Implementation Of Model Predictive Control Research Articles

Embedded linear model predictive control in field-programmable gate array using register-transfer level implementation and floating-point representation applied to a quadrotor system model

Model predictive control is increasingly becoming a popular control strategy for a wide range of applications in both industry and academia, mainly motivated by its ability to systematically handle constraints imposed on a system, regardless of its nature. However, this generates high computational demands, limiting the applicability of model predictive control. Field-programmable gate arrays are reconfigurable hardware platforms that allow the parallel implementation of model predictive control, accelerating such algorithms, but most works found in the literature opt to use high-level synthesis tools and fixed-point numeric representation to generate embedded controllers, resulting in faster-designed solutions but not exactly efficient and flexible ones, that can be applied to different scenarios. Regarding such matter, this work proposes the manual implementation (register-transfer level implementation) of linear model predictive control and the usage of floating-point numeric representation applied to a quadrotor system. The initial results obtained using the proposed controller are presented in this article, achieving 29.34 ms of calculation time at 50 MHz for the attitude control of a quadrotor model containing twelve states and four control outputs.

Field-Ready Implementation of Linear Economic Model Predictive Control for Microgrid Dispatch in Small and Medium Enterprises

The increasing share of distributed renewable energy resources (DER) in the grid entails a paradigm shift in energy system operation demanding more flexibility on the prosumer side. In this work we show an implementation of linear economic model predictive control (MPC) for flexible microgrid dispatch based on time-variable electricity prices. We focus on small and medium enterprises (SME) where information and communications technology (ICT) is available on an industrial level. Our implementation uses field devices and is evaluated in a hardware-in-the-loop (HiL) test bench to achieve high technological maturity. We use available forecasting techniques for power demand and renewable energy generation and evaluate their influence on energy system operation compared to optimal operation under perfect knowledge of the future and compared to a status-quo operation strategy without control. The evaluation scenarios are based on an extensive electricity price analysis to increase representativeness of the simulation results and are based on the use of historic real-world measurements in an existing production facility. Due to real-world restrictions (imperfect forecast knowledge, implementation on field hardware, power fluctuations), between 72.2% and 85.5% of the economic optimum (rather than 100%) is reached. Together with reduced operation cost, the economic MPC implementation on field-typical industrial ICT leads to an increased share of renewable energy demand.

Application Study of Newton-Raphson-Type Nonlinear MPC for Hydrostatic Transmissions Under Disturbance and System Uncertainty

Model predictive control is well established and has a huge practical relevance in many industrial applications, especially for chemical or thermal plants. This paper presents the design and the implementation of a nonlinear model predictive control aiming at an accurate tracking control of desired output trajectories under disturbances and uncertainties for a nonlinear hydrostatic transmission system with multiple control inputs, which represents a fast mechatronic system. The benefit of this solution is that it can be easily adapted to either velocity tracking control or torque tracking control -- which is not the case with alternative model-based approaches. The control design is based on a numerical optimization within a moving horizon using the Newton-Raphson method in combination with the optimization-over-some variables technique. The unmeasurable system state variables as well as the system disturbances are reconstructed by an unscented Kalman filter which is well suited for nonlineaer systems subject to process and measurement noise. The proposed control scheme is investigated by simulations and experimentally validated on a test rig at the Chair of Mechatronics, University of Rostock. The results indicates the robustness of the proposed control structure by a high tracking accuracy despite system disturbances and uncertainties.

Integrating a dynamic multiscale drying model into a closed loop control strategy for laboratory spray dryer

Spray drying is a widely used unit operation in synthesis of particles for production of chemicals, food, and pharmaceuticals. However, accurate control and development of this unit remains an elusive task because of the complex interactions of variables and phenomena. In this paper, we adopt and present a dynamic model of the complete drying process for a laboratory spray dryer. The dynamic mathematical model, which integrates atomization, evaporation, and particle formation models, is described by mass and energy balances. The model can predict temperature, residual moisture, and particle size of the produced powder. Model predictions are verified through datasets collected from a lab-scale spray dryer. A data-driven model based on the dynamic model is produced to interface with the control strategy. A model predictive control (MPC) strategy is then adopted to address the highly cross-coupled effects among different components of the dryer and guarantee desired product quality measures. Successful MPC implementation on the drying system is addressed, including trajectory tracking and disturbance rejection scenarios.

Synthesis of control Lyapunov functions and stabilizing feedback strategies using exit‐time optimal control Part II: Numerical approach

AbstractThis paper continues the study (Yegorov, Dower, and Grüne et al.) and develops a curse‐of‐dimensionality‐free numerical approach to feedback stabilization, whose theoretical foundation was built in Yegorov et al. and involved the characterization of control Lyapunov functions (CLFs) via exit‐time optimal control. First, we describe an auxiliary linearization‐based technique for the construction of a local CLF and discuss how to determine its appropriate sublevel set that can serve as the terminal set in the exit‐time optimal control problem leading to a global or semi‐global CLF. Next, the curse of complexity is addressed with regard to the approximation of CLFs and associated feedback strategies in high‐dimensional regions. The goal is to enable for efficient model predictive control implementations with essentially faster (though less accurate) online policy updates than in case of solving direct or characteristics‐based nonlinear programming problems for each sample instant. We propose a computational approach that combines gradient enhanced modifications of the Kriging and inverse distance weighting frameworks for scattered grid interpolation. It in particular allows for convenient offline inclusion of new data to improve obtained approximations (machine learning can be used to select relevant new sparse grid nodes). Moreover, our method is designed so as to a priori return proper values of the CLF interpolant and its gradient on the entire terminal set of the considered exit‐time optimal control problem. Supporting numerical simulation results are also presented.

Configuring the Objective Function of A Model Predictive Controller for An Integrated Thermal-Electrical Decentral Renewable Energy System

With the increasing integration of decentral renewable energy systems in the residential sector, the opportunity to enhance the control via model predictive control is available. In this article, the main focus is to investigate the objective function of the model predictive controller (MPC) of an integrated thermal-electrical renewable energy system consisting of photovoltaics, solar thermal collectors, fuel cell along with auxiliary gas boiler and electricity grid using electrical and thermal storage in a single-family house. The mathematical definition of the objective function and the depth of detailing the objectives are the prime focus of this particular article. Four different objective functions are defined and are investigated on a day-to-day basis in the selected six representative days of the whole year for the single-family house in Ehingen, Germany with a white-box simulation model simulated using TRNSYS and MATLAB. Using the clustering technique then the six representative days are weighted extrapolated to a whole year and the outcomes of the whole year MPC implementation are estimated. The results show that the detailing of the mathematical model, even though is time and personnel consuming, does have its advantages. With the detailed objective function, 9% more solar thermal fraction; 32% less power-to-heat at an expense of 32% more gas boiler usage; 6% more thermal system effectiveness along with 10% increased total self-consumption fraction with 16% decrease in space heating demand, 492 kWh more battery usage and 66% reduced fuel cell production is achieved by the MPC in comparison to the status quo controller. Except for the effectiveness of the thermal system with increased gas boiler usage, which occurs due to less power-to-heat, the detailed objective function in comparison to the simple mathematical definition does evidently increase the smartness of the MPC.

Universal identification and control of industrial manufacturing equipment as a service

Rapid prototyping as well as retrofitting and digitization of legacy manufacturing equipment often needs design and application of closed loop controllers. The analysis and modeling for such systems like energy-conversion or material transport devices is labor-intensive and needs process understanding. This paper presents a universal approach of identification and closed loop control of arbitrary linear systems delivered through web services using OPC UA as a standardized industrial communication interface. The identification service was used to model the dynamics of a 6-DOF industrial robot and a laboratory-scale water plant containing two separately controllable pumps. The control service successfully controlled the robot’s linearizable axes and the water plant’s pumps by using their respective identified state-space models. To evaluate the performance of the controllers in terms of stability, accuracy, and time response, target trajectories and disturbances like signal noise and latency in communication were introduced. Simulation and laboratory experiments show promising results for control of diverse systems with varying time-constants and imply broad applicability. So, this paper brings a guideline to efficiently implement model predictive control in manufacturing.

A thermal comfort-driven model predictive controller for residential split air conditioner

In the wake of rising cooling electricity demand in the residential building sector, there is a need to contemplate how the residential air conditioners (ACs) are operated. This study explores the residential split AC's capacity regarding its ability to provide thermal comfort to the occupants instead of just cooling through the implementation of thermal comfort-driven model predictive control (MPC). The proposed control technique is illustrated by implementing it in a real residential house. To integrate thermal comfort feedback into the controller while optimizing AC's set-point, a real-time co-simulation methodology has been developed, using EnergyPlus and Simulink. A data-driven model is used in the MPC framework to predict the set-point of AC, accounting for the environmental variables as measured disturbances and thermal comfort index, i.e., predictive mean vote (PMV) as a constraint on output. A Raspberry Pi-Arduino-based embedded system is developed to actuate the AC's set-point during real-time co-simulation. Experimental data is used to develop the numerical model of the system. The simulation study has been performed to observe the proposed control technique's value addition over the base cases. Simulation data shows that AC operated with the proposed control technique consumes (8.8–17.5%) less cooling energy compared to the base cases.

Model Predictive Control with Adaptive Building Model for Heating Using the Hybrid Air-Conditioning System in a Railway Station

A model predictive control (MPC) system with an adaptive building model based on thermal-electrical analogy for the hybrid air conditioning system using the radiant floor and all-air system for heating is proposed in this paper to solve the heating supply control difficulties of the railway station on Tibetan Plateau. The MPC controller applies an off-line method of updating the building model to improve the accuracy of predicting indoor conditions. The control performance of the adaptive MPC is compared with the proportional-integral-derivative (PID) control, as well as an MPC without adaptive model through simulation constructed based on a TRNSYS-MATLAB co-simulation testbed. The results show that the implementation of the adaptive MPC can improve indoor thermal comfort and reduce 22.2% energy consumption compared to the PID control. Compared to the MPC without adaptive model, the adaptive MPC achieves fewer violations of constraints and reduces energy consumption by 11.5% through periodic model updating. This study focuses on the design of a control system to maintain indoor thermal comfort and improve system efficiency. The proposed method could also be applied in other public buildings.

Weight-scheduling for linear time-variant model predictive wind turbine control toward field testing

Modern multi-megawatt wind turbines require powerful control algorithms which consider several control objectives at the same time and respect process constraints. Model predictive control (MPC) is a promising control method and has been a research topic for years. So far, very few studies evaluated MPC algorithms in field tests. This work aims to prepare a real-time MPC system for a full-scale field test in a 3 MW wind turbine. To this end, we introduce a weight-scheduling scheme for a linear time-variant MPC in order to ensure control operation over the entire operating range from the partial to the full load range. We use a rapid control prototyping process, in particular with comprehensive software-in-the-loop (SiL) tests, in order to design and validate the MPC system for the field test.In this contribution, we present the implementation of the linear time-variant MPC with weight-scheduling to be tested in the field test. With the weight-scheduling for the optimization problem inside the MPC, we achieved good performance over the entire operating range of the wind turbine. In the SiL tests, the proposed MPC algorithm achieved loads, comparable to the baseline controller of the wind turbine and improved the reference tracking of the power output and the rotational speed. The proposed linear time-variant MPC with weight-scheduling is fully validated in the presented software-in-the-loop tests and is ready for full-scale field test in the 3 MW wind turbine. We present the experimental field test results of the introduced MPC system in a separated contribution.

Implementation of model predictive control in a large-sized, low-energy office building

Modern and energy-optimized buildings often lack an intelligent and advanced control strategy. Instead, conventional rule-based control (RBC) strategies are still mainly used today, which do not exploit the full performance potential of these buildings. Model predictive control (MPC) has proven in simulation studies and pilot cases to be a promising approach to reduce the energy consumption of buildings, while improving occupants’ comfort. However, there is still a lack of implementing MPC in real, large-scale and fully occupied buildings, to further prove this potential in real building operations. This paper describes the implementation and operation of MPC in a large-sized, low-energy office building. The MPC controller was implemented in a section of the building during a three-month test period from February to April 2020, controlling the supply temperature of heating circuits for thermally activated building systems (TABS). Its performance was compared to the default rule-based control which is active in the other building sections. This allows for a detailed evaluation of MPC versus RBC under identical environmental and operational conditions. The MPC controlled building section used 30% less heating energy than RBC controlled building sections, while the existing high level of thermal comfort could be maintained. Especially in transition periods (i. e. interseasonal periods like late winter/early spring) , the MPC is superior to the conventional heating-curve based control strategy, with heating energy savings of 75%.

Annual Evaluation of a Model Predictive Controller in an Integrated Thermal-Electrical Renewable Energy System Using Clustering Technique

Abstract Whitebox model in a model predictive controller (MPC) for energy systems, though does help in developing an accurate system model, requires a long time for optimization. In this article, an adaptation of the clustering technique used in hardware-in-the-loop testbench is proposed for evaluation of the MPC on an annual scale with selected six representative days in a year for that particular system and location. Initially, the various input parameters for clustering (algorithm, distance metric, and datapoint input dimensions) are studied for the selected thermal-electrical integrated renewable energy system (with solar thermal collectors, auxiliary gas boiler, stratified thermal storage, micro fuel cell combined heat and power (FC-CHP), photovoltaic system, a lithium-ion battery) for a Sonnenhaus standard single-family residential building. Finally, the proposed methodology is used to compare the annual derived energy values and key performance indicators (KPIs) for an MPC implementation with a status quo controller as a reference. Also, extreme exemplary weather days are investigated as the selected representative days were only average days in each season. Despite the conflict of using the FC-CHP on cold sunny days, instead of utilizing the battery and increased gas boiler energy input, a 9% increase in decentral system fraction is reported. Via the use of MPC instead of status quo controllers, the results indicate −18% space heating (SH) demand; +30% solar thermal energy production; −29% gas boiler energy supply; −52% power-to-heat thermal energy supply; −52% electrical fuel cell production; +240 kWh battery utilization; and −52% reduced grid import at the expense of 1.2% of the electrical load demand as grid import.

Convex model predictive control for collision avoidance

This manuscript proposes a model predictive control for collision avoidance for the regulation problem of deterministic linear systems, which provides a priori guarantees of strong system theoretic properties, such as positive invariance and asymptotic stability, and high computational efficiency. Notion of safe distance sets is introduced, and also utilized as a novel approach to ensure collision avoidance via suitably defined convex constraints. The proposed convex model predictive control for collision avoidance is obtained by employing interactive strategic-tactical structure for overall decision-making. The strategic stage of the overall algorithm employs direct algebraic manipulations in order to construct safe distance sets that ensure collision avoidance. The tactical stage of the overall algorithm employs strictly convex quadratic programs for the optimization of local finite horizon predicted control processes. The dynamically compatible interaction of strategic and tactical stages of the overall algorithm is ensured by construction, which guarantees structural and computational benefits. These novel and unique features effectively enable both real time implementation and real life utilization of model predictive control for collision avoidance.

Finite-word-length FPGA implementation of model predictive control for ITER resistive wall mode control

In advanced tokamak scenarios, active feedback control of unstable resistive wall modes (RWM) may be required. A RWM is an instability due to plasma kink at higher plasma pressure, moderated by the presence of a resistive wall surrounding the plasma. We address the dominant kink instability associated with the main non-axisymmetric (n = 1) RWM, described by the CarMa model. Model predictive control (MPC) is used, with the aim of enlarging the domain of attraction of the unstable RWM modes subject to power-supply voltage constraints. The implementation of MPC is challenging, because the related quadratic programming (QP) on-line optimization problems must be solved at a sub-ms sampling rate. Using complexity-reduction pre-processing techniques and a primal fast gradient method (FGM) QP solver, sufficiently short computation times for ITER are reachable using a standard personal computer (PC). In this work we explore even faster finite-word-length (FWL) implementation using field-programmable gate arrays (FPGA), which would facilitate experimental testing of such control algorithms on dynamically faster medium-sized tokamaks, and compare the computational accuracy and time with the PC implementation.

Nonlinear model predictive control for distributed parameter systems by time–space‐coupled model reduction

AbstractNonlinear high‐dimensional distributed parameter systems (DPSs) described by sets of parabolic partial different equations (PDEs) exhibit a dominant, low‐dimensional slow behavior that can be captured using model reduction. A time–space‐coupled model reduction architecture combining encoder–decoder networks with recurrent neural networks (RNNs) was presented in our previous work, for modeling the spatiotemporal dynamics of DPSs without recourse to the governing equations. In this work, we further understand the stability of the training dynamics of the deep architecture by using the Lyapunov exponents (LEs). Subsequently, we construct nonlinear model predictive control (MPC) formulations for the DPS based on the learned, dimensional‐reduced model. We use a path‐integral optimal control algorithm for MPC implementation to avoid any analytic derivatives of the dynamics. The effectiveness of integration of a deep neural network‐based model with MPC is demonstrated in a tubular reactor with recycle cases. The results of the simulation also show that the LE can serve as a readout of training stability for the learned dynamical model.

A Methodology for the Enhancement of the Energy Flexibility and Contingency Response of a Building through Predictive Control of Passive and Active Storage

Optimal management of thermal energy storage in a building is essential to provide predictable energy flexibility to a smart grid. Active technologies such as Electric Thermal Storage (ETS) can assist in building heating load management and can complement the building’s passive thermal storage capacity. The presented paper outlines a methodology that utilizes the concept of Building Energy Flexibility Index (BEFI) and shows that implementing Model Predictive Control (MPC) with dedicated thermal storage can provide predictable energy flexibility to the grid during critical times. When the utility notifies the customer 12 h before a Demand Response (DR) event, a BEFI up to 65 kW (100% reduction) can be achieved. A dynamic rate structure as the objective function is shown to be successful in reducing the peak demand, while a greater reduction in energy consumption in a 24-hour period is seen with a rate structure with a demand charge. Contingency reserve participation was also studied and strategies included reducing the zone temperature setpoint by 2∘C for 3 h or using the stored thermal energy by discharging the device for 3 h. Favourable results were found for both options, where a BEFI of up to 47 kW (96%) is achieved. The proposed methodology for modeling and evaluation of control strategies is suitable for other similar convectively conditioned buildings equipped with active and passive storage.

Design and implementation of model predictive control for microgrid energy system with power quality improvement features

ABSTRACT The harmful outcome of fossil fuel emission and growing concern about the deficiency of power resources has started a new requirement of cleaner, reliable, and sustainable energy resources. Thus, wind power and solar energy based systems are the best emerging energy sources amongst the various renewable energy resources. The proposed system involves a boost converter with an inverter circuit, where first solar and wind energy is regulated, and the inverter is employed for grid integration. In the proposed work, model predictive control is applied to a 3-phase inverter and it uses a model to estimate the predictions of upcoming values of the system voltage for a provided sequence of voltages. Further, the cosine firing angle arrangement is also used for adjusting the output voltage of the boost converter. The three-phase inverter is also employed as a harmonic reduction device, this allows the utility grid to continuously supply or absorb the good quality of power. The proposed approach escapes the use of nonlinear and linear controllers and it does not include the modulator, hence this is a simple method and the control algorithm is easy to implement. The outcomes show that the planned scheme has excellent performance.

Data-driven fatigue-oriented MPC applied to wind turbines Individual Pitch Control

Horizontal Axis Wind Turbine (HAWT) rotor is a system whose components are particularly exposed to fatigue damage, due to non-uniform winds and the rotating nature of the rotor. Individual Pitch Control (IPC) can help alleviating the fatigue loads on the rotor blades by rotating the blades independently from each other on their longitudinal axis. However, reducing the blades fatigue damage is often compensated by an increase in pitch activity, damaging the blade pitch actuators. An IPC regulator must thus optimize a trade-off between the fatigue damage of the blades and blade pitch actuators. This paper presents the derivation and implementation of a fatigue-oriented adaptive Model Predictive Control (MPC) IPC regulator using a data-driven fatigue-oriented cost function. This MPC allows to efficiently optimize the IPC fatigue trade-off and significantly reduce the expectancy of an HAWT rotor economic fatigue cost, compared to a finely tuned non-adaptive MPC. The methodology used for the derivation of the presented MPC allows to efficiently reduce an economic fatigue cost, while limiting the sensitivity to controller tuning.

Maximum wind energy extraction of large-scale wind turbines using nonlinear model predictive control via Yin-Yang grey wolf optimization algorithm

Wind energy extraction for large-scale variable-speed wind turbines could be improved by nonlinear model predictive control. However, the latter entails a sequential global optimization problem with a nonconvex cost function that brings about the heavily computational burden and impedes its real-time application. In this paper, a novel nonlinear model predictive control via Yin-Yang grey wolf optimization algorithm is proposed for maximum wind energy extraction of wind turbines. A dynamic optimization problem with both state and control constraints is constructed, and the single-objective nonlinear function is formulated by using a weighting factor to integrate the extracted wind energy and the generator torque variation within a prediction period of several seconds. On this basis, a complete framework of the nonlinear model predictive control via intelligent algorithm is developed to offer a new paradigm for the design and implementation of the nonlinear model predictive control for wind turbines. Specifically, a new Yin-Yang grey wolf optimization algorithm is proposed, in which the concept of balance between cooperation and competition inspired by Yin-Yang-pair optimization is adopted to achieve the efficient convergence and global optimum. Simulation results verify the superiority of the proposed nonlinear model predictive control via the new Yin-Yang grey wolf optimization algorithm.

Streamlining Active Set Method in MPC using Cache Memory

Abstract This paper investigates how various caching strategies can reduce the computational effort of the active set method (ASM) applied to solve constrained model predictive control problems with quadratic objective function and linear constraints. Specifically, we show that during closed-loop operation, the active set method often re-visits the same combination of active constraints while searching for optimal control inputs by factoring Karush-Kuhn-Tucker (KKT) systems. By storing the factors of the corresponding KKT system in a cache, these repetitive calculations can be simplified to a mere cache search and evaluation of the appropriate factors. Since the cache memory is typically fairly restricted, the efficiency of the scheme depends on how well the cache space can be utilized. In particular, when the cache is fully utilized, and a new element needs to be stored, the cache replacement policy needs to determine which element should be removed from the cache to make space for the new one. In the paper, we scrutinize various cache replacement policies and how well they work as a function of the cache size. The results show that by using a cache of modest size, the number of computational operations performed by the ASM can be reduced by up to 80%, thus significantly accelerating the implementation of model predictive control.