Analysis and design of model predictive control frameworks for dynamic operation -- An overview

This article provides an overview of model predictive control (MPC) frameworks for dynamic operation of nonlinear constrained systems. Dynamic operation is often an integral part of the control objective, ranging from tracking of reference signals to the general economic operation of a plant under online changing time-varying operating conditions. We focus on the particular challenges that arise when dealing with such more general control goals and present methods that have emerged in the literature to address these issues. The goal of this article is to present an overview of the state-of-the-art techniques, providing a diverse toolkit to apply and further develop MPC formulations that can handle the challenges intrinsic to dynamic operation. We also critically assess the applicability of the different research directions, discussing limitations and opportunities for further researc

Data-driven stabilization and safe control of nonlinear systems

The recent successes of machine learning solutions have inspired the research of new control algorithms derived directly from the available data without any intermediate step. Being able to design a stabilizing controller directly from data has the main advantage that, since it does not rely on a model of the system to control, the controller design is not influenced by any modeling error.Most of the time real systems are simplified with linear models to reduce the overall complexity in the controller design discarding all the complex nonlinear behaviors. A linear approximation could be an excessive simplification for complex system where the presence of nonlinear dynamics are important to understand those processes and nonlinearities can not be ignored. However, the analysis and control of a nonlinear model is often challenging. This thesis investigates data-based control methods for continuous and discrete-time nonlinear systems that do not require to model the system. In particular, we have developed a solution to obtain a stabilizing state feedback controller for the case of nonlinear systems. Stabilizing a closed-loop system is critical, but sometimes it is not enough. Safety is another important criteria considered in the design of a controller. We were able to formulate a new data-driven procedure to find a stabilizing controller that can also guarantee that the state of the system never violates the safety constraints.For all the solutions presented, we discussed how to handle real noisy measurements

Optimal model reference control design for grid connected voltage source converters

Texto en inglés y resumen en inglés y españolEsta tesis se centra en el diseño de controladores H∞ basados en modelos de referencia para su aplicación en el control de convertidores electrónicos de potencia en fuente de tensión (VSC). Se persiguen dos objetivos: el conformado de la admitancia de entrada de un VSC controlado en corriente y el óptimo amortiguamiento activo de filtros resonantes.El diseño de controladores óptimos H∞ aporta ciertas ventajas con respecto al diseño clásico. La principal técnica de diseño H∞ utilizada en la literatura se centra en la minimización de la función de sensibilidad. Ésta permite lidiar con diferentes problemas de compromiso en el diseño de controladores de forma sencilla, como el conformado de la función de lazo, el seguimiento de referencias, la estabilidad del sistema o la limitación del ancho de banda de control. Sin embargo, esta técnica carece de la habilidad de conformar la fase de funciones en lazo cerrado. La técnica H∞ basada en modelos de referencia soluciona este problema.La principal contribución de esta tesis es la aplicación de esta técnica para el moldeado de la admitancia en lazo cerrado de VSCs, la cual juega un importante papel tanto en la estabilidad de sistemas complejos como en la mejora de la calidad de energía en la red. Utilizando la técnica propuesta, el diseñador podrá especificar, en un gran ancho de banda y en un solo marco de diseño, tanto la admitancia del convertidor del convertidor (en modulo y en fase), como el comportamiento del seguimiento de referencias. El proceso de diseño finaliza con la síntesis de un controlador discreto ejecutable en una plataforma digital (DSP).Las posibilidades que presenta esta nueva metodología de diseño son amplias. La presente propuesta se ilustra con el control de un rectificador activo conectado a la red, pero es lo suficientemente flexible como para aplicarse en otros esquemas de control y topologías de convertidor. Se considerarán tres aplicaciones del control de admitancia: el diseño de aplicaciones resistivas en un gran ancho de banda, las cuales mejoran la robustez en la conexión estable a red débiles, el diseño de aplicaciones con una admitancia baja, las cuales mejoran el rechazo de (sub/inter)armónicos de la tensión de red en el control de corriente, y el diseño de aplicaciones con una admitancia alta, que al conectarse en paralelo a la red actúan como estabilizadores de ésta. La metodología de diseño de cada controlador, así como sus limitaciones, implementación y los resultados experimentales obtenidos son detallados.De forma complementaria, se explora la técnica de diseño basada en modelos de referencia para el amortiguamiento óptimo de resonancias en filtros LCL. La idea es diseñar un amortiguador activo que, una vez conectado, moldee la dinámica del filtro LCL de tal manera que este se comporte como un filtro L. Esto permitirá el posterior uso de sencillos controladores de corriente diseñados para filtro L, evitando la complejidad del diseño de controladores para filtros LCL, sin renunciar con ello a su gran capacidad de filtrado. La metodología de diseño es lo suficientemente general como para presentar diferentes estructuras de entrada/salida para el amortiguador. Los resultados obtenidos demuestran la mejora en la robustez del sistema

Uniform finite time stabilisation of non-smooth and variable structure systems with resets

This thesis studies uniform finite time stabilisation of uncertain variable structure and non-smooth systems with resets. Control of unilaterally constrained systems is a challenging area that requires an understanding of the underlying mechanics that give rise to reset or jumps while synthesizing stabilizing controllers. Discontinuous systems with resets are studied in various disciplines. Resets in states are hard nonlinearities. This thesis bridges non-smooth Lyapunov analysis, the quasi-homogeneity of differential inclusions and uniform finite time stability for a class of impact mechanical systems. Robust control synthesis based on second order sliding mode is undertaken in the presence of both impacts with finite accumulation time and persisting disturbances. Unlike existing work described in the literature, the Lyapunov analysis does not depend on the jumps in the state while also establishing proofs of uniform finite time stability. Orbital stabilization of fully actuated mechanical systems is established in the case of persisting impacts with an a priori guarantee of finite time convergence between t he periodic impacts. The distinguishing features of second order sliding mode controllers are their simplicity and robustness. Increasing research interest in the area has been complemented by recent advances in Lyapullov based frameworks which highlight the finite time Convergence property. This thesis computes the upper bound on the finite settling time of a second order sliding mode controller. Different to the latest advances in the area, a key contribution of this thesis is the theoretical proof of the fact that finite settling time of a second order sliding mode controller tends to zero when gains tend to infinity. This insight of the limiting behaviour forms the basis for solving the converse problem of finding an explicit a priori tuning formula for the gain parameters of the controller when and arbitrary finite settling time is given. These results play a central role ill the analysis of impact mechanical systems. Another key contribution of the thesis is that it extends the above results on variable structure systems with and without resets to non-smooth systems arising from continuous finite time controllers while proving uniform finite time stability. Finally, two applications are presented. The first application applies the above theoretical developments to the problem of orbital stabilization of a fully actuated seven link biped robot which is a nonlinear system with periodic impacts. The tuning of the controller gains leads to finite time convergence of the tracking errors between impacts while being robust to disturbances. The second application reports the outcome of an experiment with a continuous finite time controller

Invariant Set-based Methods for the Computation of Input and Disturbance Sets

This dissertation presents new methods to synthesize disturbance sets and input constraints set for constrained linear time-invariant systems. Broadly, we formulate and solve optimization problems that (a) compute disturbance sets such that the reachable set of outputs approximates an assigned set, and (b) compute input constraint sets guaranteeing the stabilizability of a given set of initial conditions. The proposed methods find application in the synthesis and analysis of several control schemes such as decentralized control, reduced-order control, etc., as well as in practical system design problems such as actuator selection, etc. The key tools supporting the develpment of the aforementioned methods are Robust Positive Invariant (RPI) sets. In particular, the problems that we formulate are such that they co-synthesize disturbance/input constraint sets along with the associated RPI sets. This requires embedding existing techniques to compute RPI sets within an optimization problem framework, that we facilitate by developing new results related to properties of RPI sets, polytope representations, inclusion encoding techniques, etc. In order to solve the resulting optimization problems, we develop specialized structure-exploiting solvers that we numerically demonstrate to outperform conventional solution methods. We also demonstrate several applications of the methods we propose for control design. Finally, we extend the methods to tackle data-driven control synthesis problems in an identification-for-control framework