Economic Model Predictive Control Research Articles

Design and Performance Analysis of a Cascaded Model Predictive Controller and Command Governor for Fuel-Efficient Control of Heavy-Duty Trucks

Abstract This paper presents the design and analysis of a predictive ecological control strategy for a heavy-duty truck that achieves substantial fuel savings while maintaining safe following distances in the presence of traffic. The hallmark of the proposed algorithm is the fusion of a long-horizon economic model predictive controller (MPC) for ecological driving with a command governor (CG) for safe vehicle following. The performance of the proposed control strategy was evaluated in simulation using a proprietary medium-fidelity Simulink model of a heavy-duty truck. Results show that the strategy yields substantial fuel economy improvements over a baseline, the extent of which are heavily dependent on the horizon length of the CG. The best fuel and vehicle-following performance are achieved when the CG horizon has a length of 20–40 s, reducing fuel consumption by 4–6% when compared to a Gipps car-following model.

Multi-Objective Load Dispatch Control of Biomass Heat and Power Cogeneration Based on Economic Model Predictive Control

This paper proposes a multi-objective load dispatch algorithm based on economic predictive control to solve the real-time multi-objective load dispatch problem of biomass heat and power cogeneration. According to the energy conservation law and production process, a real-time multi-objective load dispatch optimization model for heat and power units is established. Then, the concept of multi-objective utopia points is introduced, and the multi-objective load comprehensive objective function is defined to coordinate the conflict between the economic performance and pollutant emission performance of the units. Furthermore, using the online receding optimization characteristics of economic predictive control, the comprehensive objective function of multi-objective load dispatching is optimized online. Then, the fuel rate satisfying the economic performance and pollutant emission performance of the units is calculated to realize the economic performance and environmental protection operation of biomass heat and power cogeneration. Finally, the proposed multi-objective load dispatch control method is compared to traditional dispatch strategies by using industrial data. The results show that the method presented here can well balance the production cost and pollutant emission objective under the fluctuation of the thermoelectric load demand, and provides a feasible scheme for real-time dispatching of the multi-objective load dispatch problem of biomass heat and power cogeneration.

Statistical information based two-layer model predictive control with dynamic economy and control performance for non-Gaussian stochastic process

In this paper, a two-layer model predictive control (MPC) hierarchical architecture of dynamic economic optimization (DEO) and reference tracking (RT) is proposed for non-Gaussian stochastic process in the framework of statistical information. In the upper layer, with state feedback and dynamic economic information, the economically optimal trajectories are estimated by entropy and mean based dynamic economic MPC, which uses the nonlinear dynamic model instead of the steady-state model. These estimated optimal trajectories from the upper layer are then employed as the reference trajectories of the lower layer control system. A survival information potential based MPC algorithm is used to maintain the controlled variables at their reference trajectories in the nonlinear system with non-Gaussian disturbances. The stability condition of closed-loop system dynamics is proved using the statistical linearization method. Finally, a numerical example and a continuous stirred-tank reactor are used to illustrate the merits of the proposed economic optimization and control method.

Model Predictive Control of Smart Districts With Fifth Generation Heating and Cooling Networks

Fifth Generation District Heating and Cooling (5GDHC) networks, in which low temperature water is distributed to water-source heat pumps (WSHPs) in order to meet thermal demands, are expected to have a significant impact on the decarbonisation of energy supply. Thermal storage installed in these networks offers operational flexibility that can be leveraged to integrate renewable electrical and thermal energy sources. Thus, when considered as part of a smart multi-energy district, 5GDHC substation devices (e.g., WSHPs, storage) may be optimally operated using Model Predictive Control (MPC) in order to match demand with low-cost supply of electricity. However, the application of MPC requires the ability to model 5GDHC networks within the context of a multi-energy system. Hence, this paper extends an existing, generalised control-oriented modelling framework for multi-energy systems to accommodate 5GDHC networks. Additions include the ability to represent hydraulic pumps, thermodynamic cycle devices (such as WSHPs) and multi-energy networks within the framework. Furthermore, an economic MPC (eMPC) scheme is proposed for energy management of 5GDHC-based smart districts. Finally, a case study is presented in which the proposed eMPC controller is compared with rule-based control for economic operation of a smart district.

A new formulation of Economic Model Predictive Control without terminal constraint

In this paper, it is shown that a simple formulation of Economic Model Predictive Control can be used which possesses two features that are generally viewed as mutually exclusive, namely, a rather short prediction horizon (reachability-compatible) on one side, and the absence of final constraint on the other side. Practical stability at an arbitrarily small neighborhood of the optimal unknown steady-state pair is shown when some design parameters increase. It is also shown that when the system is originated from the time discretization of a continuous-time dynamics, the size of the terminal region can be reduced by decreasing the sampling period for the same design parameter setting. A commonly used example is given to illustrate the results.

A distributed network‐based economic model predictive control for networked smart energy systems considering communication network constraints

Generally, the modern networked energy systems are constructed from some coupled sub-systems interconnected via their states and share their information through a communication network featuring time delays. This article suggests an efficient multi-agent based cooperative-distributed networked economic model predictive control scheme for energy consumption optimisation and reducing the cost of consumed electricity in network-based smart energy systems considering communication network delays. In this regard, a buffer-based moving horizon strategy with estimator is suggested to estimate the own states of every sub-system and the coupled states, that is, the states in which their information exchange among sub-systems and their values are not accessible due to communication time delays. Moreover, the boundedness of the estimation error as well as the stability of the closed-loop system are established. The usability and proficiency of the suggested scheme are proved by applying the developed approach on two case studies.

Practical Economic MPC

AbstractAs opposed to tracking Model Predictive Control (MPC), economic MPC directly optimizes a given performance objective rather than penalizing the distance from a reference. On the one hand this typically improves performance. On the other hand, however, this also poses challenges in terms of stability and computational burden. In order to make economic MPC implementable in practice, we recently proposed some techniques that address both issues. In this contribution, we give a brief overview on economic MPC and the related literature and discuss how to exploit existing results in order to apply economic MPC in practice. Finally, we present a new promising research direction towards data‐driven economic MPC: the use of reinforcement learning to obtain optimality for the real system, rather than for the (unavoidably inaccurate) model used by MPC.

XE112-2000 Wind Turbine Yaw Strategy With Adaptive Yaw Speed Using DEL Look-Up Table

With the increasing capacity of wind turbines, the importance of the yaw system has gradually become more prominent. The supervisory control and data acquisition (SCADA) system of XEMC Windpower Co., Ltd. is used in this paper to analyze the yaw data of the No. 5 wind turbine of Baozhong Mountain Wind Farm in Hunan Province. In order to evaluate the power generation and the damage equivalent load (DEL) of the yaw bearing during the yaw process, an economic model predictive control (EMPC) yaw strategy based on light detection and ranging (LIDAR) was proposed. EMPC takes the yaw error and wind speed as the disturbance of the cost function (CF) at the same time by establishing the yaw bearing DEL look-up table in advance. Discrete adaptive yaw speed control set is proposed to adapt to different wind conditions sets. Finally, the effectiveness of EMPC is verified using the model of XE112-2000 wind turbine in simulation software Bladed.

A New Control Strategy for the Aluminum Reduction Process Using Economic Model Predictive Control

Abstract In the Hall-Heroult process, the evolving design and operating conditions require an advance on the development of new process control strategies. Especially, with the technology of individual anode current measurement now available, it becomes possible to monitor and control the localized conditions in an aluminum reduction cell. In this paper, a new cell control strategy is developed based on the Economic Model Predictive Control method, aiming to improve the current efficiency of the aluminum reduction process and hence maximize its economic benefits through advanced control algorithms. In addition, a more balanced cell condition is achieved through reduced spatial and temporal variations of process variables, such as alumina concentration, anode cathode distance, anode current. The simulation results demonstrate the superiority of the new method by comparing its control performance with that of the traditional method.

An Adaptive Correction Scheme for Offset-Free Asymptotic Performance in Deep Learning-based Economic MPC

Abstract There has been an increasing interest in explicit and cheap-to-evaluate control policies that approximate (computationally expensive) control laws such as model predictive control (MPC). However, approximate control policies are subject to approximation errors, leading to asymptotic performance losses. The contribution of this paper is three-fold: (i) a closed-loop training scheme is presented for deep neural network approximation of economic MPC; (ii) an online adaptive correction scheme is presented to account for the performance losses induced by approximation errors; and (iii) an offline performance verification scheme is presented to ensure that the approximate control policy converges to an equilibrium point of the system. The proposed approach is illustrated using a Williams-Otto reactor problem.

Robust Economic Model Predictive Control with Zone Control

Abstract This paper presents a robust economic Model Predictive Control (EMPC) formulation for discrete-time uncertain nonlinear systems. The proposed controller not only ensures that the closed-loop system is robust to disturbances, but also ensures that the economic performance does not deteriorate in the presence of the disturbances. The key idea is to have the controller track a robust control invariant subset of the state space with specified economic properties at all times, and within the zone optimize the process economics. To this end, we introduce the notion of risk factor in the controller design and provide an algorithm to determine the economic zone to be tracked. The risk factor determines the conservativeness of the controller. Our proposed controller is computationally less demanding as it only makes use of the system model without disturbances. A nonlinear CSTR example is presented to demonstrate the performance of the proposed formulation.

Verification of Dissipativity and Evaluation of Storage Function in Economic Nonlinear MPC using Q-Learning

In the Economic Nonlinear Model Predictive (ENMPC) context, closed-loop stability relates to the existence of a storage function satisfying a dissipation inequality. Finding the storage function is in general -- for nonlinear dynamics and cost -- challenging, and has attracted attentions recently. Q-Learning is a well-known Reinforcement Learning (RL) techniques that attempts to capture action-value functions based on the state-input transitions and stage cost of the system. In this paper, we present the use of the Q-Learning approach to obtain the storage function and verify the dissipativity for discrete-time systems subject to state-input constraints. We show that undiscounted Q-learning is able to capture the storage function for dissipative problems when the parameterization is rich enough. The efficiency of the proposed method will be illustrated in the different case studies.

Transient Performance of Tube-based Robust Economic Model Predictive Control

In this paper, we provide non-averaged and transient performance guarantees for recently developed, tube-based robust economic model predictive control (MPC) schemes. In particular, we consider both tube-based MPC schemes with and without terminal conditions. We show that the closed-loop performance obtained by applying such MPC schemes is approximately optimal when evaluated both on finite and infinite time horizons. These performance bounds are similar to those derived previously for nominal economic MPC. The theoretical results are discussed in a numerical example.

Economic Model Predictive Control of HVAC System in Electric Vehicles

Economic Model Predictive Control of HVAC System in Electric Vehicles

A 2.5MW Wind Turbine TL-EMPC Yaw Strategy Based on Ideal Wind Measurement By LiDAR

This paper analyzes the yaw data of the 2.5MW wind turbine of XEMC Windpower Company, and the real wind information collected by the wind farm, and proposes a two-level economic model predictive control (TL-EMPC) yaw strategy based on ideal wind measurement by light detection and ranging (LiDAR). This strategy comprehensively considers the power loss caused by yaw misalignment and the structural loads of the yaw bearing during the yaw process, making the yaw system more efficient and economical: In the high wind speed range, the yaw system has a higher sensitivity by setting the threshold of the yaw error angle, so as to fully capture wind energy; in the low wind speed range, fully consider the fatigue load of the critical parts of the wind turbine during the yaw process, thus Improve the economy of the wind turbine yaw system. The fatigue load and limit load of the yaw actuator at different yaw speeds are analyzed, and the best yaw speed is obtained. The finite control set of the yaw speed is established, which is used as the constraint set of the second-level minimum objective function. Finally, an external controller was used to simulate the 2.5MW wind turbine model in Bladed, and the effectiveness of the control strategy was verified.

Performance estimates for economic model predictive control and their application in proper orthogonal decomposition-based implementations

<p style='text-indent:20px;'>In this paper performance indices for economic model predictive controllers (MPC) are considered. Since existing relative performance measures, designed for stabilizing controllers, fail in the economic setting, we propose alternative absolute quantities. We show that these can be applied to assess the performance of the closed loop trajectories on-line while the controller is running. The advantages of our approach are demonstrated by simulations involving a convection-diffusion-system. The method is also combined with proper orthogonal decomposition, thus demonstrating the possibility for both efficient and performant MPC for systems governed by partial differential equations.</p>

Maximization of Solar Power Generation for a Spacecraft Controlled by a Single Rotor Based on Monte Carlo Economic Model Predictive Control

Maximization of Solar Power Generation for a Spacecraft Controlled by a Single Rotor Based on Monte Carlo Economic Model Predictive Control

Deep Learning Explicit Differentiable Predictive Control Laws for Buildings

Abstract We present a differentiable predictive control (DPC) methodology for learning constrained control laws for unknown nonlinear systems. DPC poses an approximate solution to multiparametric programming problems emerging from explicit nonlinear model predictive control (MPC). Contrary to approximate MPC, DPC does not require supervision by an expert controller. Instead, a system dynamics model is learned from the observed system’s dynamics, and the neural control law is optimized offline by leveraging the differentiable closed-loop system model. The combination of a differentiable closed-loop system and penalty methods for constraint handling of system outputs and inputs allows us to optimize the control law’s parameters directly by backpropagating economic MPC loss through the learned system model. The control performance of the proposed DPC method is demonstrated in simulation using learned model of multi-zone building thermal dynamics.

First Results on Turnpike Bounds for Stabilizing Horizons in NMPC

Abstract The stability analysis of NMPC schemes has seen significant progress in recent years, which includes schemes with and without terminal ingredients such as penalties and constraints. In the context of economic MPC, turnpike properties, which are closely related to dissipativity properties of the underlying optimal control problem, have enabled novel insights on stability conditions. In the present note, we show that turnpike properties naturally enable to bound the required stabilizing horizon length in MPC. The main idea is to define the turnpike with respect to a level-set of the terminal penalty. This way we derive a bound on the stabilizing horizon which guarantees that a terminal constraint is satisfied without being explicitly stated in the underlying optimal control problem. A numerical example indicates that if the terminal set is not too small, the horizon bound is not overly conservative.

Economic Model Predictive Control for optimal struvite recovery

Resource recovery from municipal wastewater has been a prime focus for a decade. Although several recovery processes already exist in the market today, the high cost of material, inherent disturbance in the influent quality, lack of real time monitoring of critical parameters, and lack of a robust automation system may result in suboptimal performance. This work attempts to construct a model based predictive control for optimal operation of a struvite recovery unit in a full scale WRRF. A multi-parameter based predictive control has been developed by implementing an Economic Model Predictive Controller (EMPC) for optimal dosing of magnesium hydroxide in a struvite recovery unit. The EMPC used customized objective function for real-time optimization of performance and economical parameters of the crystallization unit. The effectiveness of the proposed EMPC controller is verified through tests conducted on the Benchmark Simulation Model No. 2 (BSM2d.). The results obtained from the simulator-based evaluation of EMPC demonstrate a significant improvement in resource recovery at reduced operational costs. The economic advantages of implementing an EMPC compared to proportional and constant magnesium dosage has also been enumerated.