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

CONTROL TECHNIQUES APPLIED TO INTEGRATED SHIP MOTION CONTROL

Fins stabilisers are devices which are fitted to the hull of a ship and utilised to ameliorate its rolling motions. They apply a regulated moment about the ship's axis of roll in order to oppose the sea induced disturbances. Recognising their unsurpassed performance, the Royal Navy, since the 1950's, equips all its vessels with fin stabilisers. It can be shown that the rudders, in vessels of appropriate size, also have the potential to be harnessed as roll stabilisers Rudder Roll Stabilisation (RRS) without degrading the ship's course-keeping. Thus creating a more stable platform for the human operators and equipment. The reported success of RRS imparted an impetus to the Royal Navy to initiate this study. The objectives are to ascertain whether RRS is possible without rudder modifications and to establish whether enhanced levels of stabilisation would accrue if the fins and RRS were operated in congress. The advantages in this novel approach being: avoidance of redesign and refit of rudders, three modes of operation (fins alone, RRS alone and combined RRS and fins), reduced fin activity and by implication self-generated noise, and amenability to be retrofitted by simple alteration of any existing ship's autopilot software. The study initially examined the mathematical models of the ship dynamics, defining deficiencies and evaluating sources of uncertainty. It was postulated that the dual purpose of the rudder can be separated into non-interacting frequency channels for controller design purposes. An integrated design methodology is adopted to the roll stabilisation problem. Investigating the capabilities of the rudder servomechanism, a new scheme, the Anti-Saturation Algorithm (ASA) was proposed which can eliminate slew rate saturation. Application of the ASA is generic to any servomechanism. The effects of lateral accelerations of the ship on human operators was examined. This resulted in an unique contribution to the Lateral Force Estimator problem in terms of generating time domain models and defining the limitations of the applicability of a control design strategy. Linear Quadratic Guassian and two types of classical controllers were constructed for the RRS and fins. A novel application of linear robust control theory to the ship roll stabilisation problem resulted in H . controllers whose performance was superior to the other design methods. This required the development of weight functions and the identification and quantification of possible sources of uncertainty. The structured singular value utilised this information to give comparable measures of robustness. The sea trials conducted represent the first experience of the integrated ship roll stabilisation approach. Experimental results are detailed. These afforded an invaluable opportunity to validate the software employed to predict ship motion. The data generated from the sea trials concurs with the simulations data in predicting that enhanced levels of roll stabilisation are possible without any modification to the rudder system. They also confirm that when the RRS is acting in congress with the fin stabilisers the activity of both actuators diminishes

Survey of Gain-Scheduling Analysis & Design

The gain-scheduling approach is perhaps one of the most popular nonlinear control design approaches which has been widely and successfully applied in fields ranging from aerospace to process control. Despite the wide application of gain-scheduling controllers and a diverse academic literature relating to gain-scheduling extending back nearly thirty years, there is a notable lack of a formal review of the literature. Moreover, whilst much of the classical gain-scheduling theory originates from the 1960s, there has recently been a considerable increase in interest in gain-scheduling in the literature with many new results obtained. An extended review of the gainscheduling literature therefore seems both timely and appropriate. The scope of this paper includes the main theoretical results and design procedures relating to continuous gain-scheduling (in the sense of decomposition of nonlinear design into linear sub-problems) control with the aim of providing both a critical overview and a useful entry point into the relevant literature

Stability of gain scheduling control for aircraft with highly nonlinear behavior

"The main goal of this work is to study the stability properties of an aircraft with nonlinear behavior, controlled using a gain scheduled approach. An output feedback is proposed which is able to guarantee asymptotical stability of the task-coordinates origin and safety of the operation in the entire flight envelope. The results are derived using theory of hybrid and singular perturbed systems. It is demonstrated that both body velocity and orientation asymptotic tracking can be obtained in spite of nonlinearities and uncertainty. The results are illustrated using numerical simulations in F16 jet.

Hybrid control of power converters

Cette thèse propose la conception de lois de commandes hybrides pour les convertisseurs électroniques de puissance. Ce nouveau type de lois de commande est basé sur l'utilisation de modèles hybrides qui capturent les comportements dynamiques macroscopiques de ces dispositifs électroniques, essentiellement leur nature hybride. Dans le contexte de la régulation des convertisseurs DC-DC ou AC-DC, en appliquant la théorie des systèmes hybrides, il est ainsi prouvé que les lois de commandes proposées assurent la stabilité de la boucle fermée ainsi que certaines performances de type LQ. Pour un onduleur en demi-pont (convertisseur DC-AC), une loi de commande hybride est proposée afin que la tension de sortie suive une référence sinusoïdale souhaitée. Dans le cas d'une charge inconnue, une loi de commande adaptative est alors couplée à la commande hybride permettant l'estimation de la charge et donc une régulation ou un suivi de trajectoire plus précis. Notons que pour obtenir une régulation ou un suivi parfait, une fréquence infinie est souvent obligatoire pour les lois de contrôle proposées, ce qui est inappropriée en pratique. Pour résoudre ce problème, une régularisation de l'espace d'état ou du temps est ajoutée à la boucle fermée assurant un temps de maintien entre deux sauts consécutifs et réduisant ainsi considérablement la fréquence de commutation.This thesis proposes the design of hybrid control laws for power electronics converters. These new type of control laws are based on some hybrid models which capture the macroscopic dynamical behaviors of such electronic devices, essentially its hybrid nature. In the context of the regulation of DC-DC or AC-DC converters, applying the hybrid dynamical theory, the proposed control laws are proved to ensure the stability of the closed loop as well as some LQ performances. For a half-bridge inverter (DC-AC converter), a hybrid control law is proposed in order that the output voltage tracks a desired sinusoidal reference. In the case of unknown load, an adaptive control law is coupled to the hybrid control allowing the estimation of the load and therefore leading to a more precise regulation or tracking. Notice that in order to achieve a perfect regulation or tracking, an infinite frequency is often mandatory for the proposed control laws, which is inappropriate in practice. To tackle this problem, a space- or time-regularization are added to the hybrid closed-loop ensuring a dwell time between two consecutive jumps and reducing thus drastically the switching frequency

Diseño de controladores continuos convergentes por un tiempo fijo para sistemas dinámicos con incertidumbre

Este documento presenta controladores no lineales que proveen convergencia en tiempo fijo al origen (o a una vecindad del origen) para sistemas dinámicos de alto orden sujetos a incertidumbres (disturbios deterministicos no desvanescentes y disturbios estocásticos desvanescentes dependientes de los estados y el tiempo). Dos de los tres controladores diseñados incluyen un diferenciador convergente en tiempo fijo, un observador de disturbios convergente en tiempo fijo, y un regulador convergente en tiempo fijo. El diferenciador se da en el caso que el ´único estado medible del sistema dinámico es el de mayor grado relativo. El observador de disturbios convergente en tiempo fijo se emplea para estimar variaciones de disturbios no desvanecentes y no acotados. En caso de que las cotas para los disturbios sean desconocidas se incluye un observador adaptable convergente en tiempo fijo caracterizado por no incrementar de manera excesiva las ganancias del controlador. En cuanto a la presencia simultanea de disturbios determinísticos no desvanescentes y disturbios estocásticos desvanescentes dependientes de los estados y el tiempo, se presenta un algoritmo Super-twisting estocástico convergente en tiempo fijo. El problema de estimación del tiempo de convergencia de los controladores se resuelve calculando una cota superior uniforme del tiempo fijo de convergencia. Finalmente, los algoritmos diseñados se verifican en dos casos de estudio: Un motor DC con armadura y un problema de gestión de stocks. Resultados de las simulaciones confirman convergencia en tiempo fijo y robustez de los controladores diseñados

On simple scheme of finite/fixed-time control design

International audienceControl laws are designed for stabilization of a chain of integrators of arbitrary degree in finite and fixed time. Presented control laws are obtained with use of Lyapunov function method and homogeneity concept. The present analysis is based on use of explicitly defined Lyapunov function that is the hallmark with respect to similar works. This analysis allows to get simple procedure of parameters tuning and obtain new estimates for settling-time function. The theoretical results are supported by numerical examples