Economic Nonlinear Model Predictive Control

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.

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

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.

Diversification of electricity generation sources and changing consumer demand as well as electricity pricing could hinder the performance of a post combustion capture plant attached to a fossil-fueled power plant. This has necessitated advanced control algorithms to ensure safe, flexible and economical operation of the plant. In this work, economic model predictive control (EMPC) was applied to a post-combustion capture plant. The performance of the EMPC was compared to the one given by a set-point tracking model predictive controller (MPC) in terms of emission reduction and reboiler heat requirements. The results show that EMPC has the potential to improve the economic performance of the process.

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 paper proposes an economic model predictive control (EMPC) strategy for the inventory routing problem under demand uncertainty. The strategy is illustrated using an application on industrial gas distribution systems, where the product is transported to customers in small tanks and the inventory levels at the customers’ sites are monitored and controlled by the supplier following a vendor managed inventory approach. The objective is to produce balanced decisions for the joint routing and the inventory control problem over the planning horizon with respect to the decision maker’s perspective against stock-out risk. The proposed EMPC strategy makes use of a mixed integer mathematical programming optimization model that describes the deterministic inventory routing problem with simultaneous pickups and deliveries over a specific planning horizon. A time series decomposition forecasting model is used for predicting future demand and an exact linearization of the quadratic term of the objective function guarantees optimality of the solutions. The proposed methodology is illustrated using two examples featuring a single distribution centre, and three customers with simple and complex demand profiles. It is shown that EMPC offers a useful tool for producing balanced decisions between transportation and inventory costs and tracking of the safety inventory levels.

Nowadays, real-time optimization (RTO) and nonlinear as well as linear model predictive control (MPC) are standard methods in operation and process control systems. Hence there exists a good understanding of how to combine RTO and set point tracking MPC schemes. However, recently, there has been substantial progress in analyzing the properties of so-called economic MPC schemes. This paper proposes a conceptual framework to blend ideas from (output) modifier adaptation and offset-free economic MPC with recent results on economic MPC without terminal constraints. Specifically, we leverage recent insights into economic MPC based on turnpike and dissipativity properties of the underlying optimal control problem. Interestingly, the proposed scheme alleviates the need for a dedicated computation of steady-state targets by exploiting the turnpike property in the open-loop predictions. Two detailed simulation examples show that the proposed schemes deliver excellent performance, while being conceptually much simpler.

The wave energy converter (WEC) control problem aims to make the best use of wave excitation to maximize energy capture and ensure safe operation across a broad range of sea states. This falls into the recently developed economic model predictive control (EMPC) framework, subject to wave excitation being treated as a predictable additive disturbance in the control problem. However, there are few theoretical developments on EMPC theory that can be directly used, as the persistent disturbances bring nontrivial problems to optimal operation, safety etc. Whilst the disturbance is beneficial for the energy production objective, it may cause safe operation problems. This article develops a systematic WEC EMPC design approach for WECs with essential linear hydrodynamical characteristics. By introducing terminal weight and terminal state constraint design into the WEC EMPC structure, important features such as convexity, satisfaction of safety constraints, and recursive feasibility can be guaranteed. Contrary to our intuition, we show that (1) the proposed EMPC with a terminal weight provides an unbiased estimate of the ideal conceptual infinite horizon solution, and (2) the WEC operational range, in terms of the operational sea states, is extended by imposing a terminal constraint. Finally, numerical simulations are provided to verify the efficacy of the proposed approach.

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.

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.

This chapter contains a brief background on economic model predictive control (EMPC) methods. The background on EMPC methods is meant to provide context to the EMPC design methodologies of the subsequent chapters. In particular, stability and performance under EMPC is discussed. The chapter concludes with a benchmark chemical process application where EMPC is applied to evaluate the closed-loop properties under EMPC.

Space heating demand response potential of retrofitted residential apartment blocks

Economic versus energetic model predictive control of a cold production plant with thermal energy storage

In this chapter, several computationally-efficient two-layer frameworks for integrating dynamic economic optimization and control of nonlinear systems are presented. In the upper layer, economic model predictive control (EMPC) is employed to compute economically optimal time-varying operating trajectories. Explicit control-oriented constraints are employed in the upper layer EMPC. In the lower layer, a model predictive control scheme is used to force the system to track the optimal time-varying trajectory computed by the upper layer EMPC. The properties, i.e., stability, performance, and robustness, of closed-loop systems under the two-layer EMPC methods are rigorously analyzed. The two-layer EMPC methods are applied to chemical process examples to demonstrate the closed-loop properties.