Economic MPC based on LPV model for thermostatically controlled loads

In this work, we propose a conceptual framework for integrating dynamic economic optimization and model predictive control (MPC) for optimal operation of nonlinear process systems. First, we introduce the proposed two-layer integrated framework. The upper layer, consisting of an Economic MPC (EMPC) system that uses real-time measurements, computes economically optimal time-varying operating trajectories for the process by optimizing a time-dependent economic cost function over a finite prediction horizon subject to a nonlinear dynamic process model. The lower feedback control layer may utilize conventional MPC schemes or even classical control to compute feedback control actions that force the process state to track the time-varying operating trajectories computed by the upper layer EMPC. Such a framework takes advantage of the EMPC ability to compute optimal process time-varying operating policies using a dynamic process model instead of steady-state models, and the incorporation of suitable constraints on the EMPC allows calculating operating process state trajectories that can be tracked by the control layer. Second, we prove practical closed-loop stability including an explicit characterization of the closed-loop stability region. Finally, we demonstrate through extensive simulations using a chemical process model that the proposed framework can achieve stability.

The charging process of lithium‐ion batteries is necessary for normal operation, and improper lithium‐ion battery charging strategy can cause side reactions, significant temperature rise, performance degradation, and safety concerns. This paper proposes a two‐layer dynamic economic nonlinear model predictive control economic model predictive control (EMPC) method for lithium‐ion battery charge management in which the non‐Gaussian random noise of voltage and current signal are taken into account. In the two‐layer EMPC, the upper layer finds the optimal reference trajectory, and the power in the future prediction horizon is chosen as an economic indicator to optimize the upper layer. The lower layer tracks the optimal trajectory, and model predictive control based on generalized correntropy is used. The economic cost of the system and the dynamic changes of the process are considered to greatly reduce the computational complexity and realize rapid battery charge management. Finally, the simulation results show that the tracking error of the two‐layer EMPC method based on generalized correntropy is stable around 0, while the tracking error of the two‐layer EMPC method based on MSE is stable around 0.003. The average control action times of the proposed two‐layer EMPC and single‐layer EMPC are 0.0052 and 0.0267 s, respectively. It is verified that the proposed method performs better for the lithium‐ion battery charging process with random disturbances.

Cyber physical systems (CPS), which realize the real-time perception, dynamic control and information services of large-scale engineering systems through the organic integration and deep collaboration of 3C (Computer, Communication, Control) technologies, are a highly anticipated technology to solve the issues of modern plants innovatively. The significance of CPS is to connect the physical device to the internet, allowing the physical device to have five functions of computing, communication, precise control, remote coordination and autonomy. Among these CPS technologies used in industrial processes, economic model predictive control (MPC), which is a control scheme for industrial process with optimization economic as an indicator, is considered a forerunner approach towards plant process automation. However, most published papers on economic MPC applications have focused on continuous processes and only a few researchers have turned their attention to batch processes. This research studies economic MPC strategies for batch processes to evaluate its applicability. Most batch processes exhibit highly nonlinear and time-varying behavior, which makes it difficult to control them. We applied economic MPC and PID control scheme to a batch process, observing that economic MPC scheme showed better control performance in speed, disturbance suppression and efficiency. Moreover, from a simulation result of max production rate control with economic MPC, it was revealed that process constraints affect production rate considerably, which indicates that economic MPC can be used not only for process control but also for process design. Off-line study with economic MPC can assess the effect of plant specification on plant efficiency quantitively. This paper revealed that economic MPC can improve both design and control of batch processes.

The aim of this paper is to mitigate the problem of high power demand peak and load oscillations in the operation of a large population of thermostatically controlled loads (TCLs) operated by model predictive control (MPC) at the TCL level. Two desynchronized MPC schemes are introduced: 1) adding random delays in reference signals and 2) extra penalizations on MPC objective functions. For characterizing and validating the proposed desynchronization MPC schemes, a partial differential equation (PDE) model is developed to represent the evolution of the operational states of the TCLs controlled by MPC in a population. The focus of this paper is put on the control of cooling fans in server racks of datacenters, whereas the proposed approach is applicable to other types of TCLs. Numerical simulation studies are carried out and the obtained results confirm the validity and the applicability of the developed approach.

Smart home scheduling, facilitated by advanced metering, monitoring, and manipulation technology, plays an important role in the energy transition in terms of accommodating intermittent renewable energy and improving energy consumption efficiency. The key functionalities of home energy scheduling are usually implemented by leveraging the flexibility of household appliances, such as thermostatically controlled loads (TCLs) and energy storage units, to improve the peak-to-average ratio for utilities and reduce energy bills for customers. However, the consumption patterns of appliances are greatly influenced by a variety of factors, including real-time tariffs, ambient temperature profiles, indoor activities, and solar irradiance. Hence, smart home energy scheduling is a challenging task because most of these impacting factors are stochastic and difficult to predict. To properly model and manage the uncertainty factors associated with smart home appliance scheduling, an economic model predictive control (MPC)-based bilevel smart scheduling scheme is proposed in this paper. The comprehensive modeling of distributed generation and household appliances is performed at the single-household level. The home energy scheduling problem is formulated on two levels, with the upper level emphasizing the economic impact and the lower level focusing on capturing TCL responses. The correlations among different TCLs and their performance under the influence of various uncertainty factors, such as environmental impacts and user behaviors, are considered. The efficiency of the proposed MPC-based bilevel optimization model and the effectiveness of the home energy scheduling strategy in managing uncertainties are validated and illustrated in numerical studies.

Integrating dynamic economic optimization and model predictive control for optimal operation of nonlinear process systems

The research is motivated by real applications, such as pasteurization plant, water networks and autonomous system, which each of them require a specific control system to provide proper management able to take into account their particular features and operating limits in presence of uncertainties related to their operation and failures from component breakdowns. According to that most of the real systems have nonlinear behaviors, it can be approximated them by polytopic linear uncertain models such as Linear Parameter Varying (LPV) and Takagi-Sugeno (TS) models. Therefore, a new economic Model Predictive Control (MPC) approach based on LPV/TS models is proposed and the stability of the proposed approach is certified by using a region constraint on the terminal state. Besides, the MPC-LPV strategy is extended based on the system with varying delays affecting states and inputs. The control approach allows the controller to accommodate the scheduling parameters and delay change. By computing the prediction of the state variables and delay along a prediction time horizon, the system model can be modified according to the evaluation of the estimated state and delay at each time instant. To increase the system reliability, anticipate the appearance of faults and reduce the operational costs, actuator health monitoring should be considered. Regarding several types of system failures, different strategies are studied for obtaining system failures. First, the damage is assessed with the rainflow-counting algorithm that allows estimating the component’s fatigue and control objective is modified by adding an extra criterion that takes into account the accumulated damage. Besides, two different health-aware economic predictive control strategies that aim to minimize the damage of components are presented. Then, economic health-aware MPC controller is developed to compute the components and system reliability in the MPC model using an LPV modeling approach and maximizes the availability of the system by estimating system reliability. Additionally, another improvement considers chance-constraint programming to compute an optimal list replenishment policy based on a desired risk acceptability level, managing to dynamically designate safety stocks in flow-based networks to satisfy non-stationary flow demands. Finally, an innovative health-aware control approach for autonomous racing vehicles to simultaneously control it to the driving limits and to follow the desired path based on maximization of the battery RUL. The proposed approach is formulated as an optimal on-line robust LMI based MPC driven from Lyapunov stability and controller gain synthesis solved by LPV-LQR problem in LMI formulation with integral action for tracking the trajectory.

This paper presents a new economic optimization model predictive control (MPC) for constrained continuous-time nonlinear systems. In order to relax the terminal state constraint, a particular dual-mode method is used to design the economic MPC, where the local (terminal) controller is resulted from control Lyapunov functions (CLFs) and is nonlinear, with some free-parameters. These free-parameters are computed online when the states are in the terminal region. Iterative feasibility and asymptotical stability of the closed-loop system are achieved, which further yields an asymptotical average performance being better than the optimal steady-state performance. Finally, an example of the isothermal CSTR is exploited to illustrate the effectiveness of the proposed method.

Training and validating algorithms in a simulation testbed can accelerate research and applications of optimal control of residential loads to improve energy flexibility and grid resilience. We developed an open-source simulation environment, AlphaBuilding ResCommunity, that can be used to train and validate algorithms to control a single thermostatically controlled load (TCL) or coordinate a group of TCLs. We used reduced-order models to simulate the thermodynamics of TCLs, and the parameter values were determined from the connected smart thermostat data of real households. The environment was built upon the standardized OpenAI Gym interface. Ancillary functions, such as retrieving the parameters and weather forecasts, are provided to facilitate control strategies that require predictive information. Compared with existing efforts, AlphaBuilding ResCommunity has three advantages: (1) more realistic model settings because the parameter values are identified from actual household operating data, and modelling and measurement uncertainty are considered; (2) passive thermal storage control; and (3) ease of use due to a simple software dependency and standardized interface. We demonstrated the applications of the environment by implementing a Kalman Filter and Model Predictive Control on a single TCL and a Priority-Stack-Based Control and Alternating Direction Method of Multipliers to coordinate multiple TCLs for load tracking.

This paper proposes an operational planning framework for large-scale thermostatically controlled load (TCL) dispatch. The proposed framework consists of a day-ahead scheduling stage and a real-time operation stage. A thermal comfort model is employed to estimate the occupants' thermal comfort degree. A self-adaptive TCL grouping method is proposed to group the TCLs based on the similarity of the TCL model parameters. Then, a hierarchical day-ahead scheduling model is proposed to make the optimal dispatch plan for the TCL aggregators based on the day-ahead forecasted information. In the real-time operation stage, a predictive control model is proposed for the TCL aggregators to make the real-time TCL dispatch decision based on the updated real-time information. The simulation results prove the efficiency of the proposed framework.

Model predictive control (MPC) is the most widely used advanced process control technique. Traditionally, MPC is often used in a hierarchical process control architecture and is mainly designed for tracking set-points determined by the real-time optimization (RTO) layer. The huge success of MPC in industrial applications owes much to its ability to optimally handle process constraints and interactions. However, with the increasing demand for profitability and flexibility in process operations, the hierarchical process control architecture is not sufficient in many applications. In the past decade, a new form of MPC called economic MPC (EMPC) has been developed and is considered as a promising next-generation advanced control method. Unlike MPC that optimizes a quadratic cost function penalizing the deviation of the system state and input from the target steady state, EMPC optimizes a general cost function that is often directly linked to the economic metrics (profit, efficiency, sustainability) of the process. The direct incorporation of an economic cost into EMPC makes it a very flexible decision-making tool. In this chapter, a brief introduction to EMPC is given. Then, the applications of EMPC to a few representative energy-related systems including a post-combustion carbon capture plant, a coal-fired boiler-turbine generating system, a wind energy conversion system and oil sand separation process will be presented. The benefits of EMPC and the challenges in its implementation compared with the traditional tracking MPC will be discussed.

Demand response can provide services to the power network, however, coordination of spatially distributed demand response resources generally requires coping with imperfect communication networks. This work investigates methods to manage communication constraints (e.g., Delays and bandwidth limitations), faced by demand response aggregators who manipulate the on/off modes of residential thermostatically controlled loads (TCLs). We present two model predictive control (MPC) algorithms that exploit a priori knowledge of delay statistics. We also present three Kalman filter-based state estimation methods that handle measurements with heterogeneous delays that are known a posteriori. We simulate the closed loop system to quantify the error while the system tracks simplified power system signals of various frequencies. We find that the MPC algorithm incorporating the full delay distribution, versus only the mean delay, reduces the average tracking error 39%. Also, incorporating individual TCL models, identified on-line, within the state estimator versus only using a TCL aggregation model reduces the average estimation error 19%.

Modeling and Control of Diesel Engine Emissions using Multi-layer Neural Networks and Economic Model Predictive Control

A linear parameter-varying model (LPVM) is developed for nonlinear dynamic systems using a radial basis function (RBF) neural network. The training of the LPVM is formulated as the least-squares problem and the recursive orthogonal least-squares algorithm is applied. Model adaptation is also developed with a localized forgetting method for on-line weight updating. The LPVM-based model predictive control (MPC) is developed and the convexity of the optimization is preserved. The developed LPVM is applied to a laboratory-scaled chemical reactor rig. The real data modelling and on-line control implementation are presented. Decentralized proportional–integral–derivative (PID) control is also designed and implemented for the reactor for comparison. The superiority of the tracking performance by the LPVM-based MPC over that by PID control is clearly demonstrated. The performance using the fixed LPVM is also improved by using the adaptive model.

In this paper, we propose an economic feedback model predictive control (MPC) scheme to improve energy conversion efficiency of wave energy converters (WECs) and guarantee their safe operation over a wide range of sea conditions. The proposed MPC control law consists of two terms: one state feedback gain designed offline to maximize operating range and one term calculated online to maximize the energy output. Compared with the existing MPC strategies developed for the WEC control problem, the proposed feedback economic MPC strategy has the following distinguishing advantages: First, the satisfaction of safety constraints and the recursive feasibility can be guaranteed to ensure WEC's safe operation in a large range of sea states. Second, the novel MPC can notably improve energy production efficiency. Third, the controller design procedure is more convenient and straightforward compared with the existing MPC strategies. The efficacy of the proposed MPC strategy is demonstrated by numerical simulations with a point absorber as a case study. By comparison with a representative existing MPC strategy, the proposed economic MPC can significantly improve energy output.