Economic Model Predictive Control Research Articles

Gaussian Process-Based Economic MPC with Delay Compensation for SNCR-SCR Combined Denitration Systems

Gaussian Process-Based Economic MPC with Delay Compensation for SNCR-SCR Combined Denitration Systems

Artificial Neural Networks for Energy Demand Prediction in an Economic MPC‐Based Energy Management System

ABSTRACTMicrogrids are a development trend and have attracted a lot of attention worldwide. The control system plays a crucial role in implementing these systems and, due to their complexity, artificial intelligence techniques represent some enabling technologies for their future development and success. In this paper, we propose a novel formulation of an economic model predictive control (economic MPC) applied to a microgrid designed for a faculty building with the inclusion of a predictive model to deal with the energy demand disturbance using a recurrent neural network of the long short‐term memory (RNN‐LSTM). First, we develop a framework to identify an RNN‐LSTM using historical data registered by a smart three‐phase power quality analyzer to provide feedforward power demand predictions. Next, we present an economic MPC formulation that includes the prediction model for the disturbance within the optimization problem to be solved by the MPC strategy. We carried out simulations with different scenarios of energy consumption, available resources, and simulation times to highlight the results obtained and analyze the performance of the energy management system. In all cases, we observed the correct operation of the proposed control scheme, complying at all times with the objectives and operational restrictions imposed on the system.

Distributed Economic Nonlinear Model Predictive Control for Flexible Electrified Biodiesel Production─Part II: Sequential and Iterative Architectures with Computational Delay Compensation

Distributed Economic Nonlinear Model Predictive Control for Flexible Electrified Biodiesel Production─Part II: Sequential and Iterative Architectures with Computational Delay Compensation

Dual-time-scale zone economic model predictive control of micro gas turbine cogeneration systems

The utilization of decentralized micro gas turbine combined heat and power (MGT-CHP) units is considered as a prospective technique in power generation due to its high levels of fuel utilization rates and low emissions. However, the inherent strong coupling and complex timescale multiplicity make it challenging to realize optimal operation. To this end, this paper first establishes a precise mechanism model to attain a thorough understanding of the system properties. By conducting singular perturbation theory, the complex nonlinear system is decomposed into a fast power subsystem and a slow heat subsystem. Then, a dual-time-scale zone economic model predictive control (D-ZEMPC) algorithm, which is comprised of a fast EMPC and a slow EMPC, is applied to achieve dynamic synergy between heat and power supply by actively coordinating the two sub-controllers. Moreover, a zone tracking method is introduced for room temperature control, thereby yielding increased freedom in balancing the economic profits and thermal comfort. The simulation results in three scenarios along with the qualitative and quantitative discussions show that compared with the other two centralized EMPC algorithms, the proposed D-ZEMPC can significantly alleviate computational loads and reduce the simulation time by over 64.5 % while maintaining required thermal comfort with minimum fuel consumption.

A heat-measurement-free strategy for Economic Model Predictive Control of hydronic radiators

Cost-efficient measurement of room-level heat output from hydronic radiators is a major barrier to large-scale implementation of Economic Model Predictive Control (EMPC) in residential space heating for demand-side management. This paper therefore presents a novel EMPC strategy for hydronic radiators that relies on measurements of radiator pipe temperatures as a proxy for the radiator heat output, thus eliminating the need for costly flow-based meters at each radiator in a building. Simulation-based experiments indicate that the proposed proxy-based EMPC matches the performance of its heat-based counterpart. The proxy-based EMPC achieved a 16.6 % cost reduction compared to the heat-based EMPC's 16.8 %, with no comfort violations in both cases. Furthermore, the strategy shows resilience towards uncertainties in the user-estimated radiator exponent and maximum heating capacity. The proposed EMPC scheme also allows system operators to fine-tune the balance between cost savings and return temperatures using the proxy's upper limit. The findings presented in this paper suggest that the proposed proxy-based EMPC scheme provides a practical pathway for broader applications of EMPC in hydronic-based space heating with the prospect of unlocking significant load shifting potential, cost savings for end-users, and enhanced efficiency in individual and collective energy systems.

Efficiency-Oriented Model Predictive Control: A Novel MPC Strategy to Optimize the Global Process Performance.

Existing control strategies, such as Real-time Optimization (RTO), Dynamic Real-time Optimization (DRTO), and Economic Model Predictive Control (EMPC) cannot enable optimal operation and control behavior in an optimal fashion. This work proposes a novel control strategy, named the efficiency-oriented model predictive control (MPC), which can fully realize the potential of the optimization margin to improve the global process performance of the whole system. The ideas of optimization margin and optimization efficiency are first proposed to measure the superiority of the control strategy. Our new efficiency-oriented MPC innovatively uses a nested optimization structure to optimize the optimization margin directly online. To realize the computation, a Periodic Approximation technique is proposed, and an Efficiency-Oriented MPC Type I is constructed based on the Periodic Approximation. In order to alleviate the strict constraint of Efficiency-Oriented MPC Type I, the zone-control-based optimization concept is used to construct an Efficiency-Oriented MPC Type II. These two well-designed efficiency-oriented controllers were compared with other control strategies over a Continuous Stirred Tank Reactor (CSTR) application. The simulation results show that the proposed control strategy can generate superior closed-loop process performance, for example, and the Efficiency-Oriented MPC Type I can obtain 7.11% higher profits than those of other control strategies; the effectiveness of the efficiency-oriented MPC was, thereby, demonstrated.

Globalization of distributed parameter self‐optimizing control

AbstractNumerous nonlinear distributed parameter systems (DPSs) operate within an extensive range due to process uncertainties. Their spatial distribution characteristic, combined with nonlinearity and uncertainty, poses challenges in optimal operation under two‐step real‐time optimization (RTO) and economic model predictive control (EMPC). Both methods necessitate substantial computational power for prompt online reoptimization. Recent local distributed parameter self‐optimizing control (DPSOC) achieves optimality without repetitive optimization. However, its effectiveness is confined to a narrow range around a nominal operation. Here, globalized DPSOC is introduced to surmount the limitation of the local DPSOC. A global loss functional concerning controlled variables (CVs) is formulated using linear operators and Fubini's theorem. Minimizing the loss with a numerical optimization procedure yields CVs exhibiting global optimality. Maintaining these CVs at constants ensures such a process has a minimal average loss in a large operating space. The effectiveness of the proposed method is substantiated through a transport reaction simulation.

Distributed Economic Model Predictive Load Frequency Control for the Multiarea Interconnected Power System With WTs

Distributed Economic Model Predictive Load Frequency Control for the Multiarea Interconnected Power System With WTs

Distributed economic model predictive control of wind farms

Distributed economic model predictive control of wind farms

Virtually coupled train set control subject to space-time separation: A distributed economic MPC approach with emergency braking configuration

The emerging virtual coupling technology aims to operate multiple train units in a Virtually Coupled Train Set (VCTS) at a minimal but safe distance. To guarantee collision avoidance, the safety distance should be calculated using the state-of-the-art space-time separation principle that separates the Emergency Braking (EB) trajectories of two successive units during the whole EB process. In this case, the minimal safety distance is usually numerically calculated without an analytic formulation. Thus, the constrained VCTS control problem is hard to address with space-time separation, which is still a gap in the existing literature. To solve this problem, we propose a Distributed Economic Model Predictive Control (DEMPC) approach with computation efficiency and theoretical guarantee. Specifically, to alleviate the computation burden, we transform implicit safety constraints into explicitly linear ones, such that the optimal control problem in DEMPC is a quadratic programming problem that can be solved efficiently. For theoretical analysis, sufficient conditions are derived to guarantee the recursive feasibility and stability of DEMPC, employing compatibility constraints, tube techniques and terminal ingredient tuning. Moreover, we extend our approach with globally optimal and distributed online EB configuration methods to shorten the minimal distance among VCTS. Finally, experimental results demonstrate the performance and advantages of the proposed approaches.

Wind farm control using distributed economic MPC scheme under the influence of wake effect

As wind farms (WFs) expand in scale, there is a growing need for active power control to track the reference power benchmark issued by the grid dispatch center and also the imperative to reduce the fatigue load on key components of each wind turbine (WT). The presence of the wake effect causes a decrease in power generation for downstream WTs and an increase in the fatigue load. Consequently, the suppression of the wake effect has emerged as a critical control objective for WFs. For tackling the challenge, this article designs a hierarchical WF control framework. The upper-level controller employs a sequential convex programming (SCP) approach to maximize the WF's captured wind energy function and determine the optimal induction factors for the WTs. The lower-layer controller uses a distributed economic model predictive control (DEMPC) scheme to control the WT locally to achieve reference power tracking while reducing the fatigue load on each WT. Finally, the effectiveness of the designed algorithm was verified by conducting the simulation on a wind farm containing nine WTs.

Self-stabilizing economic nonlinear model predictive control applied to modular systems

Recent advances have been made in self-stabilizing Economic Nonlinear Model Predictive Control (eNMPC) formulation without pre-calculated setpoints, which leverages norm-based steady-state optimality conditions to enhance system robustness. To enable practical implementation, a generalized time-domain formulation is proposed, accommodating the discrete-time nature of control instrumentation and the continuous-time nature of first-principles models. A case study involving a modular membrane reactor illustrates the applicability of self-stabilizing eNMPC in real-world industrial scenarios.

Output feedback distributed economic model predictive control for parallel system in process networks

Abstract This paper proposes a distributed economic model predictive control algorithm for parallel systems which uses only output feedback. Such parallel systems are a fundamental system architecture frequently encountered in process networks where, in many cases, the state of the plant is not measurable. Economic performance is a key consideration in the operation of such industrial plants and it is of interest to develop theoretically rigorous approaches to tackle what is a practically very relevant scenario. The competitive couplings and competitive constraints inherent in parallel systems are explicitly addressed in the proposed controller design framework. Three measures are considered for optimization of such parallel systems including an economic stage cost function, energy efficiency and tracking accuracy. An economic cost function is optimized by the resulting distributed controller which can realize global control performance while also reducing the computational time for large-scale parallel systems. Stability of the system is formally proved using the principles of dissipativity. Finally, the effectiveness of the proposed theoretical approach is verified by both numerical simulation and experimentation to demonstrate practical relevance.

End-to-end reinforcement learning of Koopman models for economic nonlinear model predictive control

(Economic) nonlinear model predictive control ((e)NMPC) requires dynamic models that are sufficiently accurate and computationally tractable. Data-driven surrogate models for mechanistic models can reduce the computational burden of (e)NMPC; however, such models are typically trained by system identification for maximum prediction accuracy on simulation samples and perform suboptimally in (e)NMPC. We present a method for end-to-end reinforcement learning of Koopman surrogate models for optimal performance as part of (e)NMPC. We apply our method to two applications derived from an established nonlinear continuous stirred-tank reactor model. The controller performance is compared to that of (e)NMPCs utilizing models trained using system identification, and model-free neural network controllers trained using reinforcement learning. We show that the end-to-end trained models outperform those trained using system identification in (e)NMPC, and that, in contrast to the neural network controllers, the (e)NMPC controllers can react to changes in the control setting without retraining.

Economic model predictive control for building HVAC system: A comparative analysis of model-based and data-driven approaches using the BOPTEST Framework

Model Predictive Control (MPC) has demonstrated its capability to significantly enhance energy efficiency while ensuring indoor comfort. This study focuses on the development and fair comparison of two Economic Model Predictive Control(EMPC) frameworks with the goal of optimizing demand response for utility cost reduction and ensuring thermal comfort in residential buildings. The first framework, known as RC-MPC, utilizes a reduced-order thermal Resistance–Capacitance network model to represent the thermal dynamics of the building. It formulates the optimization problem as a Linear Programming (LP) task, which is solved using CPLEX. The second framework, known as ANN-MPC, employs an Artificial Neural Network model capture the thermal behavior of the building, It addresses a non-convex optimization problem through projected stochastic gradient descent. To evaluate the performance of these frameworks, experiments are conducted using a single-zone dwelling within the BOPTEST framework. The results demonstrate that both approaches effectively reduce operational costs and enhance comfort, achieving comparable performance and outperforming the baseline Rule-Based Control (RBC) method. The discomfort reductions range from 30% to 95%, and energy expense savings range from 17% to 34%. Furthermore, the study examines the impact of various MPC hyperparameters. The findings highlight that a proper control horizon and formulating the objective function accurately are crucial for achieving optimal control performance. Additionally, tightening the comfort range is found to be important in managing the comfort violations, and the choice of solver can influence both the control performance and computational efficiency.

A distributed economic model predictive control-based FPPT scheme for large-scale solar farm

Increasing solar-photovoltaic-power penetration necessitates the implementation of flexible power point tracking (FPPT) in solar farms. However, coordinating multiple solar photovoltaic (PV) power generation systems (SPVPGSs) poses a significant challenge due to their inherent intermittency and varying dynamic characteristics, complicating FPPT implementation. To overcome this challenge, this paper proposes a distributed economic model predictive control (DEMPC) scheme to achieve FPPT, while simultaneously enhancing overall economic performance in solar farms. By integrating solar farm control and local control into one optimal control framework, this scheme eliminates the need for power allocation, PV voltage reference calculation, and pulse width modulation. Leveraging the SPVPGS model and soft power constraint, DEMPC controllers are designed to achieve the economic targets of solar farms, which cooperate through a communication network to realize FPPT and economic optimization. Additionally, the strong nonlinearity of SPVPGS causes a non-convex mixed integer nonlinear programming (MINLP) problem, solved by a MINLP algorithm using finite converter switching states. Simulations under step-changed irradiance and power reference, as well as urgent maintenance conditions, demonstrate that the DEMPC-based FPPT scheme significantly outperforms the traditional hierarchical model predictive control-based FPPT scheme, presenting both superior dynamic response and enhanced economic performance in FPPT implementation.

Innovative air supply management in fuel cells: An economic predictive control approach without pre-measured OER

Existing fuel cell air supply control methods improve the economic performance of Proton Exchange Membrane Fuel Cells (PEMFC) under steady-state conditions through oxygen excess ratio curve, while ignoring the transient process of the air supply system under varying operating conditions. Furthermore, the oxygen excess ratio curve may exhibit deviations due to fuel cell aging and measurement inaccuracies, which would further diminish the economic performance derived from the control process. Not relying on pre-measuring the oxygen excess ratio curve, an EMPC (Economic Model Predictive Control) method is proposed for fuel cell air supply systems. It incorporates an economic cost function reflecting the economic objectives of the air supply system. By dynamically optimizing the parasitic power of the air compressor, this method enhances the overall economic performance by achieving performance optimization for both transient and steady-state processes of the fuel cell system. The asymptotic stability of PEMFC is achieved through the utilization of terminal penalty functions and terminal domain constraints. Stability and convergence analysis is carried out by employing auxiliary optimization problems and the Lyapunov method. In transient processes, EMPC method can achieve a maximum 4.97 % improvement in the economic performance of PEMFC. A hardware in loop (HIL) experiment was finally conducted to show the real-time capacity of the proposed EMPC method.

Optimal IOFL-based economic model predictive control technique for boiler-turbine system

The optimal control design of the boiler-turbine system is vital to ensure feasibility and high responsiveness over desired load variations. Using the traditional linear control techniques realization of this task is difficult, as the boiler-turbine mechanism has strong nonlinearities. Besides, environmental and economic concerns have replaced existing tracking control ones as the primary concerns of advanced power plants. Thus, this study proposes an optimal economic model predictive controller (EMPC) scheme for this unit on the basis of the input/output feedback linearization (IOFL) method. By employing the IOFL method, this unit is decoupled into a new linearized model that is utilized for developing the suggested optimal IOFL EMPC technique. The proposed control scheme is formulated in an economic quadratic programming form that considers the input-rate and input limits of the unit for optimal economic performance. In addition, an adaptive iterative algorithm is utilized for constraints mapping with guaranteeing a feasible solution in a finite number of steps without violation of original constraints over the entire predictive horizon. The outcomes of the simulation show that the suggested optimal IOFL EMPC scheme offers an improved dynamic and economic output performance over fuzzy hierarchical MPC, fuzzy EMPC, and nonlinear EMPC techniques during various load variations.

Shrinking economic MPC of constrained nonlinear systems: An event‐triggered constraint relaxation approach

AbstractThis article proposes a novel event‐triggered economic model predictive control (EMPC) scheme with shrinking prediction horizon of nonlinear systems subject to the constraints on the state and control. Some auxiliary positive‐definite functions at economic optimal equilibrium points are defined for economic performance functions. The optimal value function of the auxiliary function is used to design an adjustable stability constraint, which is imposed on the original EMPC optimization problem. The stability constraint is relaxed to design the triggered scheme avoiding Zeno behavior, while the prediction horizon is shrinked in different degrees by judging whether the last state within the triggered interval is in the terminal region. The involved parameter can be used to achieve a sensible compromise between system performance and computational complexity. The sufficient conditions guaranteeing the recursive feasibility and stability of the EMPC are derived. Finally, the effectiveness of the algorithm is illustrated by a continuously stirred tank reactor example.

Model-based control strategy with linear parameter-varying state-space model for rack-based cooling data centers

Cooling system energy consumption occupies approximately 40% of the total energy consumption in data centers, and efficient control is crucial for improving cooling efficiency and reducing the operational costs of data centers. This paper introduced a novel economic model predictive control (EMPC) strategy based on a linear parameter-varying state-space model. The primary objective was to maintain the thermal environment of data centers while minimizing the energy consumption of the cooling system. Therein, a linear parameter-varying state-space model was developed based on the parameter identification method to precisely predict the temperature field of the rack-based cooling data center in real-time. The energy management and thermal regulation performance of the EMPC and the proportion integration differentiation (PID) controller were comparatively analyzed through simulation experiments. Moreover, the impacts of the server workload level and optimization time domain on the performance of EMPC were comprehensively investigated. The results show that, the proposed EMPC was able to minimize the energy consumption by optimizing the supplied cold air temperature and airflow rate simultaneously. In comparison with the PID controller, EMPC not only achieves a 9.7% energy saving by preventing server over-cooling but also diminishes server temperature fluctuations, promoting the safe and stable operation of the server. The research shows that the EMPC reveals excellent performance along with all server workload levels. In addition, the length of the prediction horizon has a notable impact and three minutes is suggested for the rack-based cooling system.