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Model Predictive Control for systems with changing setpoints
No full textEsta tesis trata el problema del diseño de un controlador predictivo para sistemas caracterizados por cambios en el punto de operación. La clásica formulación del controlador predictivo, para regular el sistema al nuevo punto de operación deseado, garantiza se ... guimiento de referencia en caso de sistemas que no estén sujeto a restricciones, pero no resuelve el problema cuando hay restricciones. En esos casos, un cambio de referencia puede producir una pérdida de la factibilidad del problema de optimización por una de las siguientes causas: (I) la restricción terminal para el nuevo punto de equilibrio puede no ser un invariante y (II) la región terminal para el nuevo punto de operación podría no ser alcanzable en N pasos. Para recuperar la factibilidad, se requeriría el recálculo del horizonte por lo que un cambio de referencia conllevaría el rediseño on-line del controlador, lo que no será siempre posible.En este trabajo de tesis se presenta una nueva formulación de control predictivo que permite solucionar este problema. Las principales características de esta nueva formulación son: un punto de equilibrio artificial considerado como variable de decisión, un coste que penalice la distancia entre la trayectoria predicha y el punto de equilibrio artificial, un coste adicional que penalice la distancia entre el punto de equilibrio artificial y el punto de equilibrio deseado, llamado coste de offset, y una restricción terminal extendida, el conjunto invariante para seguimiento. Este controlador garantiza estabilidad y factibilidad recursiva para cualquier cambio de referencia. En esta tesis se demuestra que una adecuada elección del coste de offset garantiza la propiedad de la optimalidad local del controlador. Además, se presenta una caracterización de las regiones en las cuales esta propiedad se cumple.El coste de offset juega el papel de un optimizador en tiempo real (RTO) incorporado en el mismo controlador predictivo. Así, este coste de offset permite trabajar con plantas no cuadradas, o con puntos de operación no alcanzables. En este último caso, el controlador lleva el sistema al punto de equilibrio más cercano, en el sentido que se minimiza el coste de offset. Además se demuestra que este coste de offset se puede formular como distancia a un conjunto. Esta formulación hace el controlador predictivo para tracking propuesto, adecuado también para problemas de control por zonas. En estos problemas el objetivo no es un punto fijo; es más bien una región dentro de la cual se desea que las salidas permanezcan. Para este caso, en la tesis se propone un controlador robusto basado en predicciones nominales y en restricciones contractivas.En este trabajo se trata también el tema del control de sistemas de gran escala. Estos sistemas se pueden ver como una serie de unidades operativas, interconectadas entre ellas. Por lo tanto, esas plantas se pueden dividir en diferentes subsistemas que comunican entre ellos por medio de redes de varias naturalezas. El control total de esas plantas usando controladores centralizados - un solo agente controlando todos los subsistemas - es difícil de realizarse, por un lado por la elevada carga computacional, y por el otro lado por la difícil organización y el mantenimiento del controlador centralizado. Por lo tanto, una estrategia de control alternativa es el control distribuido. Se trata de una estrategia basada en diferentes agentes controlando los diferentes subsistemas, que pueden o no intercambiar informaciones entre ellos. La diferencia entre las diferentes estrategias de control predictivo, es la manera de tratar el intercambio de informaciones. En el control distribuido noncooperativo, cada agente toma decisiones sobre su propio subsistemas considerando solo localmente las informaciones de los otros subsistemas. Las prestaciones de la planta suelen converger a un equilibrio de Nash. Los controladores distribuidos cooperativo, por otro lado, consideran el efecto de todas las acciones de control sobre todos los subsistemas de toda la red. Cada agente optimiza un coste global, como por ejemplo un coste centralizado. Por lo tanto, las prestaciones de estos controladores convergen a un equilibrio de Pareto, como en el caso centralizado. En este trabajo de tesis se propone una estrategia de control predictivo para seguimiento distribuido cooperativo y se demuestra que el controlador lleva el sistema al óptimo del centralizado.La tesis toma en consideración también los sistemas nolineales. En particular, el controlador propuesto se extiende al caso de sistemas no lineales y se proponen tres formulaciones, respectivamente con restricción terminal de igualdad, restricción terminal de desigualdad y sin restricción terminal. En particular, para la formulación con restricción de igualdad, se propone un método basado en el modelado LTV de las plantas. La idea es diseñar un conjunto de controladores locales, cuya región de factibilidad cubra el entero conjunto de puntos de equilibrio.Finalmente, el trabajo de tesis trata el problema del diseño de controladores predictivos con optimalidad económica. Esta formulación considera un funcional de coste basado en objetivos económicos, en lugar del clásico funcional basado en errores de seguimiento, y provee mejores prestaciones con respeto al objetivo que los estándar controladores para seguimiento. En la tesis se presenta un controlador predictivo económico para objetivos económicos cambiantes. Ese controlador es una formulación híbrida entre el control predictivo para seguimiento y el controlador predictivo económico, dado que hereda la factibilidad garantizada para cualquier cambio del objetivo del primero, y la optimalidad con respeto al objetivo del segundo
Editorial Model Predictive Control for Energy Systems: Economic and Distributed Approaches
No full text
Economic optimality in MPC: A comparative study
No full textModel Predictive Control (MPC) is one of the most used advanced control strategy in the industries, mainly due to its capability to fulfill economic objectives, taking into account a simplified dynamic model of the plant, constraints, and stability requirements. In the last years, several economic formulations of MPC have been presented, which overcome the standard setpoint-tracking formulation. The goal of this work is to provide, by means of application to a highly nonlinear plant, a comparison of different strategies, focusing mainly on economic optimality, computational burden, and economic performance (understood as transient economic optimality)
Offset-free multi-model economic model predictive control for changing economic criterion
No full textEconomic Model Predictive Controllers, consisting of an economic criterion as stage cost for the dynamic regulation problem, have shown to improve the economic performance of the controlled plant. However, throughout the operation of the plant, if the economic criterion changes – due to variations of prices, costs, production demand, market fluctuations, reconciled data, disturbances, etc. – the optimal operation point also changes. In industrial applications, a nonlinear description of the plant may not be available, since identifying a nonlinear plant is a very difficult task. Thus, the models used for prediction are in general linear. The nonlinear behavior of the plant makes that the controller designed using a linear model (identified at certain operation point) may exhibit a poor closed-loop performance or even loss of feasibility and stability when the plant is operated at a different operation point. A way to avoid this issue is to consider a collection of linear models identified at each of the equilibrium points where the plant will be operated. This is called a multi-model description of the plant. In this work, a multi-model economicMPC is proposed, which takes into account the uncertainties that arise from the difference between nonlinear and linear models, by means of a multi-model approach: a finite family of linear models is considered (multi-model uncertainty), each of them operating appropriately in a certain region around a given operation point. Recursive feasibility, convergence to the economic setpoint and stability are ensured. The proposed controller is applied in two simulations for controlling an isothermal chemical reactor with consecutive-competitive reactions, and a continuous flow stirred-tank reactor with parallel reactions
MPC-based artificial pancreas accounting for circadian variability of insulin sensitivity
No full textIn the context of closed-loop glycemic control, MPC has shown the skillfulness to improve glucose regulation in patients with type 1 diabetes mellitus (T1DM). To reduce its complexity, many of the proposed control strategies have been designed based on linear time-invariant (LTI) models, without accounting for intraday parametric fluctuations. In this work, a pulsatile Zone Model Predictive Control (pZMPC) is examined under a realistic patterns of intraday insulin sensitivity ( SI ), according to the recent updates of the FDA-approved UVA/Padova simulator. Nominal updates of the postprandial insulin sensitivity are explicitly taken into account in the control-oriented model to improve the glucose predictions. The resulting controller is tested ‘in-silico’ with the FDA-approved UVA/Padova simulator, while its behavior is analyzed by comparing the usual statistical metrics with the corresponding time-invariant configuration. As expected, results show significant improvements, which justifies the (reasonable) increment in the controller complexity
Distributed MPC for tracking. Application to a 4 tanks plant
Get PDFThe problem of controlling large scale systems, usually divided into subsystems controlled by different agents, is solved using cooperative distributed control schemes, where the agents share open-loop information in order to improve closed-loop performance. In a recent paper, a cooperative distributed linear model predictive control strategy applicable to any finite number of subsystems, has been presented. This controller is able to steer the system to any admissible setpoint in an admissible way. Feasibility is ensured under any changing of the target steady state. In this paper, this controller is applied to the plant proposed for the HD-MPC Benchmark: the four tanks plant situated in the lab of the University of Seville
Economic MPC for a changing economic criterion for linear systems
No full textEconomic Model Predictive Controllers, consisting of an economic criterion as stage cost for the dynamic regulation problem, have shown to improve the economic performance of the controlled plant, as well as to ensure stability of the economic setpoint. However, throughout the operation of the plant, economic criteria are usually subject to frequent changes, due to variations of prices, costs, production demand, market fluctuations, reconciled data, disturbances, etc. A different economic criterion determines a change of the optimal operation point and this may cause a loss of feasibility and/or stability. In this paper a stabilizing economic MPC for changing economic criterion for linear prediction models is presented. The proposed controller always ensures feasibility for any given economic criterion, thanks to the particular choice of the terminal ingredients. Asymptotic stability is also proved, providing a Lyapunov function
A robust gradient-based MPC for integrating Real Time Optimizer (RTO) with control
No full textA gradient-based model predictive control (MPC) strategy was recently proposed to reduce the computational burden derived from the explicit inclusion of an economic real time optimization (RTO). The main idea is to compute a suboptimal solution, which is the convex combination of a feasible solution anda solution of an approximated (linearized) problem. The main benefits of this strategy are that convergence is still guaranteed and good economic performances are obtained, according to several simulation scenarios. The formulation, however, is developed only for the nominal case, which significantly reduces its applicability. In this work, an extension of the gradient-based MPC to explicitly account for disturbances is made. The resulting robust formulation considers a nominal prediction model, but restricted constraints (in order to account for the effect of additive disturbances). The nominal economic performance is preserved and robust stability is ensured. An illustrative example shows the benefits of the proposal
Data-driven Model Predictive Control strategies for blood glucose regulation in Artificial Pancreas
Get PDFL'obiettivo di questa tesi è quello di sviluppare algoritmi di controllo per la gestione dei livelli di glicemia nel sangue dei pazienti diabetici di tipo 1, basati sui dati del paziente, in modo da ottenere algoritmi personalizzati e creare dispositivi sempre più autonomi. Nello specifico, viene utilizzato il Model Predictive Control (MPC) come algoritmo di controllo, basato sulla CHoKI (Componentwise Holder Kinky Inference) come metodo di apprendimento basato sui dati.
Nella tesi sono presentati diversi tipi di CHoKI-based MPC, con strutture diverse e tutti sono stati testati sui pazienti virtuali del simulatore UVA/Padova, accettato dall'FDA per gli studi preclinici.
I risultati sono soddisfacenti, in quanto i vari controllori proposti sono in grado di ridurre i tempi in ipoglicemia (ovvero quando i valori di glicemia sono inferiori a 70 mg/dL), vista la sua pericolosità nel breve periodo.The objective of this thesis is to develop control algorithms for managing blood glucose levels in type 1 diabetic patients, which are based on patient data, in order to obtain personalized algorithms and to create increasingly autonomous devices. Specifically, Model Predictive Control (MPC) is used as the control algorithm, based on the CHoKI (Componentwise Holder Kinky Inference) as a data-driven learning method.
The thesis presents different types of CHoKI-based MPC, with different structures, all of which have been tested on virtual patients in the UVA/Padova simulator, accepted by the FDA for preclinical studies.
The results are satisfactory, as the various controllers proposed are able to reduce the time spent in hypoglycemia (i.e., when blood glucose levels are below 70 mg/dL), given its short-term danger
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