Economic Model Predictive Control Research Articles

Hierarchical nonlinear model predictive control of offshore hybrid power systems

This paper presents an approach for controlling ofshore hybrid power systems consisting of gas turbines, offshore wind, and batteries for satisfying an exogenous power demand. A hierarchical controller is developed comprising a high-level economic nonlinear model predictive controller that distributes the power demand according to some economic objective, a low-level nonlinear tracking model predictive controller that actuates on the hybrid power system, and a nonlinear moving horizon estimator to estimate the system state. Simulation results and concluding remarks reveal the advantage of such a hierarchical approach for a simple simulation study.

Optimizing methane and methanol production from integrated steelworks process off-gases through economic hybrid model predictive control

Within integrated steelworks, process off-gases are important energy carriers. After suitable treatment, they are typically exploited for heating purposes and for production of steam and electricity. However, their main compounds (CO x and H 2 ) can also be valorized through synthesis reactors, which provide valuable products, such as methane and methanol, while reducing CO 2 emissions. To this aim, large quantities of cheaply and greenly produced hydrogen must be available to enrich process off-gases and make them suitable to the synthesis processes. The enrichment and valorization of process off-gases requires an advanced control system that ensure optimal economic valorization and safe operation of the plants. This paper proposes a solution relying on a dispatch controller based on Economic Hybrid Model Predictive Control, which integrates a set of process models based on physical/chemical laws and machine learning-based models for disturbances forecasting. The controller implements a mixed integer linear programming approach after the linearization of the dynamics of controlled systems every control step. The optimization problem also includes a set of constraints related to the operating condition limits of each equipment. Economic and environmental impacts of the proposed approach are compared with respect to the standard use of process off-gases. The feasibility of the approach strictly depends on the cost of hydrogen, and, in the case of low-cost green electricity sources, the results are highly encouraging. The approach was successfully tested on-line to supervise the operation of pilot methanol and methane reactors.

Actuator Cyberattack Handling Using Lyapunov-based Economic Model Predictive Control

Cybersecurity has gained increasing interest as a consequence of the potential impacts of cyberattacks on profits and safety. While attacks can affect various components of a plant, prior work from our group has focused on the impact of cyberattacks on control components such as process sensors and actuators and the development of detection strategies for cybersecurity derived from control theory. In this work, we provide greater focus on actuator attacks; specifically, we extend a detection and control strategy previously applied for sensor attacks and based on an optimization-based control technique called Lyapunov-based economic model predictive control (LEMPC) to detect attacks impacting the control action applied by the actuators when the state measurements provided to the controller are accurate. Closed-loop stability guarantees are rigorously derived. A continuous stirred tank reactor is simulated to elucidate aspects of the detection strategy proposed.

Convex Neural Network-Based Cost Modifications for Learning Model Predictive Control

Developing model predictive control (MPC) schemes can be challenging for systems where an accurate model is not available, or too costly to develop. With the increasing availability of data and tools to treat them, learning-based MPC has of late attracted wide attention. It has recently been shown that adapting not only the MPC model, but also its cost function is conducive to achieving optimal closed-loop performance when an accurate model cannot be provided. In the learning context, this modification can be performed via parametrizing the MPC cost and adjusting the parameters via, e.g., reinforcement learning (RL). In this framework, simple cost parametrizations can be effective, but the underlying theory suggests that rich parametrizations in principle can be useful. In this paper, we propose such a cost parametrization using a class of neural networks (NNs) that preserves convexity. This choice avoids creating difficulties when solving the MPC problem via sensitivity-based solvers. In addition, this choice of cost parametrization ensures nominal stability of the resulting MPC scheme. Moreover, we detail how this choice can be applied to economic MPC problems where the cost function is generic and therefore does not necessarily fulfill any specific property.

Economic Model Predictive Control for Post-Combustion CO2 Capture System Based on MEA

For the post-combustion CO2 capture (PCC) system, the time variability of the economic performance is key to the production process of such an actual industrial process. However, the performance index used by the conventional model predictive control (MPC) does not reflect the economy of the production process, so the economic cost function is used instead of the traditional performance index to measure the economy of the production process. In this paper, a complete dynamic model of the PCC system is constructed in Aspen Plus Dynamics. The effectiveness of the model is verified by dynamic testing; subspace identification is carried out using experimental data, a state-space equation between flue gas flow and lean solvent flow; the CO2 capture rate is obtained; and dynamic models and control algorithm models of accused objects are established in Matlab/Simulink. Under the background of the environmental protection policy, an economic model predictive control (EMPC) strategy is proposed to manipulate the PCC system through seeking the optimal function of the economic performance, and the system is guaranteed to operate under the economic optimal and excellent quality of the MPC control strategy. The simulation results verify the effectiveness of the proposed method.

Supervisory Control for NO$_\text{x}$ Emission Compliance of Heavy-Duty Vehicles

This article provides a detailed description of a supervisory control problem for a heavy-duty vehicle equipped with a diesel engine and an exhaust aftertreatment system (EATS). The control problem considers the coupling between the engine and EATS and assumes the availability of predictive driving information for a long horizon. The article also proposes a computationally efficient supervisory control algorithm, which is implemented in an existing engine electronic control unit. The algorithm is based on distributed economic nonlinear MPC. It minimizes total fuel consumption (by the diesel engine and EATS) and fulfils Euro VI real-driving and world harmonized transient cycle based NO <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_\text{x}$</tex-math></inline-formula> emission legislation for the heavy-duty diesel vehicle. The performance of the algorithm is evaluated using a high-fidelity simulation platform, which includes a validated GT-POWER model of a 13 L turbo compound diesel engine and the first-principles model of an EATS. Simulation results show that the supervisory controller has 1.7% less total fuel consumption, and 88.4% less NH <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_3$</tex-math></inline-formula> slip, compared to a baseline controller, to achieve the same real-driving NO <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_\text{x}$</tex-math></inline-formula> emission.

Framework for produced water discharge management with flow-weighted mean concentration based economic model predictive control

Offshore discharges of produced water (PW) is heavily regulated by government authorities through flow-weighted mean concentration (FWMC). To cope with regulations, treatment facilities are commissioned to reduce the oil content in water. However, disturbances may affect their performance, leading to regulation infringement. Produced water re-injection (PWRI) facilities can affect the FWMC by reducing oil discharge, and increasing re-injection. This strategy can aid the offshore facility in achieving the regulation requirements. Nevertheless, if improperly done, energy consumption can significantly increase, and regulations might still be violated. Therefore, we developed a framework for an Economical Model Predictive Control (EMPC) based on FWMC. It comprises an EMPC to which FWMCs are added as constraints; and a logic algorithm to maintain the necessary conditions for feasibility of the environmental constraint. Closed-loop results show that this strategy complies with environmental regulation, and adapts discharges of PW and pumping energy consumption based on facilities’ historical data.

Periodically time-varying economic model predictive control with applications to nonlinear continuous stirred tank reactors

The economic cost functions can be periodically time-varying due to various economic factors such as the variations of product prices, energy consumptions, operating costs and customer demand changes. These time-varying parameters can lead to instability because the optimal steady state may not be asymptotically stable. In this paper, a periodically time-varying economic model predictive control algorithm is proposed. As the time-varying parameters in the economic cost functions vary, the average constraints are used to enforce the convergence without modifying the original economic cost functions so the transient economic performance can be improved. The time-varying terminal regions are included in the economic optimization problem in order to ensure recursive feasibility. The asymptotic convergence is proved by using the Lyapunov-like analysis. The developed predictive control algorithm is applied to the nonlinear continuous stirred tank reactors in order to gain the highest economic profits.

Modular Model Composition for Rapid Implementations of Embedded Economic Model Predictive Control in Microgrids

Economic model predictive control in microgrids combined with dynamic pricing of grid electricity is a promising technique to make the power system more flexible. However, to date, each individual microgrid requires major efforts for the mathematical modelling, the implementation on embedded devices, and the qualification of the control. In this work, a field-suitable generalised linear microgrid model is presented. This scalable model is instantiated on field-typical hardware and in a modular way, so that a class of various microgrids can be easily controlled. This significantly reduces the modelling effort during commissioning, decreases the necessary qualification of commissioning staff, and allows for the easy integration of additional microgrid devices during operation. An exemplary model, derived from an existing production facility microgrid, is instantiated, and the characteristics of the results are analysed.

Robust economic model predictive control with zone tracking

This paper presents a robust economic model predictive control (EMPC) formulation with zone tracking for discrete-time uncertain nonlinear systems. The proposed design ensures that the zone tracking objective is achieved in finite steps and at the same time optimizes the economic performance. In the proposed design, instead of tracking the original target zone, a robust control invariant set within the target zone is determined and is used as the actual zone tracked in the proposed EMPC. This approach ensures that the zone tracking objective is achieved within finite steps and once the zone tracking objective is achieved (the system state enters the robust control invariant set), the system state does not come out of the target zone anymore. To optimize the economic performance within the zone in the presence of disturbances, we introduce the notion of risk factor in the controller design. An algorithm to determine the economic zone to be tracked is provided. The risk factor determines the conservativeness of the controller and provides a way to tune the EMPC for better economic performance. A nonlinear chemical example is presented to demonstrate the performance of the proposed formulation.

Energy‐efficient cabin climate control of electric vehicles using linear time‐varying model predictive control

AbstractA cabin climate control system, often referred to as a heating, ventilation, and air conditioning (HVAC) system, is one of the largest auxiliary loads of an electric vehicle (EV), and the real‐time optimal control of HVAC brings a significant energy‐saving potential. In this article, a linear‐time‐varying (LTV) model predictive control (MPC)‐based approach is presented for energy‐efficient cabin climate control of EVs. A modification is made to the cost function in the considered MPC problem to simplify the Hessian matrix in utilizing quadratic programming for real‐time computation. A rigorous parametric study is conducted to determine optimal weighting factors that work robustly under various operating conditions. Then, the performance of the proposed LTV‐MPC controller is compared against a rule‐based (RB) controller and a nonlinear economic MPC (NEMPC) benchmark. Compared with the RB controller benchmark, the LTV‐MPC reaches the target cabin temperature at least 69 s faster with 3.2% to 15% less HVAC system energy consumption, and the averaged cabin temperature difference is 0.7°C at most. Compared with the NEMPC, the LTV‐MPC controller can achieve comparable performance in temperature regulation and energy consumption with fast computation time: the maximum differences in temperature and energy consumption are 0.4°C and 2.6%, respectively, and the computational time is reduced 72.4% on average with the LTV‐MPC.

Adaptive Sampling of Dynamic Systems for Generation of Fast and Accurate Surrogate Models

AbstractFor economic nonlinear model predictive control and dynamic real‐time optimization fast and accurate models are necessary. Consequently, the use of dynamic surrogate models to mimic complex rigorous models is increasingly coming into focus. For dynamic systems, the focus so far had been on identifying a system's behavior surrounding a steady‐state operation point. In this contribution, we propose a novel methodology to adaptively sample rigorous dynamic process models to generate a dataset for building dynamic surrogate models. The goal of the developed algorithm is to cover an as large as possible area of the feasible region of the original model. To demonstrate the performance of the presented framework it is applied on a dynamic model of a chlor‐alkali electrolysis.

Budget-constrained economic model predictive control: A user-friendly proposal for HVAC

Cost optimization of heating, ventilation and air conditioning systems (HVAC) in buildings has been approached by using sophisticated methodologies such as model predictive control (MPC) and real-time optimization. However, such techniques are not usually user-friendly to individuals without a process control background. Namely, it can be very difficult for building managers to estimate the economic impact of set point changes. For this reason, it is proposed an economic nonlinear model predictive control (eMPC) using a budget constraint. Using this concept, building managers will be able to balance the trade-off between operational cost and thermal comfort. To demonstrate the proposed approach, a first-principles model of a HVAC system is extended from a previous authors contribution to consider two new features: (1) thermal lag due to energy accumulation in the building envelope; (2) energy consumption by the fans. Then, the implemented HVAC system is tested in open- and closed-loop conditions. The closed-loop simulations showed the advantage for building managers of using the budget-constrained eMPC over the classical approach and On–Off control when using two different budget strategies. This approach ensures an user-friendly interface between building managers (i.e., non-expert users) and eMPC.

Precise control of water and wastewater treatment systems with non-ideal heterogeneous mixing models and high-fidelity sensing

Non-ideal heterogeneous mixing models are developed and incorporated within advanced closed-loop control strategies utilizing high-resolution sensing to maximize the resiliency and minimize the energy consumption of water treatment processes with intelligent model-based decision-making approaches. The proposed non-ideal heterogeneous mixing models capture continuity (heat and mass conservation), yet are extremely simple with few parameters, so they lend themselves to fast online prediction (with extrapolation capabilities) and regular recalibration. Further, they are more accurate than computational fluid dynamics (CFD) (60% less error) and symbolic regression data-driven models (73% less error). Real-time high-resolution sensor data are collected for observing spatiotemporal responses of state variables (conductivity, pH, and temperature) to transient influent shocks. Deterministic global dynamic optimization is used for training and recalibration of the non-ideal heterogeneous mixing models to guarantee the best-possible fits to the sensor data. The models are then deployed within standard model-predictive control and two economic model-predictive control strategies to demonstrate model-based decision-making for disturbance rejection and optimal operation of aeration in a continuous flow nitrification system utilizing high-resolution sensor data from several spatial positions. The new technology platform, consisting of high-resolution sensors, non-ideal heterogeneous mixing modeling, deterministic global dynamic optimization, and model-predictive control, offers superior performance over current approaches in water and wastewater treatment processes.

On continuous-time infinite horizon optimal control—Dissipativity, stability, and transversality

This paper analyzes the interplay between dissipativity and stability properties in continuous-time infinite-horizon Optimal Control Problems (OCPs). We establish several relations between these properties, which culminate in a set of equivalence conditions. Moreover, we investigate convergence and stability of the infinite-horizon optimal adjoint trajectories. The workhorse for our investigations is a notion of strict dissipativity in OCPs, which has been coined in the context of economic model predictive control. With respect to the link between stability and dissipativity, the present paper can be seen as an extension of the seminal work on least squares optimal control by Jan C. Willems (1971). Furthermore, we show that strict dissipativity provides a conclusive answer to the question of adjoint transversality conditions in infinite-horizon optimal control which has been raised by Hubert Halkin (1974). Put differently, we establish conditions under which the adjoints converge to their optimal steady-state value. We draw upon several examples to illustrate our findings. Moreover, we discuss the relation of our findings to results available in the literature.

Parallelized POD-based suboptimal economic model predictive control of a state-constrained Boussinesq approximation

Motivated by an energy efficient building application, we want to optimize a quadratic cost functional subject to the Boussinesq approximation of the Navier-Stokes equations and to bilateral state and control constraints. Since the computation of such an optimal solution is numerically costly, we design an efficient strategy to compute a sub-optimal (but applicationally acceptable) solution with significantly reduced computational effort. We employ an economic Model Predictive Control (MPC) strategy to obtain a feedback control. The MPC sub-problems are based on a linear-quadratic optimal control problem subjected to mixed control and state constraints and a convection-diffusion equation, reduced with proper orthogonal decomposition. To solve each sub-problem, we apply a primal-dual active set strategy. The method can be fully parallelized, which enables the solution of large problems with real-world parameters.

Emerging approaches for nonlinear parameter varying systems

Emerging approaches for nonlinear parameter varying systems

Large-scale wind farm control using distributed economic model predictive scheme

The reliable control of the large-scale wind farm is crucial for the stability and security of the renewable power system with high wind power penetration. Due to the uncertain and variable nature of wind power, the traditional control strategy is difficult to work. Regarding the large-scale, geographically dispersed wind farm, an efficient distributed economic model predictive control strategy is proposed, which integrates the power tracking and economic optimization of the wind farm into one optimal control framework. By adopting the global economic cost function, the Nash optimal solutions under distributed framework approach the Pareto optimum. Thus, the reference power from the transmission system operator is accurately tracked, while the global dynamic economic optimality is guaranteed. The simulation results under step wind speed and practical wind speed variations verify the efficiency and reliability of the proposed control strategy.

Economic heat control of mixing loop for residential buildings supplied by low-temperature district heating

Increasing the penetration of Renewable Energy Sources (RES), the heat pumps are an alternative solution to facilitate the integration of RES into district heating. To hedge against the intermittency of RES, the flexibility potentials of the thermal inertia of buildings are unlocked and integrated into power systems. This paper suggests a novel structure to control the mixing loop of residential heating systems supplied by electrically operated district heating. The Economic Model Predictive Control (EMPC) is proposed to optimize the heat demand of the buildings in response to electricity market price. The EMPC controls the temperature and flow rate of forward/return water in the mixing loop to minimize the energy consumption cost of households. The thermal dynamics of the buildings are modeled by 3-state differential equations to integrate the flexibility potentials of thermal inertia into the district heating. The approach optimizes the heat consumption of the building with multi-temperature zones. The Continuous-Time Stochastic Model (CTSM) is addressed to determine the thermal dynamics of the building using sensor data. Finally, a 150 m2 Danish test house with four temperature zones is simulated. The simulation results show that the suggested approach not only minimizes the energy consumption cost but also provides flexibility for the Danish Electricity Market.

Performance analysis using economic model predictive control for hydrolysis of tallow fat

AbstractTallow is a resource for glycerine and oleochemicals produced by subsequent hydrolysis, saponification, or transesterification. Since steam hydrolysis, an industrial practice, uses continuous high pressure and temperature, is energy intensive; this has been replaced by use of pressurized hot water from top and bottom of hydrolyzing tower. The fat and water form continuous phase in the heat exchange part where hydrolysis takes place in approximately 3 h. The degree of hydrolysis depends on vapor–liquid equilibrium of water which is a function of temperature and pressure. It has been found that degree of hydrolysis is feasible at 256°C. Continuous countercurrent flow is maintained by the density difference between the two phases in the heat exchange sections. There is a need for improving degree of hydrolysis along the safe operating region in the temperature–pressure domain of energy‐utility spectrum by using model predictive control (MPC). A nonlinear mathematical model, representing glycerine concentration and temperature in fat and aqueous phases, for the fat hydrolysis system is used for system identification and synthesizing model‐based tuning rules for the said process. Auto‐tuning algorithms (multiloop with IMC‐PID–Laurent tuning) are developed for PID tuning. The conventional control algorithms (IMC‐PI and MPC) focus on error minimization and performance optimization; hence, economic model predictive control (EMPC) is adopted (incorporating reaction kinetics into objective function) to optimize the process utility via improved energy efficiency. A closed‐loop comparison (PI, MPC, and economic MPC) of performance indices reveals that economic MPC gives satisfactory results.