Application Of Model Predictive Control Research Articles

Comprehensive Review on Model Predictive Control Applied to Power Electronics

Model Predictive Control (MPC) in the field of power electronics has recently gained a lot of interest in the research community. Even though the computations are very complex in MPC algorithm, the availability of powerful processors has helped this approach to acquire a notable place in the area of control. They can take into account the nonlinearities and constraints very precisely. Having these advantages, they are found to be very attractive for controlling power converters and drives. This paper presents the review of growth and applications of MPC applied to power converters and drives. Some of the key elements like prediction model and its discretization, cost function, weighing factor and optimization algorithm are highlighted in this paper.

Nonlinear temperature regulation of solar collectors with a fast adaptive polytopic LPV MPC formulation

Temperature control in solar collectors is a nonlinear problem: the dynamics of temperature rise vary according to the fluid flowing through the collector and to the temperature gradient along the collector area. In this way, this work investigates the formulation of a Model Predictive Control (MPC) application developed within a Linear Parameter Varying (LPV) formalism, which serves as a model of the solar collector process. The proposed system is an adaptive MPC, developed with terminal set constraints and considering the scheduling polytope of the model. At each instant, two Quadratic Programming (QPs) programs are solved: the first considers a backward horizon of N steps to find a virtual model-process tuning variable that defines the best LTI prediction model, considering the vertices of the polytopic system; then, the second QP uses this LTI model to optimize performances along a forward horizon of N steps. The paper ends with a realistic solar collector simulation results, comparing the proposed MPC to other techniques from the literature (linear MPC and robust tube-MPC). Discussions regarding the results, the design procedure and the computational effort for the three methods are presented. It is shown how the proposed MPC design is able to outrank these other standard methods in terms of reference tracking and disturbance rejection.

Improving cooling load prediction reliability for HVAC system using Monte-Carlo simulation to deal with uncertainties in input variables

Accurate and reliable cooling load prediction is the basis for model predictive control (MPC) of HVAC systems. Cooling load prediction process is constrained by many input variables. These input variables contain different kinds of uncertainties that should not be ignored in pursuing a reliable prediction result. However, previous load prediction methods usually improve the prediction accuracy by optimizing model structure but fail to consider the influence of input variables uncertainties. To reduce the influence of uncertainty of input variables forecast data scientifically, this paper proposes an improved cooling load prediction reliability method in which the input variables are calibrated offline with Monte-Carlo simulations and stochastic treatment before inputting them into the prediction model. A machine learning algorithm (support vector machine, SVM) is used as the prediction model. Uncertainties in weather parameters, indoor heat gains, and historical cooling load were taken into consideration. Uncertainty analysis results showed that prediction accuracy with calibrated input variables was much better (R2 = 0.9627) than those predicted with forecast input data directly (R2 = 0.9488), which was closer to load prediction obtained by using measured input data (R2 = 0.9632). The coefficient of variation (CV) value using the calibrated input data was less than 15%. The reliable cooling load prediction results are beneficial for more informed, reliable decisions on MPC application, thereby promoting energy conservation potential of HVAC systems.

Current Control Method for Independent Double Three-phase Winding Interior Permanent Magnet Synchronous Motor Applying Model Predictive Control

Current Control Method for Independent Double Three-phase Winding Interior Permanent Magnet Synchronous Motor Applying Model Predictive Control

Leveraging Demand Flexibility by Exploiting Prosumer Response to Price Signals in Microgrids

The diffusion of distributed energy resources in distribution networks requires new approaches to exploit the users’ capabilities of providing ancillary services. Of particular interest will be the coordination of microgrids operating as an aggregate of demand and supply units. This work reports a model predictive control (MPC) application in microgrids for the efficient energy management of energy storage systems and photovoltaic units. The MPC minimizes the economic cost of aggregate prosumers into a prediction horizon by forecasting generation and absorption profiles. The MPC is compared in realistic conditions with a heuristic strategy that acts in a instant manner, without taking into account signals prediction. The work aims at investigating the effect that different types of energy tariffs have in enhancing the end-users’ flexibility, based on three examples of currently applied tariffs, comparing the two storage control modes. The MPC always achieves a better solution than the heuristic approach in all considered scenarios from the cost minimization point of view, with an improvement that is amplified by increasing the energy price variations between peak and off-peak periods. Furthermore, the MPC approach provides a cost saving when compared to the case considering a microgrid endowed with only photovoltaic units, in which no storage is installed. Findings in this work confirm that storage units better perform when some knowledge of future demand and supply trends is provided, ensuring an economic cost saving and an important service for the overall community.

Analytic Expressions in Stochastic Max-Plus-Linear Algebra and their Application in Model Predictive Control

The class of max-plus-linear systems can model discrete event systems with synchronization but no choice. Model mismatch and/or disturbances can be characterized as stochastic uncertainties. In stochastic max-plus-linear systems one often needs to compute the expectation of a max-plus-scaling (MPS) function or the chance constraint of a MPS function. The algorithms available in literature are either computationally too expensive or only give an approximation. In this article, we derive an analytic expression for both the expectation and the chance constraint of a MPS function. Both can be written in the form of a piecewise polynomial function in the components of the control variables. The analytic function can be derived offline and can be evaluated online in a quick and efficient way. We also show how the expressions can be used in a model predictive control setting and show the efficiency of the proposed approach with a worked example.

Highly Efficient and Robust Grid Connected Photovoltaic System Based Model Predictive Control with Kalman Filtering Capability

Renewable energy sources, especially photovoltaic (PV) ones, are gaining more and more interest due to the predicted lack of conventional sources over the coming years. That shortage is not the only concern, as environmental issues add to this concern also. Thus, this study proposes two-stage PV grid connected system, which is supported with extended Kalman filter (EKF) for parameter estimation. In the first stage, maximum power point tracking (MPPT) for the boost converter is accomplished using new MPPT method in which the switching state of the converter is directly generated after the measurement stage, so it is called direct switching MPPT technique. This technique is compared with the conventional finite control set model predictive control (FCS-MPC) method, where the design of the cost function is based on minimizing the error between the reference and the actual current. The reference current is obtained by employing perturb and observe (P&O) method. In the second stage, the two-level inverter is controlled by means of model predictive control (MPC) with reduced computation burden. Further, to overcome the parameter variations, which is a very common problem in MPC applications, an extended Kalman filter is utilized to eliminate the control algorithm’s dependency on the parameters by providing an efficient estimation. After the inverter, an RL filter is inserted to guarantee the quality of the currents injected into the grid. Finally, the system is validated using Matlab under different operating conditions of atmospheric variation and parameter changes.

Coalitional Model Predictive Control on Freeways Traffic Networks

This paper discusses the application of coalitional model predictive control (MPC) to freeways traffic networks, where the goal is reducing the time spent by the drivers through a dynamic setting of variable speed limits (VSL) and ramp metering. The prediction model METANET is used to represent the traffic flows evolution. The system behavior and objective function lead to a non-convex and non-linear optimization problem, which can only be solved in a centralized fashion for small networks. The underlying motivation of this paper is the continued advance of clustering methods in the control of large-scale and spatially distributed systems. The global freeway system is partitioned into a set of coupled sub-stretches, which in turn are assigned to the different agents involved in the control problem. These local controllers can dynamically assemble into coalitions to take coordinated measures. In this work, a top-down approach is considered: the bottom layer consists of the set of controllers that compute the VSL and ramp-metering across time; and the supervisory layer changes periodically the information exchange structure to promote coalitions of those controllers that bring greater performance to the global system. In this way, a balance is sought between optimality and efficiency. Finally, the coalitional approach is simulated on a stretch of traffic freeway where cooperation with adjacent sub-stretches is allowed.

Multiobjective Model Predictive Control of a Parabolic Advection-Diffusion-Reaction Equation

In the present paper, a multiobjective optimal control problem governed by a linear parabolic advection-diffusion-reaction equation is considered. The optimal controls are computed by applying model predictive control (MPC), which is a method for controlling dynamical systems over long or infinite time horizons by successively computing optimal controls over a moving finite time horizon. Numerical experiments illustrate that the proposed solution approach can be successfully applied although some of the assumptions which are necessary to conduct the theoretical analysis cannot be guaranteed for the studied tests.

Modelling and Control of Ensembles of Variable-Speed Air Conditioning Loads for Demand Response

Air conditioners (ACs) are an important resource for demand-response (DR) services in electricity networks and have motivated much research activity in recent years. Existing approaches to model and control aggregate AC demand largely focus on ensembles of fixed-speed (on/off) compressor technology. However, AC markets are dominated by variable-speed compressor technology, which is rapidly becoming widespread. This paper presents a mean-field, first-principle modelling formalism for the analysis and control of aggregate demand of heterogeneously distributed ensembles of variable-output compressor ACs (VOCACs). This formalism posits that the model structure of an individual VOCAC fitted with the mean values of the VOCAC parameters distributed in the ensemble can accurately represent the aggregate DR of the ensemble, in complete contrast with models for fixed-speed AC ensembles. The proposition is numerically validated in two prevalent DR applications of model predictive control (MPC): shaving peak demand and firming photovoltaic generation capacity. The proposed representative model is embedded in the MPC designs to predict the aggregate demand of a heterogeneously distributed ensemble of 1,000 VOCACs by centralised manipulation of temperature setpoints. The model is extended to enable DR by constraining power consumption, which is illustrated in an MPC implementation of the Australian/New Zealand Standard AS/NZS-4755 DR modes.

A Novel Modulated Model Predictive Control Applied to Six-Phase Induction Motor Drives

Model-based predictive control techniques, with finite set control, are considered an interesting option to control multiphase drives due to their control flexibility and fast dynamic response. However, those techniques have some drawbacks such as a high computational cost, poor ( $x-y$ ) currents reduction, and steady-state error, especially at high speeds. To improve some of these drawbacks, modulation stages have been presented as an alternative. However, some of those drawbacks have not been improved. This article proposes a novel approach to the classic predictive current control (PCC) applied to an asymmetrical six-phase induction machine, where a space vector modulation with specific vectors is used in order to improve the ( $x-y$ ) currents, the steady-state error and total harmonic distortion (THD) at high operation speeds. Experimental results are presented to demonstrate the characteristics of the proposed control technique in terms of current tracking, ( $x-y$ ) currents reduction and THD of stator currents compared to the classic PCC.

Predictive Position Control of Long-Stroke Planar Motors for High-Precision Positioning Applications

This article proposes a predictive position control of long-stroke planar motors to achieve micrometer-scale positioning under long-stroke time-varying trajectory tracking for use in high-precision positioning applications. The motivation consists in the potential application of model predictive control in long-stroke planar motors for high-precision positioning systems. This control is the first of its kind for planar motors. A dynamic model of a long-stroke planar motor developed in the laboratory is built, and then a predictive model is established to predict future positions of the motor. An additional term is introduced to a cost function to improve the positioning accuracy, which provides an output feedback control action to the motor for reducing the model error of the predictive model. By minimizing the cost function, an analytically explicit solution of the optimal control sequence is obtained, which makes the computational burden of the controller low. The stability of the control system is discussed based on the closed-loop state-space model. Moreover, the selection of stable control parameters is theoretically given. Simulation and experimental results demonstrate the effectiveness of the proposed control method of long-stroke planar motors for use in high-precision positioning applications.

Optimization of Supplier Development under Market Dynamics

Over the last decades, supplier development has become an increasingly important concept to remain competitive in today’s markets. Therefore, manufacturers invest resources in their suppliers to increase their abilities and, ultimately, to reduce their product prices. Thereby, most approaches found in the literature focus on long-term supplier development programs. Nevertheless, today’s volatile and dynamic markets require flexible approaches to deal with this complexity. We apply Model Predictive Control to optimize the number of supplier development projects in order to achieve flexibility while maintaining a certain level of security for all parties. Thereby, the article focusses on a multimanufacturer scenario, where two manufacturers aim to develop the same supplier. These manufacturers can establish different levels of horizontal collaboration. While previous results already show the benefits of applying this approach to a static scenario, this article extends this formulation by introducing market dynamics in the numerical simulations as well as into the optimization approach. Thus, the article proposes to derive regression models using real-world data. The article evaluates the effects of real-world market dynamics on two use cases: an automotive use case and a use case from the mobile phone sector. The results show that assuming market dynamics during the optimization leads to increased or at least close-to-equal revenues across the involved partners. The average increase ranges from approximately 1% to 5% depending on the type and magnitude of the dynamics. Thereby, the results differ depending on the selected collaboration scheme. While a full-cooperative collaboration scheme benefits the least from regarding dynamics in the optimization, it results in the highest overall revenue across all partners.

Application of model predictive control for reduced torque ripple in orthopaedic drilling using permanent magnet synchronous motor drive

A ubiquitous procedure in many fields of medical surgery is drilling of bones. Several consequential factors are identified that affect bone drilling that results in crack initialization, thermal necrosis, burr formation, etc. The dominant reason for these causes is the varying torque produced by the drilling motor, the main unit of the drilling kit. This varying torque produces varying mechanical vibrations that cause irreversible damages to the bones. Additionally, the wear and tear of the universal motors in the drilling unit are highly recorded. This work concentrates on implementing a permanent magnet synchronous machine (PMSM) for the orthopaedic drilling application along with the motor control using model predictive control (MPC) with maximum torque per ampere (MTPA) technique. The work proposes to reduce the torque ripple and flux ripple effectively along with the reduction of the current harmonics. The work is implemented in a simulation environment and in the RT-Lab environment. The performance of the proposed work in the steady state and dynamic state is compared with that of the conventional MPC, and the effectiveness of the proposed work is presented. This paper suggests PMSM as a suitable motor for the orthopaedic drilling application.

Cloud-based implementation of white-box model predictive control for a GEOTABS office building: A field test demonstration

Model predictive control (MPC) has been proven in simulations and pilot case studies to be a superior control strategy for large buildings. MPC can utilize the weather and occupancy schedule forecasts, together with the system model, to predict the future thermal behavior of the building and minimize the overall energy use and maximize thermal comfort. However, these advantages come with the cost of increased modeling effort, computational demands, communication infrastructure, and commissioning efforts. Thus a typical approach is to, often rapidly, simplify the building modeling and MPC optimization problem while paying a price of not reaching the full performance potential. It has been shown that by employing accurate physics-based models, MPC performance can be notably increased closer to its theoretical performance bound. However, implementation of such high-fidelity MPC in real buildings remains a challenge, resulting in a lack of successful field test studies. This work presents the methodology and field test demonstration of a computationally efficient implementation of the white-box MPC in an office building in Belgium. The detailed model of the building is based on first-principle physical equations. The deployment and supervision of MPC operation in a practical setting are supported by an automated cloud-based communication infrastructure. The motivating factor behind the cloud-based architecture is its compatibility with a commercially appealing control as a service concept. The building is equipped with a ground source heat pump (GSHP) and thermally activated building structures (TABS), where the combination of both is also known as GEOTABS. From a control perspective, GEOTABS buildings are particularly challenging systems due to large scale, complex heating, ventilation and air conditioning (HVAC) system, and slow dynamics with time delays. On the other hand, there is an increased potential for energy savings due to the high thermal mass, which acts as thermal storage. The MPC operation is demonstrated during the challenging transient seasons (switching between heating and cooling), and its performance is compared to a traditional rule-based controller (RBC). We provide a proof of concept of real MPC operation for the most difficult seasons with notable GSHP energy use savings equal to 53.5% and thermal comfort improvement by 36.9%. Other MPC applications found in the literature describe tests for only cooling or only heating, and up to now only for a black-box or a grey-box approach.

Closed-loop Subspace Identification of Dual-rate Non-uniformly Sampled System under MPC with Zone Control

Frequent changes in process dynamics make re-identification of a dynamic model prerequisite for sustainable application of model predictive control. When the process needs to comply with a particular operating range for product specification or safety requirement, the model should be re-identified in closed-loop. In addition to potentially poor exciting signal for the identification, another challenge is that many industrial processes are multi-rate systems whose variables have different sampling intervals. This paper proposes a re-identification method for dual-rate non-uniformly sampled systems under closed-loop with a MPC controller by lifting the original system. The proposed identification method provides accurate and realistic model compared to the model used before the identification is conducted. We also compare the identified model and the existing model by applying to MPC.

Optimal control of demand flexibility under real-time pricing for heating systems in buildings: A real-life demonstration

The identification, quantification, and control of demand flexibility is the major challenge for future grid operations and requires innovative methods and new control strategies. Optimal control strategies such as economic model predictive control have gained attention in building energy management systems. The present experimental case study demonstrates the application of an economic model predictive controller under real-time pricing, including day-ahead prices and imbalance prices. For real-time prices in balancing and spot markets, we introduce a method that presents a flexibility service to provide demand flexibility for a notification time of 1h<t<tdayend in advance. The flexibility service can be used as an ancillary service for innovative flexibility markets. The flexibility service includes a dynamic modification of the day-ahead prices to enable the adaption of energy consumption to errors in forecasting of renewable energy generation. The developed method was tested under real-life conditions, which also included the stochastic behaviour of occupants and the dynamic behaviour of the building and heating system. During the test periods, the controller managed the total operational costs of the heat pump’s electricity consumption and achieved a prediction performance of Root Mean Square Error between 0.17 and 0.22 kWh. To show the provision of demand flexibility, key performance indicators were quantified according to the categories 1) energy and power, 2) energy efficiency, and 3) energy costs. We introduce this categorization to present the benefits of using flexibility indicators along with conventional performance indicators in real-life applications.

Particle swarm optimisation in nonlinear model predictive control; comprehensive simulation study for two selected problems

Direct model predictive control applications for nonlinear systems can result in non-convex minimisation problems, which is additionally complicated if systems are non-minimum phase. In this paper, the Particle Swarm Optimisation (PSO) is applied for these global minimisation problems and tested on two selected nonlinear systems. Obtained results show that, in comparison to the sequential quadratic programming method, PSO is less vulnerable to local minima, and, with appropriate parameters, provides superior quality in nonlinear predictive control. The main results concerning PSO application show that the higher number of particles, comparing to the number of iterations, provides improved accuracy with limited computational burden; this way up to reduction of a proposed quality index is obtained preserving unchanged time of calculations. The performance is also boosted when after several iterations of the algorithm greater emphasis is put on the local search, which is achieved by appropriate learning factors and inertia weight.

Data-driven switching modeling for MPC using Regression Trees and Random Forests

Model Predictive Control is a well consolidated technique to design optimal control strategies, leveraging the capability of a mathematical model to predict a system’s behavior over a time horizon. However, building physics-based models for complex large-scale systems can be cost and time prohibitive. To overcome this problem we propose a methodology to exploit machine learning techniques (i.e. Regression Trees and Random Forests) in order to build a Switching Affine dynamical model (deterministic and Markovian) of a large-scale system using historical data, and apply Model Predictive Control. A comparison with an optimal benchmark and related techniques is provided on an energy management system to validate the performance of the proposed methodology.

Performance evaluation of a MPPT controller with model predictive control for a photovoltaic system

ABSTRACT Efficiency has been a major factor in the growth of photovoltaic (PV) systems. Different control techniques have been explored to extract maximum power from PV systems under varying environmental conditions. This paper evaluates the performance of a new improved control technique known as model predictive control (MPC) in power extraction from PV systems. Exploiting the ability of MPC to predict future state of controlled variables, MPC has been implemented for tacking of maximum power point (MPP) of a PV system. Application of MPC for maximum power point tracking (MPPT) has been found to result into faster tracking of MPP under continuously varying atmospheric conditions providing an efficient system. It helps in reducing unwanted oscillations with an increase in tracking speed. A detailed step by step process of designing a model predictive controller has been discussed. Here, MPC has been applied in conjunction with conventional perturb and observe (P&O) method for controlling the dc-dc boost converter switching, harvesting maximum power from a PV array. The results of MPC controller has been compared with two widely used conventional methods of MPPT, viz. incremental conductance method and P&O method. The MPC controller scheme has been designed, implemented and tested in MATLAB/Simulink environment and has also been experimentally validated using a laboratory prototype of a PV system.