Economic MPC of nonlinear systems with nonmonotonic Lyapunov functions and its application to HVAC control

This paper proposes a Lyapunov‐based economic model predictive control (MPC) scheme for nonlinear systems with nonmonotonic Lyapunov functions. Relaxed Lyapunov‐based constraints are used in the MPC formulation to improve the economic performance. These constraints will enforce a Lyapunov decrease after every few steps. Recursive feasibility and asymptotical convergence to the steady state can be achieved using Lyapunov‐like stability analysis. The proposed economic MPC can be applied to minimize energy consumption in heating ventilation and air conditioning control of commercial buildings. The Lyapunov‐based constraints in the online MPC problem enable the tracking of the desired set‐point temperature. The performance is demonstrated by a virtual building composed of 2 adjacent zones.     

Integrating scheduling and control for economic MPC of buildings with energy storage

In this paper, we discuss Economic Model Predictive Control (E-MPC) in the context of buildings with active energy storage. In particular, we propose a strategy for the optimal control of building Heating, Ventilation and Air Conditioning (HVAC) systems with chilled water thermal energy storage (TES). Owing to the multiple time scale dynamic behavior of buildings, coupled with the need to account for potentially extended forecasts of disturbances (e.g., weather, energy prices), the implementation of a centralized E-MPC must consider a relatively long prediction horizon. In turn, this results in computational difficulties that impede on real-time implementation. Computational complexity is further increased by the presence of integer decision variables, related to on/off states and operating modes in the HVAC and TES systems. In response to these challenges, we introduce a novel hierarchical E-MPC framework based on (i) establishing the optimal operation of the TES by solving a dynamic scheduling problem in the slow time scale, and (ii) using a control scheme with a shorter horizon in the fast time scale, which addresses objectives related to maintaining the indoor air temperature within comfort bounds at all times during the day. A simulation case study concerning the operation of a TES system at the University of Texas Thermal Façade Laboratory is presented, showing excellent computational and control performance.     

Handling uncertainty in economic nonlinear model predictive control: A comparative case study

In the last years, the use of an economic cost function for model predictive control (MPC) has been widely discussed in the literature. The main motivation for this choice is that often the real goal of control is to maximize the profit or the efficiency of a certain system, rather than tracking a predefined set-point as done in the typical MPC approaches, which can be even counter-productive. Since the economic optimal operation of a system resulting from the application of an economic model predictive control approach drives the system to the constraints, the explicit consideration of the uncertainties becomes crucial in order to avoid constraint violations. Although robust MPC has been studied during the past years, little attention has yet been devoted to this topic in the context of economic nonlinear model predictive control, especially when analyzing the performance of the different MPC approaches. In this work, we present the use of multi-stage scenario-based nonlinear model predictive control as a promising strategy to deal with uncertainties in the context of economic NMPC. We make a comparison based on simulations of the advantages of the proposed approach with an open-loop NMPC controller in which no feedback is introduced in the prediction and with an NMPC controller which optimizes over affine control policies. The approach is efficiently implemented using CasADi, which makes it possible to achieve real-time computations for an industrial batch polymerization reactor model provided by BASF SE. Finally, a novel algorithm inspired by tube-based MPC is proposed in order to achieve a trade-off between the variability of the controlled system and the economic performance under uncertainty. Simulations results show that a closed-loop approach for robust NMPC increases the performance and that enforcing low variability under uncertainty of the controlled system might result in a big performance loss.     

Thermal comfort control using a non-linear MPC strategy: A real case of study in a bioclimatic building

The aim to maintain thermal comfort conditions in confined environments may require complex regulation procedures and the proper management of an HVAC (heating, ventilation and air conditioning) system. This problem is being widely analyzed, since it has a direct effect on users’ productivity, and an indirect effect on energy saving. This paper presents a hierarchical thermal comfort control system with two layers. The upper layer includes a non-linear model predictive controller that allows to obtain a high thermal comfort level by optimizing the use of an HVAC system in order to reduce, as much as possible, the energy consumption. On the other hand, the lower layer is formed by a PID (proportional, integrative and derivative) controller with anti-windup function which is in charge of reach the setpoints calculated by the non-linear model predictive controller. In order to probe the effectiveness of the proposed control system, suitable real results obtained in a bioclimatic building are included and commented.     

Interactions between control and process design under economic model predictive control

Economic model predictive control (EMPC) is a model-based control scheme that integrates process control and economic optimization, which can potentially allow for time-varying operating policies to maximize economic performance. The manner in which an EMPC operates a process to optimize economics depends on the process dynamics, which are fixed by the process design. This raises the question of how process and EMPC designs interact. Works which have addressed process and control design interactions for steady-state operation have sought to simultaneously develop process designs and control law parameters to find the most profitable way to operate a process that is able to prevent process constraints from being violated and to optimize capital costs in the presence of disturbances. Because EMPC has the potential to operate a process in a transient fashion, this work first focuses on how EMPC and process design interact in the absence of disturbances. Using small-scale process examples, we seek to understand the fundamental nature of the interactions between EMPC and process design, including how these interactions can impact computational complexity of the controller and the design procedure. We subsequently utilize the insights gained to suggest controller design variables which might be considered as decision variables for a simultaneous process and control design problem when disturbances are considered.     

Application to a drinking water network of robust periodic MPC

In this paper the application of a novel robust predictive controller for tracking periodic references to a section of Barcelona's drinking water network is presented. The system is modeled using a large scale uncertain differential-algebraic discrete time linear model in which it is assumed that a prediction of the water demand is available and that it is affected by unknown and bounded uncertainties. The control objective is to satisfy the water demand while trying to follow a given reference of the level of the tanks of the network. The controller considered has been modified to account for algebraic equations and large scale models and it joins a dynamic trajectory planner and a robust predictive controller in a single layer to guarantee that the closed-loop system converges asymptotically to a neighborhood of optimal reachable periodic trajectory satisfying the constraints for all possible uncertainties even in the presence of sudden changes in the reference. To demonstrate these properties three different simulation scenarios have been considered.     

RBF-ARX model-based MPC strategies with application to a water tank system

A hybrid pseudo-linear RBF-ARX model that combines Gaussian radial basis function (RBF) networks and linear ARX model structure is utilized for representing the dynamic behavior of a class of smooth nonlinear and non-stationary systems. This model is locally linear at each working point and globally nonlinear within whole working range. Based on the structural characteristics of the RBF-ARX model, three receding horizon predictive control (RBF-ARX-MPC) strategies are designed: (1) the RBF-ARX-MPC algorithm based on single-point linearization (MPC-SPL); (2) the RBF-ARX-MPC algorithm based on multi-point linearization (MPC-MPL); and (3) the RBF-ARX-MPC algorithm based on globally nonlinear optimization (MPC-GNO). In the MPC-SPL, the future multi-step-ahead predictive output of the system is obtained based on the local linearization of the RBF-ARX model at only current working-point, while in the MPC-MPL the future long-term output prediction is obtained according to the future local characteristics from previous online optimization results of the RBF-ARX model based MPC. In the MPC-GNO, the globally nonlinear characteristics of the RBF-ARX model are fully used for online getting control variables of the MPC. Real-time control experiments for the three type MPCs are carried out on a water tank system, which are also compared with a classical PID control and a traditional linear ARX model-based MPC. The results verify that the modeling method and the model-based predictive control strategies are realizable and effective for the nonlinear and unstable system. Moreover, it is also shown that the MPC-GNO can obtain better control performance but need more computation time compared to the other MPCs, which makes it possible to be applied into some slowly varying processes.     

Fuel efficiency‐oriented platooning control of connected nonlinear vehicles: A distributed economic MPC approach

This paper considers the fuel efficiency‐oriented platooning control problem of connected vehicles. We present a novel distributed economic model predictive control (EMPC) approach to solve the problem of the vehicle platoon subject to nonlinear dynamics and safety constraints. In order to improve fuel economy of the whole vehicle platoon, the fuel consumption criterion is used to design the distributed EMPC strategy for the platoon. Meanwhile, the car‐tracking performance is exploited to guarantee stability and string stability of the platoon. Then the fuel efficiency control problem of the platoon is formulated as a distributed dual‐layer economic optimal control problem, which is solved in a fashion of receding horizon. It is proved that the proposed strategy guarantees asymptotic stability and predecessor‐follower string stability as well as fuel economy of the whole platoon by minimizing the fuel consumption cost. Finally, the effectiveness of the proposed strategy is highlighted by comparing its performance with that of the traditional distributed MPC strategy in numerical simulations.     

MPC算法在机载传感器规划中的应用

针对传感器规划过程中传感器对移动目标的实时跟踪探测问题,将模型预测控制(MPC)的基本思想与卡尔曼滤波理论相结合,提出了一种改进MPC算法的传感器规划方法。仿真实验结果表明:该算法在解决传感器对移动目标实时跟踪探测方面具有良好的效果,能够快速、准确地搜索到移动目标。     

Reduction of the QP-MPC cascade structure to a single layer MPC

Some commercial MPC packages are implemented in two layers, the QP static layer and the MPC dynamic layer. In the absence of an upper Real Time Optimization layer, the static layer solves a simplified economic optimization problem, which defines optimum feasible targets for the dynamic layer. Since the LP/QP static layer and the MPC dynamic layer are usually executed within the same sampling period, it is not trivial to guarantee that the interaction between the two layers will not disrupt the stability of the whole structure. In this paper, it is proposed an approach to reduce the two-layer structure of some commercial MPCs to a single dynamic layer where the control cost function is extended to include the economic objective. In the proposed approach the convergence and stability of the closed-loop system can be obtained if the economic term of the cost function is properly weighted. A simulation example of a simple industrial system shows the efficiency of the proposed strategy.     

On the performance of economic model predictive control with self-tuning terminal cost

In this paper, we analyze the closed-loop performance of a recently introduced economic model predictive control (MPC) scheme with self-tuning terminal cost. To this end, we propose to use a generalized terminal region constraint instead of a generalized terminal equality constraint within the repeatedly solved optimization problem, which allows us to obtain improved closed-loop asymptotic average performance bounds. In particular, these bounds can be obtained a priori. We discuss how the necessary parameters for the generalized terminal region setting can be calculated, and we illustrate our findings with two numerical examples.     

Distributed Economic MPC for Synergetic Regulation of the Voltage of an Island DC Micro-Grid

In this paper, distributed model predictive control(DMPC) for island DC micro-grids(MG) with wind/photovoltaic(PV)/battery power is proposed, which coordinates all distributed generations(DG) to stabilize the bus voltage together with the insurance of having computational efficiency under a real-time requirement. Based on the feedback of the bus voltage, the deviation of the current is dispatched to each DG according to cost over the prediction horizon. Moreover, to avoid the excessive fluctuati...     

A hybrid Gaussian process approach to robust economic model predictive control

This paper proposes a hybrid Gaussian process (GP) approach to robust economic model predictive control under unknown future disturbances in order to reduce the conservatism of the controller. The proposed hybrid GP is a combination of two well-known methods, namely, kernel composition and nonlinear auto-regressive. A switching mechanism is employed to select one of these methods for disturbance prediction after analyzing the prediction outcomes. The hybrid GP is intended to detect not only patterns but also unexpected behaviors in the unknown disturbances by using past disturbance measurements. A novel forgetting factor concept is also utilized in the hybrid GP, giving less weight to older measurements, in order to increase prediction accuracy based on recent disturbances values. The detected disturbance information is used to reduce prediction uncertainty in economic model predictive controllers systematically. The simulation results show that the proposed method can improve the overall performance of an economic model predictive controller compared to other GP-based methods in cases when disturbances have discernible patterns.     

Optimal electricity rate structures for peak demand reduction using economic model predictive control

Economic model predictive control (EMPC) has recently gained popularity for managing energy consumption in buildings that are exposed to non-constant electricity prices, such as time-of-use prices or real-time prices. These electricity prices are employed directly in the objective function of the EMPC problem. This paper considers how electricity prices can be designed in order to achieve a specific objective, which in this case is minimizing peak electricity demand. A primal-dual formulation of the EMPC problem is presented that is used to determine optimal prices that minimize peak demand. The method is demonstrated on a simulated community of 900 residential homes to create a pricing structure that minimizes the peak demand of the community of homes. The pricing structure shows that homes should be given a 1-h peak demand duration, and that the peak prices given to the homes should be spread unevenly across 6 h of the afternoon.     

Bridging the gap between the linear and nonlinear predictive control: Adaptations for efficient building climate control

The linear model predictive control which is frequently used for building climate control benefits from the fact that the resulting optimization task is convex (thus easily and quickly solvable). On the other hand, the nonlinear model predictive control enables the use of a more detailed nonlinear model and it takes advantage of the fact that it addresses the optimization task more directly, however, it requires a more computationally complex algorithm for solving the non-convex optimization problem. In this paper, the gap between the linear and the nonlinear one is bridged by introducing a predictive controller with linear time-dependent model. Making use of linear time-dependent model of the building, the newly proposed controller obtains predictions which are closer to reality than those of linear time invariant model, however, the computational complexity is still kept low since the optimization task remains convex. The concept of linear time-dependent predictive controller is verified on a set of numerical experiments performed using a high fidelity model created in a building simulation environment and compared to the previously mentioned alternatives. Furthermore, the model for the nonlinear variant is identified using an adaptation of the existing model predictive control relevant identification method and the optimization algorithm for the nonlinear predictive controller is adapted such that it can handle also restrictions on discrete-valued nature of the manipulated variables. The presented comparisons show that the current adaptations lead to more efficient building climate control.     

On the theory of economic MPC: ELOC and approximate infinite horizon EMPC

In recent years, the notion of Economic Model Predictive Control (EMPC) has gained significant interest. Despite a marked improvement in economic performance, it has been shown that this performance will degrade substantially if implemented with a horizon that is not sufficiently large. In the current effort, it is shown that if applied to a particular reaction process, EMPC performance will abruptly collapse at a critical horizon size. To alleviate this issue, we develop an Infinite Horizon EMPC (IH-EMPC) formulation. While this IH-EMPC problem is computationally intractable, it does lead to an approximation of the optimal policy. The resulting Approximate IH-EMPC (AIH-EMPC) is identical to the original finite horizon EMPC, but includes a final cost term that represents the objective function from the finite horizon to infinity. With two example systems, a chemical reactor and a power system with energy storage, it is shown that the AIH-EMPC policy is virtually insensitive to its computational horizon size.     

参考轨线对MPC系统性能影响分析

参考轨线是MPC(模型预测控制)系统未来输出的趋势线,弄清参考轨线对预测控制系统性能的影响有十分重要的意义.本文运用内模控制原理,深入分析了参考轨线系数β对MPC系统闭环性能影响的内在机理,并得到了在控制加权阵R=0情况下,多步预测优化控制与单步预测优化控制完全等价的结论.