheme. Initially, a fast FTESO is designed to accurately estimate both model uncertainties and external disturbances for each subsystem. Subsequently, the outer-loop and inner-loop formation controllers are developed by integrating disturbance compensation with distributed model predictive control (DMPC) theory. With full consideration of the input and state constraints, we resolve the local information-based DMPC optimization problem to obtain the control inputs for each AUV, thereby preventing actuator saturation and collisions among AUVs. Moreover, to mitigate the increased computation caused by the control structure, the Laguerre orthogonal function is applied to alleviate the computational burden in time intervals. We also demonstrate the stability of the closed-loop system by applying the terminal state constraint. Finally, based on a connected directed topology, comparative simulations are performed under various control schemes to verify the robustness and superior performance of the proposed scheme.

Harmonic closed-loop model predictive fault-tolerant control of a dual three-phase permanent magnet synchronous motor

Harmonic closed-loop model predictive fault-tolerant control of a dual three-phase permanent magnet synchronous motor

A Linear-Parameter-Varying Formulation for Model Predictive Perimeter Control in Multi-Region MFD Urban Networks

An alternative approach for real-time network-wide traffic control in cities that has recently gained attention is perimeter flow control. Many studies have shown that this method is more efficient than state-of-the-art adaptive signal control strategies for heterogeneously congested urban networks. The basic concept of such an approach is to partition heterogeneous cities into a small number of homogeneous regions (zones) and apply perimeter control to the interregional flows along the boundaries between regions. The transferring flows are controlled at the traffic intersections located at the borders between regions so as to distribute the congestion in an optimal way and minimize the total delay of the system. The focus of current work is the mathematical formulation of the original nonlinear problem in a linear parameter-varying (LPV) form so that optimal control can be applied in a (rolling horizon) model predictive concept. This work presents the mathematical analysis of the optimal control problem as well as the approximations and simplifications that are assumed in order to derive the formulation of a linear optimization problem. Numerical simulation results for the case of a macroscopic environment (plant) are presented in order to demonstrate the efficiency of the proposed approach. Results for the closed-loop model predictive control scheme are presented for the nonlinear case, which is used as “benchmark,” as well as the linear case. Furthermore, the developed scheme is applied to a large-scale microsimulation of a European city with more than 500 signalized intersections in order to better investigate its applicability to real-life conditions. The simulation experiments demonstrate the effectiveness of the scheme compared with fixed-time control because all of the performance indicators are significantly improved. Funding: This work was supported by Dit4Tram “Distributed Intelligence & Technology for Traffic & Mobility Management” project from the European Union’s Horizon 2020 research and innovation programme under [Grant agreement 953783].

Comparison of Two Different Battery Charging Methods

Abstract This paper describes charging of battery stack using model predictive control (MPC) algorithm. Temperature model and hybrid electrical model are used in algorithm. The battery stack consists of four serially connected valve-regulated lead-acid (VRLA) batteries. The objective of the optimization is to charge the proposed battery stack without violating the constraints in order to maintain the battery health. Validation of MPC algorithm for battery charging is performed using comparison between closed-loop MPC simulations and obtained characteristics of actual MPC charging. Previously, the conventional constant current constant voltage (CCCV) algorithm was proved as good, taking into account the degradation effects but not considering the speed of the charging. The comparison between charging of proposed battery stack using MPC algorithm and CCCV algorithm is performed and the comparison in charging proves MPC algorithm as better compared to the CCCV algorithm.

Energy saving and indoor temperature control for an office building using tube-based robust model predictive control

Actively controlling a building’s heating, ventilation, and air conditioning (HVAC) system can reduce costs and improve indoor comfort. Model predictive control (MPC) is an effective control algorithm that can facilitate the active control of complex systems such as the HVAC system. However, the uncertainty of the prediction model engenders many challenges in practical application. To address these issues, we propose a tube-based MPC strategy. First, a reduced-order thermal capacitance and thermal resistance model is established for the target system. Subsequently, a tube-based MPC scheme is designed to effectively handle uncertainties in real systems. The prediction uncertainty space is re-assumed in the tube, combined with the actual prediction error, to more closely correspond to the actual situation. The proposed model is tested and validated using the BOPTEST open-source testing framework. The results show that the proposed tube-based MPC can reduce the operating cost by at least 24%, compared with the traditional open-loop and closed-loop MPC, and can better control the indoor temperature when considering multiple uncertain predictions.

A Predictive Current Control Strategy for a Medium-Voltage Open-End Winding Machine Drive

This paper presents a medium-voltage drive based on an open-end winding induction machine supplied by a multilevel power converter topology. The power converter consists of cascaded two-level three-phase voltage source inverters (VSI) connected to each side of the machine windings and each VSI is fed by an isolated DC supply. The topology has been previously reported in the literature as a sinusoidal pulse-width modulation operating in an open loop. In this work, a closed-loop model predictive control (MPC) strategy is proposed. MPC offers a much simpler method to control the power switches of the inverter compared to complex modulation strategies that are typically used in multilevel converters. Moreover, the advantage of reducing the common-mode voltage offered by the open-end winding configuration is fully exploited in this work. Simulation results are presented to validate the performance of the proposed topology and control method.

Dynamic Operability Analysis for Process Design and Control of Modular Natural Gas Utilization Systems.

Process modularization is an alternative process design and construction framework, in which modular units are independent and replaceable blocks of a process system. While modular plants have higher efficiency and are safer to construct than conventional stick-built plants (Roy, S. Chem. Eng. Prog. 2017, 113, 28-31), they are significantly more challenging to operate because of the loss in the control degrees of freedom that comes with process integration and intensification (Bishop, B. A.; Lima, F. V. Processes 2021, 9, 2165). To address this challenge, in this work, operability analyses are performed to consider the design and operation of modular units. Initially, a steady-state operability analysis is employed to find a set of feasible modular designs that are able to operate considering different modular plant conditions. A dynamic operability analysis is then applied to the feasible designs to identify the operable designs that are capable of rejecting the operational disturbances. Lastly, a closed-loop control measure is introduced to compare the performances of the different operable designs. The proposed approach is implemented in a modular membrane reactor to find a set of operable designs considering different natural gas wells, and the respective closed-loop nonlinear model predictive control performance of these units is evaluated.

An active primary frequency regulation strategy for grid integrated wind farms based on model predictive control

The increasing penetration level of wind power can reduce the dependency on fossil fuels, but it is accompanied with challenges such as the jeopardized dynamic stability of the frequency of power grid. As an effective method to improve frequency dynamic stability, primary frequency regulation (PFR) is conventionally based on the feedback of measured frequency, by which means it is conducted through analyzing historical information. By taking the predictive information into account, this paper introduces an active PFR (APFR) strategy for grid integrated wind farms (WFs) to enhance control performance of PFR. According to small-signal models of power system integrated with WFs based on conventional PFR and APFR, the state-space predictive models are established to obtain the predictive states. Then, to take active measures to deal with the electrical load disturbance, the predicted frequency is optimized in a receding horizon period by adjusting the PFR power reference of WFs flexibly. Moreover, a finite terminal weighting matrix based lyapunov function is presented to prove the asymptotic stability of the closed-loop model predictive control system. Finally, extensive case studies based on the standard test systems are performed to validate the effectiveness of the theoretical analysis and the superiority of APFR strategy.

Reactive Power Injection Capability of Buck–Boost Inverter With Unfolding Circuit

New emerging power inverter topologies are aiming at high-power density and efficiency with reliable performance. The recently proposed family of single-phase single-stage buck–boost inverters with output unfolding circuits have promising features for application in different fields. Nevertheless, the incapacity of injecting reactive power by the classical unfolding inverters has been assumed as its main drawback. Thus, our focus is on the reactive power injection capability of the single-stage buck–boost inverters with unfolding circuits. This attribute enables the converter to provide some extra ancillary services for friendly integration of the renewable energy resources and energy storage systems, providing support to the smart grid/microgrid, thus contributing to its power quality welfare. By means of a comprehensive analysis and implementation of proper closed-loop model predictive control, together with an adequate selection of the output capacitor, the single-inductor unfolding buck–boost inverter is capable of delivering reactive power to the utility grid. We used the simulation and experimental tests to validate the theoretical aspects.

Robust Min-Max Model Predictive Vehicle Platooning With Causal Disturbance Feedback

Platoon-based vehicular cyber-physical systems have gained increasing attention due to their potentials in improving traffic efficiency, capacity, and saving energy. However, external uncertain disturbances arising from mismatched model errors, sensor noises, communication delays and unknown environments can impose a great challenge on the constrained control of vehicle platooning. In this paper, we propose a closed-loop min-max model predictive control (MPC) with causal disturbance feedback for vehicle platooning. Specifically, we first develop a compact form of a centralized vehicle platooning model subject to external disturbances, which also incorporates the lower-level vehicle dynamics. We then formulate the uncertain optimal control of the vehicle platoon as a worst-case constrained optimization problem and derive its robust counterpart by semidefinite relaxation. Thus, we design a causal disturbance feedback structure with the robust counterpart, which leads to a closed-loop min-max MPC platoon control solution. Even though the min-max MPC follows a centralized paradigm, its robust counterpart can keep the convexity and enable the efficient and practical implementation of current convex optimization techniques. We also derive a linear matrix inequality (LMI) condition for guaranteeing the recursive feasibility and input-to-state practical stability (ISpS) of the platoon system. Finally, simulation results are provided to verify the effectiveness and advantage of the proposed MPC in terms of constraint satisfaction, platoon stability and robustness against different external disturbances.

Robust tube-based model predictive control with Koopman operators

Koopman operators are of infinite dimension and capture the characteristics of nonlinear dynamics in a lifted global linear manner. The finite data-driven approximation of Koopman operators results in a class of linear predictors, useful for formulating linear model predictive control (MPC) of nonlinear dynamical systems with reduced computational complexity. However, the robustness of the closed-loop Koopman MPC under modeling approximation errors and possible exogenous disturbances is still a crucial issue to be resolved. Aiming at the above problem, this paper presents a robust tube-based MPC solution with Koopman operators, i.e., r-KMPC, for nonlinear discrete-time dynamical systems with additive disturbances. The proposed controller is composed of a nominal MPC using a lifted Koopman model and an off-line nonlinear feedback policy. The proposed approach does not assume the convergence of the approximated Koopman operator, which allows using a Koopman model with a limited order for controller design. Fundamental properties, e.g., stabilizability, observability, of the Koopman model are derived under standard assumptions with which, the closed-loop robustness and nominal point-wise convergence are proven. Simulated examples are illustrated to verify the effectiveness of the proposed approach.

Bayesian optimization with reference models: A case study in MPC for HVAC central plants

We present a framework for exploiting reference models in Bayesian optimization (BO). Our approach is motivated by a model predictive control (MPC) tuning application for central heating, ventilation, and air conditioning (HVAC) plants. Evaluating the closed-loop performance of MPC by trial-and-error is time-consuming (e.g., a closed-loop simulation can involve solving thousands of optimization problems). The BO algorithm can accelerate this process by treating the functional relationship between the closed-loop performance of MPC and its tuning parameters (e.g., constraint back off terms and objective weights) as a black-box model and by systematically navigating the parameter space to maximize MPC performance. Traditional BO algorithms have been recently developed to tune controllers but such frameworks tend not to use pre-existing (prior) system information. In this work, we propose to incorporate such information in the form of reference models and we show that such models can be constructed in creative ways. Specifically, we propose to construct a reference model by evaluating the closed-loop performance of a low-complexity MPC controller. We show that the use of a reference model changes the goal of BO from learning the objective function to learning the residual function (error between the reference and the objective function), which is a much easier task. Specifically, we show that the use of a reference model can help BO to more judiciously sample the parameter estimate and more rapidly discover regions where the solution exists. This feature significantly reduces the number of function evaluations and can help avoid getting stuck in local minima. The effectiveness of our BO framework is demonstrated using a central HVAC plant study with realistic data. The reference model is built by training a kriging model based on data collected for 21 low-fidelity, closed-loop MPC simulations. Using this reference model, we show that our BO method can find the optimal constraint back-off terms within 3 high-fidelity, closed-loop simulations (total computation time of 20 h). In contrast, a traditional BO approach without a reference model requires 14 high-fidelity, closed simulations (total time of 28 h). Our approach thus reduces the computational time by 28%.

Development of Double Closed-loop Vector Control Using Model Predictive Control for Permanent Magnet Synchronous Motor

Vector control has been widely used to manipulate the permanent magnet synchronous motor (PMSM), in which the traditional double proportional integral (PI) controllers have commonly been utilized. However, it is difficult to set the suitable parameters of PI and maintain the PMSM performance under the different operating regimes. In order to solve these problems, a double closed-loop model predictive control (MPC) strategy based on the vector control has been presented for PMSM in this paper. Firstly, a simplified discrete model of PMSM is established in the d-q coordinate system without considering the interference. Then, the MPC is developed to substitute the PI controller in the speed-loop and the q-axis current-loop, respectively, and a double closed-loop MPC control system is formed. Finally, some case studies are carried out. The simulation and experimental results demonstrate that the presented MPC strategy improves the dynamic and steady-state performance of PMSM.

Model Predictive Control of Priced Timed Automata Encoded With First-Order Logic

Priced timed automata (PTA) are discrete-event system models with temporal constraints and a cost function and are used to pose optimal scheduling and routing problems. To date, solutions to these problems have been found offline and executed open loop.This open-loop control strategy makes it impossible to account for disturbances, i.e., changes in costs or scheduling constraints over time. To address this shortcoming, this work’s first contribution is a closed-loop model predictive control (MPC) framework for PTA, enabling decision-making based on real-time model updates. To ensure the feasibility of an MPC problem, it is often desirable to soften constraints. However, the contemporary PTA theory does not consider soft constraints. Thus, this work’s second contribution is to integrate constraint softening with PTA control by harnessing the capabilities of new solvers enabled by the recasting of the models and control problem into first-order logic by employing modified encoding schemes based on existing works. Finally, the proposed control framework and implementation are demonstrated in a simulation case study on the guidance of a product through a manufacturing system.

Robust Model Predictive Control With Bi-Level Optimization for Boiler-Turbine System

A robust model predictive control (MPC) with bi-level optimization is proposed for nonlinear boiler-turbine system. The nonlinear dynamics are described by multiple local models linearized at distinct operating points. A global linear parameter varying (LPV) model is constructed by combining the linearized local models. In order to combine the local models smoothly, an exponential weighting coefficient determined by the system states is applied. The bi-level optimization is proposed to optimize the control moves and control policy respectively. A controller model is designed as the inner optimization to calculate the suitable control policy under different operating conditions. The closed-loop robust MPC is designed to optimize the control moves to improve economic performance. Simulations under wide operating conditions have demonstrated the effectiveness of the proposed robust MPC method, by applying which the economic performance of the nonlinear boiler-turbine system is improved.

Robust Multi-Scenario Dynamic Real-Time Optimization with Embedded Closed-Loop Model Predictive Control

Abstract Economic optimization is a key tool in ensuring competitive chemical plant operation. Traditional steady-state real-time optimization (RTO) is suboptimal in many applications where the plant exhibits frequent transitions or slow dynamics, thus requiring the use of dynamic RTO (DRTO). Additionally, DRTO algorithms exhibit faster response when able to account for the behavior of the underlying model predictive control (MPC) systems. This work seeks to combine closed-loop (CL) prediction of the plant response under the action of MPC with a scenario based robust modeling approach to account for plant uncertainty. The CL prediction is handled by directly modeling the MPC calculations and reformulating the resulting multilevel optimization problem as a single-level mathematical program with complementarity constraints (MPCC). The proposed robust CL DRTO formulation is compared against a single-scenario nominal CL DRTO in terms of maximizing economic performance in a case study involving a nonlinear CSTR. The robust DRTO is shown to outperform the nominal DRTO in this metric on average across the scenarios tested.

Stability of Optimal Closed-Loop Cleaning Scheduling and Control with Application to Heat Exchanger Networks under Fouling

Heat exchanger networks subject to fouling are an important example of dynamic systems where performance deteriorates over time. To mitigate fouling and recover performance, cleanings of the exchangers are scheduled and control actions applied. Because of inaccuracy in the models, as well as uncertainty and variability in the operations, both schedule and controls often have to be revised to improve operations or just to ensure feasibility. A closed-loop nonlinear model predictive control (NMPC) approach had been previously developed to simultaneously optimize the cleaning schedule and the flow distribution for refinery preheat trains under fouling, considering their variability. However, the closed-loop scheduling stability of the scheme has not been analyzed. For practical closed-loop (online) scheduling applications, a balance is usually desired between reactivity (ensuring a rapid response to changes in conditions) and stability (avoiding too many large or frequent schedule changes). In this paper, metrics to quantify closed-loop scheduling stability (e.g., changes in task allocation or starting time) are developed and then included in the online optimization procedure. Three alternative formulations to directly include stability considerations in the closed-loop optimization are proposed and applied to two case studies, an illustrative one and an industrial one based on a refinery preheat train. Results demonstrate the applicability of the stability metrics developed and the ability of the closed-loop optimization to exploit trade-offs between stability and performance. For the heat exchanger networks under fouling considered, it is shown that the approach proposed can improve closed-loop schedule stability without significantly compromising the operating cost. The approach presented offers the blueprint for a more general application to closed-loop, model-based optimization of scheduling and control in other processes.