Economic Model Predictive Control with Nonlinear Constraint Relaxation for the Operational Management of Water Distribution Networks

This paper presents the application of an economic model predictive control (MPC) for the operational management of water distribution networks (WDNs) with periodic operation and nonlinear constraint relaxation. In addition to minimizing operational costs, the proposed approach aims to reduce the computational load and to improve the implementation efficiency associated with the nonlinear nature of the MPC problem. The behavior of the WDN is characterized by a set of difference-algebraic equations, where the relation of hydraulic pressure/head and flow in interconnected pipes is nonlinear. Specifically, the considered WDN model includes two categories of nonlinear algebraic equations for unidirectional and bidirectional flows in pipes, respectively. In this paper, we propose an iterative algorithm to relax these nonlinear algebraic equations into a set of linear inequality constraints that will be implemented in the economic MPC design, which improves the implementation efficiency and meanwhile optimizes the economic performance. Finally, the proposed strategy is applied to a well-known benchmark of the Richmond WDN. The closed-loop simulation results are shown and the proposed strategy is also compared with a nonlinear economic MPC using several key performance indexes.Agencia Estatal de Investigación DPI2016-76493Fondo de Desarrollo Regional DPI2016-76493Sello María de Maeztu MDM-2016-0656Subvención de FPI BES-2014-06831

A Novel Formulation of Economic Model Predictive Control for Periodic Operations

This paper proposes a novel formulation of economic model predictive control (MPC) for linear systems with periodic operations. In this economic MPC design, the optimal periodic trajectory from an economic point of view is unknown, hence it is not possible to follow a standard control strategy in which the MPC uses this trajectory to define a terminal constraint to guarantee closed-loop convergence. The economic cost function is optimized with a periodicity constraint at each time step considering all periodic trajectories in a period including the current state. The recursive feasibility and closed-loop convergence to the optimal periodic trajectory are analyzed using the Karush-Kuhn-Tucker conditions. Finally, two simulations are provided to demonstrate the main results.Agencia Estatal de Investigación DPI2013-48243-C2Agencia Estatal de Investigación DPI2016-76493- C3Ministerio de Ciencia, Innovación y Universidades MDM-2016-065

Advances in state estimation, diagnosis and control of complex systems

This dissertation intends to provide theoretical and practical contributions on estimation, diagnosis and control of complex systems, especially in the mathematical form of descriptor systems. The research is motivated by real applications, such as water networks and power systems, which require a control system to provide a proper management able to take into account their specific features and operating limits in presence of uncertainties related to their operation and failures from component malfunctions. Such a control system is expected to provide an optimal operation to obtain efficient and reliable performance. State estimation is an essential tool, which can be used not only for fault diagnosis but also for the controller design. To achieve a satisfactory robust performance, set theory is chosen to build a general framework for descriptor systems subject to uncertainties. Under certain assumptions, these uncertainties are propagated and bounded by deterministic sets that can be explicitly characterized at each iteration step. Moreover, set-invariance characterizations for descriptor systems are also of interest to describe the steady performance, which can also be used for active mode detection. For the controller design for complex systems, new developments of economic model predictive control (EMPC) are studied taking into account the case of underlying periodic behaviors. The EMPC controller is designed to be recursively feasible even with sudden changes in the economic cost function and the closed-loop convergence is guaranteed. Besides, a robust technique is plugged into the EMPC controller design to maintain these closed-loop properties in presence of uncertainties. Engineering applications modeled as descriptor systems are presented to illustrate these control strategies. From the real applications, some additional difficulties are solved, such as using a two-layer control strategy to avoid binary variables in real-time optimizations and using nonlinear constraint relaxation to deal with nonlinear algebraic equations in the descriptor model. Furthermore, the fault-tolerant capability is also included in the controller design for descriptor systems by means of the designed virtual actuator and virtual sensor together with an observer-based delayed controller.Esta tesis propone contribuciones de carácter teórico y aplicado para la estimación del estado, el diagnóstico y el control óptimo de sistemas dinámicos complejos en particular, para los sistemas descriptores, incluyendo la capacidad de tolerancia a fallos. La motivación de la tesis proviene de aplicaciones reales, como redes de agua y sistemas de energía, cuya naturaleza crítica requiere necesariamente un sistema de control para una gestión capaz de tener en cuenta sus características específicas y límites operativos en presencia de incertidumbres relacionadas con su funcionamiento, así como fallos de funcionamiento de los componentes. El objetivo es conseguir controladores que mejoren tanto la eficiencia como la fiabilidad de dichos sistemas. La estimación del estado es una herramienta esencial que puede usarse no solo para el diagnóstico de fallos sino también para el diseño del control. Con este fin, se ha decidido utilizar metodologías intervalares, o basadas en conjuntos, para construir un marco general para los sistemas de descriptores sujetos a incertidumbres desconocidas pero acotadas. Estas incertidumbres se propagan y delimitan mediante conjuntos que se pueden caracterizar explícitamente en cada instante. Por otra parte, también se proponen caracterizaciones basadas en conjuntos invariantes para sistemas de descriptores que permiten describir comportamientos estacionarios y resultan útiles para la detección de modos activos. Se estudian también nuevos desarrollos del control predictivo económico basado en modelos (EMPC) para tener en cuenta posibles comportamientos periódicos en la variación de parámetros o en las perturbaciones que afectan a estos sistemas. Además, se demuestra que el control EMPC propuesto garantiza la factibilidad recursiva, incluso frente a cambios repentinos en la función de coste económico y se garantiza la convergencia en lazo cerrado. Por otra parte, se utilizan técnicas de control robusto pata garantizar que las estrategias de control predictivo económico mantengan las prestaciones en lazo cerrado, incluso en presencia de incertidumbre. Los desarrollos de la tesis se ilustran con casos de estudio realistas. Para algunas de aplicaciones reales, se resuelven dificultades adicionales, como el uso de una estrategia de control de dos niveles para evitar incluir variables binarias en la optimización y el uso de la relajación de restricciones no lineales para tratar las ecuaciones algebraicas no lineales en el modelo descriptor en las redes de agua. Finalmente, se incluye también una contribución al diseño de estrategias de control con tolerancia a fallos para sistemas descriptores

Economic MPC-LPV control for the operational management of water distribution networks

This paper presents an Economic Model Predictive Control (EMPC) for the operational management of water distribution networks (WDNs) with periodic operation based on embedding the nonlinearity of the model to the Linear Parameter Varying (LPV) model of WDNs. The performance of the WDN is identified by a set of difference-algebraic equations while the relation of hydraulic head/pressure and flow in connected pipes is nonlinear. In particular, the WDN model consists of two sections of nonlinear algebraic equations for bidirectional and unidirectional flows in pipes, respectively. The proposed algorithm is embedded the nonlinear algebraic equations into the LPV model. The proposed control approach allows the controller to accommodate the scheduling parameters. By computing the prediction of the state variables along a prediction time horizon, the system model can be modified according to the evaluation of the estimated state at each time instant. This iterative approach improves the implementation efficiency and reduces the computational burden compared to the solution of a non-linear optimization problem. Finally, the proposed strategy is applied to a well-known benchmark of the Richmond WDN.Peer ReviewedPostprint (author's final draft

Non-linear economic model predictive control of water distribution networks

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper addresses a non-linear economic model predictive control (EMPC) strategy for water distribution networks (WDNs). A WDN could be considered as a non-linear system described by differential-algebraic equations (DAEs) when flow and hydraulic head equations are considered. As in other process industries, the main operational goal of WDNs is the minimisation of the economic costs associated to pumping and water treatment, while guaranteeing water supply with required flows and pressures at all the control/demand nodes in the network. Other operational goals related to safety and reliability are usually sought. From a control point of view, EMPC is a suitable control strategy for WDNs since the optimal operation of the network cannot be established a priori by fixing reference volumes in the tanks. Alternatively, the EMPC strategy should determine the optimal filling/emptying sequence of the tanks taking into account that electricity price varies between day and night and that the demand also follows a 24-hour repetitive pattern. On the other hand, as a result of the ON/OFF operation of parallel pumps in pumping stations, a two-layer control scheme has been used: a non-linear EMPC strategy with hourly control interval is chosen in the upper layer and a pump scheduling approach with one-minute sampling time in the lower layer. Finally, closed-loop simulation results of applying the proposed control strategy to the D-Town water network are shown.Peer ReviewedPostprint (author's final draft

Data based predictive control: Application to water distribution networks

In this thesis, the main goal is to propose novel data based predictive controllers to cope with complex industrial infrastructures such as water distribution networks. This sort of systems have several inputs and out- puts, complicate nonlinear dynamics, binary actuators and they are usually perturbed by disturbances and noise and require real-time control implemen- tation. The proposed controllers have to deal successfully with these issues while using the available information, such as past operation data of the process, or system properties as fading dynamics. To this end, the control strategies presented in this work follow a predic- tive control approach. The control action computed by the proposed data- driven strategies are obtained as the solution of an optimization problem that is similar in essence to those used in model predictive control (MPC) based on a cost function that determines the performance to be optimized. In the proposed approach however, the prediction model is substituted by an inference data based strategy, either to identify a model, an unknown control law or estimate the future cost of a given decision. As in MPC, the proposed strategies are based on a receding horizon implementation, which implies that the optimization problems considered have to be solved online. In order to obtain problems that can be solved e ciently, most of the strategies proposed in this thesis are based on direct weight optimization for ease of implementation and computational complexity reasons. Linear convex combination is a simple and strong tool in continuous domain and computational load associated with the constrained optimization problems generated by linear convex combination are relatively soft. This fact makes the proposed data based predictive approaches suitable to be used in real time applications. The proposed approaches selects the most adequate information (similar to the current situation according to output, state, input, disturbances,etc.), in particular, data which is close to the current state or situation of the system. Using local data can be interpreted as an implicit local linearisation of the system every time we solve the model-free data driven optimization problem. This implies that even though, model free data driven approaches presented in this thesis are based on linear theory, they can successfully deal with nonlinear systems because of the implicit information available in the database. Finally, a learning-based approach for robust predictive control design for multi-input multi-output (MIMO) linear systems is also presented, in which the effect of the estimation and measuring errors or the effect of unknown perturbations in large scale complex system is considered