SOBRE EL CONTROL ÓPTIMO DE UN PROBLEMA DE CONTAMINACIÓN AMBIENTAL

This article is studied the optimal control of distributed parameter systems applied to an environmental pollution problem. The model consists of a differential equation partial parabolic modeling of a pollutant transport in a fluid. The model is considered the speed with which the pollutant spreads in the environment and degradation that suffers the contaminant by the presence of a factor biological inhibitor, which breaks the contaminant at a rate that is not dependent on space and time.Using the method of Lagrange multipliers is possible to prove the existence solving the problem of control and obtaining optimality conditions for optimal control. En este artículo es estudiado el control óptimo de un sistema de parámetros distribuidos aplicado a un problema de contaminación ambiental. El modelo consiste de una ecuación diferencial parcial de tipo parabólico que modela el transporte de una sustancia contaminante en un fluido. En el modelo es considerado la velocidad con que el contaminante se propaga en el medio ambiente y la degradación que la sustancia contaminante sufre por la presencia de un factor inhibidor biológico, que descompone el contaminante a una tasa que no depende del espacio y el tiempo. Utilizando el método de los multiplicadores de Lagrange es posible probar la existencia de solución del problema de control y la obtención de las condiciones de optimalidad para el control  óptimo

Restricted structure predictive control for linear and nonlinear systems

An optimal predictive control algorithm is introduced for the control of linear and nonlinear discrete-time multivariable systems. The controller is specified in a 'restricted structure' form involving a set of given linear transfer-functions and a set of gains that minimise a Generalised Predictive Control (GPC) cost-index. The set of functions can be chosen as proportional, integral and derivative terms, however, a wide range of controller structures is possible. This is referred to as Restricted-Structure GPC control. The multi-step predictive control cost-function is novel, since it includes weightings on the ‘low-order’ controller gains and the rate of change of gains. This considerably improves the numerical computations ensuring critical inverse computations cannot lead to a singular matrix. It also provides the option of adding soft or hard constraints on the controller gains which provides additional flexibility for control design. The ability to include a plant model that can include a general nonlinear operator is also new for restricted structure control solutions. The low-order controller provides a potential improvement in robustness, since it is often less sensitive to plant uncertainties. The simple controller structure also enables relatively unskilled staff to retune the system using familiar tuning terms, and provides a potentially simpler QP problem for the constrained case

A Forward On-The-Fly Approach for Safety and Reachability Controller Synthesis of Timed Systems

RÉSUMÉ Cette thèse s’intéresse à la synthèse de contrôleurs pour des systèmes temps réel (systèmes temporisés). Partant d’un système temps réel modélisé par un réseau de Petri temporel composé de transitions contrôlables et non contrôlables (TPN), le contrôle vise à forcer, en restreignant les intervalles de franchissement des transitions contrôlables, le système à satisfaire les propriétés souhaitées. Nous proposons, dans cette thèse, un algorithme pour synthétiser de tels contrôleurs pour des propriétés de sûreté et d’accessibilité. Cet algorithme, basé sur la méthode de graphe de classes d’états, calcule à la volée les classes d’états atteignables du TPN tout en collectant progressivement les sous-intervalles de tir à éviter, afin de satisfaire les propriétés souhaitées. Avec cet algorithme, il n’est plus nécessaire de calculer les prédécesseurs contrôlables et de partitionner récursivement les classes d’états jusqu’à atteindre un point fixe, comme c’est le cas dans les autres approches basées sur l’exploration, en avant et en arrière, de l’espace des états du système. Nous prouvons formellement la correction de l’algorithme, puis nous montrons que dans la catégorie des contrôleurs basés sur la restriction des intervalles de tir, l’algorithme, proposé dans cette thèse, synthétise un contrôleur optimal (le plus permissif possible). Afin d’atténuer davantage le problème d’explosion combinatoire, nous montrons comment combiner cette approche avec une abstraction par l’inclusion, par union-convexe ou par enveloppe-convexe. Nous montrons également comment exploiter cet algorithme pour générer des contrôleurs décentralisés. Enfin, nous proposons d’appliquer cet algorithme pour contrôler des TPN par des chronomètres. Notre algorithme permet de partitionner les intervalles des transitions en “bons” et “mauvais” sous-intervalles (à éviter). L’idée est d’utiliser des chronomètres pour suspendre les tâches (transitions) durant leurs mauvais sous-intervalles et les activer dans leurs “bons sous-intervalles”. Il s’agit donc de contrôler les réseaux de Petri temporels en associant des chronomètres aux transitions contrôlables, pour obtenir ainsi des réseaux de Petri temporels contrôlés.----------ABSTRACT This thesis deals with controller synthesis for real time systems (timed systems). Given a real time system modeled as a Time Petri Net (TPN) with controllable and uncontrollable transitions, the control aims at forcing the system to satisfy properties of interest, by limiting the firing intervals of controllable transitions. We propose, in this thesis, an algorithm to synthesize such controllers for safety / reachability properties. This algorithm, based on the state class graph method, computes on-the-fly the reachable state classes of the TPN while collecting progressively firing subintervals to be avoided so that the property is satisfied. It does not need to compute controllable predecessors and then split state classes until reaching a fixpoint, as it is the case for other approaches based on backward and forward exploration of state space of the system. We prove formally the correctness of the algorithm and show that, in the category of state dependent controllers based on the restriction of firing intervals, the algorithm proposed in this thesis, synthesizes maximally permissive controllers. In order to attenuate the state explosion problem, we show how to combine efficiently this approach with an abstraction by inclusion, convex union or convex hull. Afterwards, we discuss the compatibility of this method with distributed systems and decentralized controllers. Finally, we apply this algorithm to control TPN with controllable and uncontrollable transitions by stopwatch. In this approach, we find the subintervals violating the given properties and our objective is to suspend the tasks (transitions) during their bad subintervals and to resume them later. The controller is synthesized through the same algorithm already introduced. In this approach, we suggest to control time Petri nets by associating stopwatches to controllable transitions and to achieve a controlled time Petri nets

Automatic Control of a Parabolic Trough Solar Thermal Power Plant

This thesis is interested in improving the operation of a parabolic trough technology based solar thermal power plant by means of automatic control. One of the challenging issues in a solar thermal power plant, from the control point of view, is to maintain the thermal process variables close to their desired levels. In contrast to a conventional power plant where fuel is used as the manipulated variable, in a solar thermal power plant, solar radiation cannot be manipulated and in fact it ironically acts as a disturbance due to its change on a daily and seasonal basis. The research facility ACUREX is used as a test bed in this thesis. ACUREX is a typical parabolic trough technology based solar thermal power plant and belongs to the largest research centre in Europe for concentrating solar technologies, namely the Plataforma Solar de Almería (PSA) in south-east Spain. The plant exhibits nonlinearities as well as resonance characteristics that lie well within the desired control bandwidth. Failure to adequately capture the resonance characteristics of the plant results in an undesired oscillatory control performance. Moreover, measured disturbances are an integral part of the plant and while some of the measured disturbances do not have a significant impact on the operation of the plant, others do. Hence, with the aim of handling the plant nonlinearities and capturing the plant resonance characteristics, while taking explicit account of the measured disturbances, in this thesis a gain scheduling feedforward predictive control strategy is proposed. The control strategy is based upon a family of local linear time-invariant state space models that are estimated around a number of operating points. The locally estimated linear time-invariant state space models have the key novelty of being able to capture the resonance characteristics of the plant with the minimal number of states and hence, simple analysis and control design. Moreover, while simple classical, series and parallel, feedforward configurations have been proposed and used extensively in the literature to mitigate the impact of the measured disturbances of the ACUREX plant, the proposed control strategy incorporates a feedforward systematically by including the effects of the measured disturbances of the ACUREX plant into the predictions of future outputs. In addition, a target (set point) for a control strategy is normally set at the ACUREX plant by the plant operator. However, in this thesis it is argued that, in parallel, the operator must choose between potentially ambitious and perhaps unreachable targets and safer targets. Ambitious targets can lead to actuator saturation and safer targets imply electricity production losses. Hence, in this thesis a novel two-layer hierarchical control structure is proposed with the gain scheduling feedforward predictive control strategy being deployed in a lower layer and an adequate reachable reference temperature being generated from an upper layer. The generated reference temperature drives the plant near optimal operating conditions, while satisfying the plant safety constraints, without any help from the plant operator and without adding cost. The proposed two-layer hierarchical control strategy has the potential benefits of: (i) maximising electricity production; (ii) reducing the risk of actuator saturation; (iii) extending the life span of various elements of the plant (e.g. synthetic oil, pump and valves) and (iv) limiting the role of the plant operator. The efficacy of the proposed two-layer hierarchical control strategy is evaluated using a nonlinear simulation model that approximates the dynamic behaviour of the ACUREX plant. The nonlinear simulation model is constructed in this thesis and validated in the time and frequency domain