Economic Model Predictive Control System Research Articles

Enhancing dynamic operation optimization feasibility for constrained economic model predictive control systems

AbstractBased on the hierarchical control structure, optimization and control problems of large‐scale and multivariate plants are solved sequentially. The economic performance of the plant plays an essential role in the plant‐wide modern industry. The optimal operating conditions will change as the economic criteria changes throughout the operation of the plant as the result of variations in raw material prices, product prices, production demand, market fluctuations, disturbances, and so forth. In reality, soft constraints are frequently used to denote the production requirements of various operating conditions. In order to improve economic performance and guarantee feasibility for the entire plant operation, a novel economic model predictive control (EMPC) strategy is proposed to control the constrained multi‐variable process system with varying economic performance criteria under soft constraints. By incorporating the transient steady‐state and two categories of slack variables for soft constraints, a modified economic performance index is optimized to cope with the changing criteria. In addition, a contractive constraint is added to the closed‐loop system to guarantee stability for non‐dissipative stage costs. This approach ensures recursive feasibility and asymptotic stability. The effectiveness of the proposed method is demonstrated by numerical examples and the fluid catalytic cracking unit (FCCU) process.

Experimental tests on the performance of an economic model predictive control system in a lightweight building

• Economic MPC was tested in a lightweight laboratory. • Effect of HVAC system models accuracy was discussed. • MPC improved PV self-consumption and operating costs compared to thermostat. • Oversimplified models led to higher thermal discomfort and increased consumption. European policies are fostering the electrification of energy use, including space heating and cooling systems, in order to decarbonise the building stock. The significant penetration of electrical loads and domestic photovoltaic (PV) plants has therefore become an important topic for researchers and engineers working in the building sector. In this context, this paper presents a recently constructed laboratory for testing efficient management strategies in all-electric houses. The article describes the laboratory and the Model Predictive Control (MPC) strategy developed to minimize economic costs for space heating while ensuring thermal comfort in the indoor environment with a simulated rooftop PV system. The proposed controller leverages prior knowledge about the physical and geometric properties of the building and the optimization problem is formulated using mixed-integer quadratic programming. This article reports the results of calibration and optimization performed in open loop, as well as two closed loop tests where the MPC controls the HVAC system using receding horizon. The predictive controller was able to substantially increase PV self-consumption in both tests compared to a conventional thermostat, thus cutting electricity costs for heat pump by 10–17%. Such improvement was obtained at the price of a higher thermal comfort violations, mainly due to oversimplified HVAC system models. In light of these findings, the article analyses the effect of such simplifications and suggests possible alternative modelling approaches.

Economic model predictive control for transport-reaction systems with target profiles

For transport-reaction processes with certain general cost functions indicating comprehensive profit, the existing linear–quadratic optimal control or model predictive control (MPC) methods may be conservative. Due to their spatial characteristics, dynamic evolutions and final target static spatial distributions under different control strategies may result in remarkable variation of operation performance. This article presents a novel economic model predictive control (EMPC) synthesis for systems described by hyperbolic/parabolic partial differential equations (PDEs) with pre-optimized static spatially distributed profile, from both convergence and performance points of view. Instead of deriving approximate ordinary differential equations (ODEs) and applying finite-dimensional control strategies, this work addresses the optimization and stabilization problem on the basis of infinite dimensional model itself, which is realized by Cayley–Tustin (CT) transformation without any type of spatial approximation. The accumulated economic cost, input/output constraints are explicitly considered in the finite horizon optimal control problem (FHOCP), with an additional energy-like contractive constraint accounting for closed-loop convergence toward the target optimal steady-state profile. By directly solving Lyapunov functions associated with PDEs models, the parameters in the FHOCP are suitably defined such that the composite EMPC system admits algorithm feasibility and closed-loop stability. Finally, the proposed method is applied to typical examples; numerical results indicates the effectiveness and remarkable performance improvement of the EMPC method compared to standard MPC results.

Economic Model-Based Controller Design Framework for Hydraulic Fracturing To Optimize Shale Gas Production and Water Usage

As water issues associated with hydraulic fracturing have received much attention, several optimization approaches have been developed for effective water management. However, most of them have not considered pumping schedules for hydraulic fracturing, which determine the productivity of a shale well as well as the total amount of freshwater required. Because of this, a novel model-based control framework is proposed for hydraulic fracturing to maximize the net profit from shale gas development which simultaneously minimizes the total cost associated with water management. The framework is as follows: initially a reduced-order model and a Kalman filter are developed based on the simulation data generated from a high-fidelity hydraulic fracturing model to correlate the pumping schedule and the final fracture geometry. Then, a numerical reservoir simulator and mixed-integer nonlinear programming model are used to generate two maps describing the revenue from selling shale gas produced and cost from managing wastewater recovered, respectively. Finally, by applying a data-based dynamic input–output model to connect the two maps, an economic model predictive control system is formulated. The proposed control framework enables 62% of the generated wastewater to be reused through the application of thermal membrane distillation technology in the treatment process and results in a 11% reduction in overall freshwater consumption, while maintaining the productivity of a shale well at its theoretical maximum.

Safeness Index-Based Economic Model Predictive Control of Stochastic Nonlinear Systems

Process operational safety plays an important role in designing control systems for chemical processes. Motivated by this, in this work, we develop a process Safeness Index-based economic model predictive control system for a broad class of stochastic nonlinear systems with input constraints. A stochastic Lyapunov-based controller is first utilized to characterize a region of the state-space surrounding the origin, starting from which the origin is rendered asymptotically stable in probability. Using this stability region characterization and a process Safeness Index function that characterizes the region in state-space in which it is safe to operate the process, an economic model predictive control system is then developed using Lyapunov-based constraints to ensure economic optimality, as well as process operational safety and closed-loop stability in probability. A chemical process example is used to demonstrate the applicability and effectiveness of the proposed approach.

Handling Process Safety and Stochastic Uncertainty in Economic Model Predictive Control

Abstract Process operational safety plays an important role in designing control systems for chemical processes. Motivated by this, in this work, we develop a process Safeness Index-based economic model predictive control system for a broad class of stochastic nonlinear systems with input constraints. A stochastic Lyapunov-based controller is first utilized to characterize a region of the state-space surrounding the origin starting from which the origin is rendered asymptotically stable in probability. Using this stability region characterization and a process Safeness Index function which characterizes the region in state-space in which it is safe to operate the process, an economic model predictive control system is then developed using Lyapunov-based constraints to ensure economic optimality, process operational safety and closed-loop stability in probability. A chemical process example is used to demonstrate the applicability and effectiveness of the proposed approach.

Handling Plant Variation via Error-Triggered On-line Model Identification: Application to Economic Model Predictive Control

Abstract: In the present work, an error-triggered on-line model identification approach is introduced for closed-loop systems that is able to detect and compensate for significant disturbances and variations in the plant. A moving horizon error detector is used to quantify the model accuracy and to trigger the model re-identification on-line when necessary. The proposed approach is applied in the context of economic model predictive control (EMPC), which is a feedback control approach that optimizes plant economics on-line by utilizing a process model. The on-line model identification scheme coupled with the EMPC system was applied to a benchmark catalytic chemical reactor example where the reaction rates decrease with time due to catalyst deactivation. In the presence of such plant variation, more accurate state predictions were made under the proposed EMPC scheme with on-line model identification than under an EMPC for which the model was not updated, which significantly impacted the plant economics.

Real‐time preventive sensor maintenance using robust moving horizon estimation and economic model predictive control

Conducting preventive maintenance of measurement sensors in real‐time during process operation under feedback control while ensuring the reliability and improving the economic performance of a process is a central problem of the research area focusing on closed‐loop preventive maintenance of sensors and actuators. To address this problem, a robust moving horizon estimation (RMHE) scheme and an economic model predictive control system are combined to simultaneously achieve preventive sensor maintenance and optimal process economic performance with closed‐loop stability. Specifically, given a preventive sensor maintenance schedule, a RMHE scheme is developed that accommodates varying numbers of sensors to continuously supply accurate state estimates to a Lyapunov‐based economic model predictive control (LEMPC) system. Closed‐loop stability for this control approach can be proven under fairly general observability and stabilizability assumptions to be made precise in the manuscript. Subsequently, a chemical process example incorporating this RMHE‐based LEMPC scheme demonstrates its ability to maintain process stability and achieve optimal process economic performance as scheduled preventive maintenance is performed on the sensors. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3374–3389, 2015

On identification of well‐conditioned nonlinear systems: Application to economic model predictive control of nonlinear processes

The focus of this work is on economic model predictive control (EMPC) that utilizes well‐conditioned polynomial nonlinear state‐space (PNLSS) models for processes with nonlinear dynamics. Specifically, the article initially addresses the development of a nonlinear system identification technique for a broad class of nonlinear processes which leads to the construction of PNLSS dynamic models which are well‐conditioned over a broad region of process operation in the sense that they can be correctly integrated in real‐time using explicit numerical integration methods via time steps that are significantly larger than the ones required by nonlinear state‐space models identified via existing techniques. Working within the framework of PNLSS models, additional constraints are imposed in the identification procedure to ensure well‐conditioning of the identified nonlinear dynamic models. This development is key because it enables the design of Lyapunov‐based EMPC (LEMPC) systems for nonlinear processes using the well‐conditioned nonlinear models that can be readily implemented in real‐time as the computational burden required to compute the control actions within the process sampling period is reduced. A stability analysis for this LEMPC design is provided that guarantees closed‐loop stability of a process under certain conditions when an LEMPC based on a nonlinear empirical model is used. Finally, a classical chemical reactor example demonstrates both the system identification and LEMPC design techniques, and the significant advantages in terms of computation time reduction in LEMPC calculations when using the nonlinear empirical model. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3353–3373, 2015

Integrated Design of Control Actuator Layer and Economic Model Predictive Control for Nonlinear Processes

In the present work, an economic model predictive control (EMPC) system is designed that accounts for the dynamics of the control actuators. A combined process-actuator dynamic model is developed to describe the process and control actuator dynamics and is used within the EMPC system. Integrating the design of the regulatory control layer, which controls the control actuators, and the supervisory control layer consisting of an EMPC system is an important consideration given the fact that EMPC may force an unsteady-state operating policy to optimize the process economics and the dynamics of the control actuator layer may affect the closed-loop process-actuator dynamics. Moreover, integral or average input constraints are often imposed within the EMPC solution. However, if the actuator layer is not accounted for in the EMPC system, the actuator output trajectory may not satisfy the integral input constraints. To address closed-loop stability of the combined process-actuator closed-loop system, stability constraints, designed via Lyapunov-based techniques, are imposed on the EMPC problem to guarantee closed-loop stability of the process system under the EMPC. An EMPC system accounting for the control actuator dynamics is applied to a benchmark chemical process example to study the impact of the actuator dynamics on closed-loop economic performance and reactant material constraint satisfaction.

Selection of control configurations for economic model predictive control systems

Economic model predictive control (EMPC) is a feedback control method that dictates a potentially dynamic (time‐varying) operating policy to optimize the process economics. The objective function used in the EMPC system may be a general nonlinear function that describes the process/system economics. As this function is not derived on the sole basis of classical control considerations (stabilization, tracking, and optimal control action calculation) but rather on the basis of economics, selecting the appropriate control configuration, and quantifying the influence of a given input on an economic cost is an important task for the proper design and computational efficiency of an EMPC scheme. Owing to these considerations, an input selection methodology for EMPC is proposed which utilizes the relative degree and the sensitivity of the economic cost with respect to an input to identify and select stabilizing manipulated inputs with the most dynamic and steady‐state influence on the economic cost function to be assigned to EMPC. Other considerations for input selection for EMPC are also discussed and integrated into a proposed input selection methodology for EMPC. The control configuration selection method for EMPC is demonstrated using a chemical process example. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3230–3242, 2014

Economic model predictive control of parabolic PDE systems: Addressing state estimation and computational efficiency

In a previous work [20], an economic model predictive control (EMPC) system for parabolic partial differential equation (PDE) systems was proposed. Through operating the PDE system in a time-varying fashion, the EMPC system demonstrated improved economic performance over steady-state operation. The EMPC system assumed the knowledge of the complete state spatial profile at each sampling period. From a practical point of view, measurements of the state variables are typically only available at a finite number of spatial positions. Additionally, the basis functions used to construct a reduced-order model (ROM) for the EMPC system were derived using analytical sinusoidal/cosinusoidal eigenfunctions. However, constructing a ROM on the basis of historical data-based empirical eigenfunctions by applying Karhunen-Loève expansion may be more computationally efficient. To address these issues, several EMPC systems are formulated for both output feedback implementation and with ROMs based on analytical sinusoidal/cosinusoidal eigenfunctions and empirical eigenfunctions. The EMPC systems are evaluated using a non-isothermal tubular reactor example, described by two nonlinear parabolic PDEs, where a second-order reaction takes place. The model accuracy, computational time, input and state constraint satisfaction, and closed-loop economic performance of the closed-loop tubular reactor under the different EMPC systems are compared.

Performance Monitoring of Economic Model Predictive Control Systems

A framework for performance monitoring of economic model predictive control (EMPC) systems is presented which includes the computation of an acceptable operating region, which is a well-defined region in state-space, for EMPC systems to operate a process in a time-varying fashion to optimize process economics while meeting input constraints and stabilizability requirements. To capture the interplay between sources of common cause variance caused by various sources like sensor noise, imperfect actuator operation, and model inaccuracy, a residual variable taken to be the difference of actual real-time economic cost and the predicted (expected) economic cost is defined. Utilizing exponentially weighted moving average (EWMA) and historical closed-loop process data, an upper control limit and a lower control limit are established which defines normal operation (i.e., operation with common cause variation). The limits are utilized to monitor the performance of EMPC by comparing real-time process operation data ...

Economic Model Predictive Control of Transport-Reaction Processes

This work focuses on the development of economic model predictive control (EMPC) systems for transport-reaction processes described by nonlinear parabolic partial differential equations (PDEs) and their applications to a non-isothermal tubular reactor where a second-order chemical reaction takes place. The tubular reactor is modeled by two nonlinear parabolic PDEs. Galerkin’s method is used to derive finite-dimensional systems that capture the dominant dynamics of the parabolic PDEs which are subsequently used for the EMPC design. The EMPC formulation uses the integral of the reaction rate along the length of the reactor as an economic cost function subject to constraints on the control action and states over an operation period. Closed-loop simulations are conducted of a low-order EMPC system, formulated with a constraint on the available reactant material over each operation period, applied to a high-order discretization of the PDEs and of a high-order EMPC system formulated with a specific state constraint and with the constraint on the available reactant material. Simulation results demonstrate that the EMPC operates the process in a time-varying fashion and improves the economic cost over steady-state operation using the same amount of reactant material over a fixed period of operation, as well as meeting state constraints.