Cette thèse aborde trois problèmes liés à l’ABS dans le cadre de la dynamique de la roue : l’estimation de la rigidité de freinage étendue (XBS) des pneus lors du freinage d’urgence, la commande de l’ABS basée sur l’estimation de l’XBS, et l’estimation de la vitesse et de l’accélération angulaires de la roue à partir des mesures provenant d’un codeur avec des imperfections. L’objectif général de ce travail est de développer des outils visant à améliorer la performance des systèmes de freinage, en utilisant des techniques adaptées de l'automatique non linéaire. La première partie de la thèse est consacrée à la construction d’un observateur adaptatif commuté pour l’XBS, c’est-à-dire un observateur adaptatif dont les gains d’estimation commutent entre deux valeurs possibles en fonction du signe de la sortie mesurée du système. La stabilité de l’observateur est analysée en utilisant des outils pour des systèmes commutés et en cascade, ainsi que des concepts tels qu’excitation permanente et transformations singulières d’échelle de temps. La deuxième partie de la thèse est dédiée à la conception d’une loi de commande pour l’ABS. L’objectif de contrôle est formulé en termes de l’XBS et une loi de commande hybride est conçue afin de faire en sorte que les trajectoires du système satisfassent les conditions requises pour l’estimation de l’XBS. La stabilité du contrôleur est analysée en utilisant l'application de Poincaré. La troisième partie de la thèse aborde la construction d’un algorithme pour estimer la vitesse et l’accélération angulaires de la roue et éliminer des perturbations qui sont introduites par les imperfections du codeur, et dont l’amplitude et la fréquence sont une fonction de la position, la vitesse, et l’accélération angulaires (réelles) de la roue. L’algorithme est basé sur la méthode connue comme « time-stamping algorithm », ainsi que sur des techniques de filtrage est d’estimation de paramètres. Des essais expérimentaux et des simulations numériques illustrent la performance des algorithmes d’estimation et de contrôle présentés dans cette thèse. Dans tous les cas nos résultats sont comparés par rapport à l’état de l’art. / This thesis addresses three problems related to the antilock braking system (ABS) in the context of the wheel dynamics: the estimation of the tyre extended braking stiffness (XBS) during an emergency braking situation, the control of the ABS based on the estimation of the XBS, and the estimation of the angular velocity and acceleration of the wheel from the measurements of an incremental encoder with imperfections. The general objective of this work is to develop tools aimed at improving the performance of braking systems by using techniques adapted from nonlinear control theory. The first part of the manuscript is devoted to the construction of a switched adaptive observer for the XBS, that is, an adaptive observer whose estimation gains switch between two possible values based on the sign of the system’s measured output. The stability of the observer is analyzed using tools for switched and cascaded systems, as well as concepts such as persistency of excitation and singular time-scale transformations. The second part of the manuscript is dedicated to the design of a control algorithm for the ABS. The control objective is formulated in terms of the XBS and a hybrid controller is designed so that the trajectories of the system satisfy the conditions required for the estimation of the XBS. The stability of the controller is analyzed using the Poincaré map. The third part of the manuscript focuses on the construction of an algorithm to estimate angular velocity and acceleration of the wheel and remove perturbations which are introduced by the encoder imperfections and whose amplitude and frequency are a function of the wheel's (real) position, velocity, and acceleration. The algorithm is based on the method known as time-stamping algorithm, as well as filtering and parameter estimation techniques. Experimental tests and numerical simulations illustrate the performance of the estimation and control algorithms presented in this thesis. In all cases our results are compared with respect to the state of the art.

The contributions of this thesis lie in the area of global finite-time observer design for a class of nonlinear systems with bounded rational and mixed rational powers imposed on the incremental rate of the nonlinear terms whose solutions exist and are unique for all positive time. In the thesis, two different kinds of nonlinear global finite-time observers are designed by employing of finite-time theory and homogeneity properties with different methods. The global finite-time stability of both proposed observers is derived on the basis of Lyapunov theory. For a class of nonlinear systems with rational and mixed rational powers imposed on the nonlinearities, the first global finite-time observers are designed, where the global finite-time stability of the observation systems is achieved from two parts by combining asymptotic stability and local finitetime stability. The proposed observers can only be designed for the class of nonlinear systems with dimensions greater than 3. The observers have a dynamic high gain and two homogenous terms, one homogeneous of degree greater than 1 and the other of degree less than 1. In order to prove the global finite-time stability of the proposed results, two homogeneous Lyapunov functions are provided, corresponding with the two homogeneous items. One is homogeneous of degree greater than 1, which makes the observation error systems converging into a spherical area around the origin, and the other is of degree less than 1, which ensures local finite-time stability. The second global finite-time observers are also proposed based on the high-gain technique, which does not place any limitation on the dimension of the nonlinear systems. Compared with the first global finite-time observers, the newly designed observers have only one homogeneous term and a new gain update law where two new terms are introduced to dominate some terms in the nonlinearities and ensure global finite-time stability as well. The global finite-time stability is obtained directly based on a sufficient condition of finite-time stability and only one Lyapunov function is employed in the proof. The validity of the two kinds of global finite-time observers that have been designed is illustrated through some simulation results. Both of them can make the observation error systems converge to the origin in finite-time. The parameters, initial conditions as well as the high gain do have some impact on the convergence time, where the high gain plays a stronger role. The bigger the high gain is, the shorter the time it needs to converge. In order to show the performance of the two kinds of observers more clearly, two examples are provided and some comparisons are made between them. Through these, it can be seen that under the same parameters and initial conditions, although the amplitude of the observation error curve is slightly greater, the global finite-time observers with a new gain update law can make the observation error systems converge much more quickly than the global finite-time observers with two homogeneous terms. In the simulation results, one can see that, as a common drawback of high gain observers, they are noise-sensitive. Finding methods to improve their robustness and adaptiveness will be quite interesting, useful and challenging. / Thesis (PhD)--University of Pretoria, 2013. / gm2014 / Electrical, Electronic and Computer Engineering / unrestricted

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This report evaluates the option of using an equal slip controller, an effective rolling radius and rolling resistance force observer in a 4WD wheel loader. The vehicle studied is an under development- vehicle designed by Volvo CE. A wheel loader is an over actuated, articulated vehicle that is mainly used with low velocities in construction operations. The efficiency subject has been studied earlier by many manufacturers in order to analyze the environmental and economical losses and profits. This has provided research opportunities of optimizing efficiency of different kinds. Since the tire is the only part of a vehicle that is in contact with the ground, the characteristic of the tire effects the dynamics. The analysis shows that the efficiency of a tire is directly connected to the slip ratio which in turn is a component of the overall efficiency ratio. Studies show that the slip ratio should be controlled in such a way that the highest value of efficiency rate is obtained. This optimal value is dependent on all four wheel’s slip conditions. Therefore a strategy should be formulated in order to apply changes to all wheels and not only one. Further analysis shows that the maximum efficiency in a 4WD wheel loader is obtained when the vehicle runs in such a way that the slip ratio is equal for all wheels. I order to maintain same amount of slip for all wheels a control strategy is required. In the control strategy the current amount of slip of each wheel is determined. Further, the average value of slip ratio is calculated. Finally the equal amount of slip is achieved using corresponding optimal torque inputs for each individual wheel. Thus a stable, robust controller is required. The controller used to achieve this goal is a sliding mode controller that is popular among control engineers for its stability, robustness against uncertainties, speed and easy implementation. For an accurate control, states of the rolling resistance and the effective rolling radius need to be determined. The pressure acting on the tire will cause deformation on the tire itself. This leads to a dynamic radius of the tire. This deformation is highly dependent on vertical stress and the structure of tire. Further more velocity, inflation pressure, vertical load etc. also have effect on rolling resistance. Rolling resistance has a great impact on the fuel consumption of the vehicle and the driving characteristics. These estimated variations of effective radius and rolling resistance build a feedback system to the controller which in turn derives the system to the desired slip ratio. As it turns out, the slip efficiency is increased using an equal slip controller. However, it is highly dependent on the ratio of thrust between front and rear wheels. / Denna rapport utvärderar möjligheten att använda en olinjär regulator i syfte att sätta lika stor ’slip’ på fordonets alla fyra hjul. Vidare ska en olinjär observerare modelleras för att uppskatta den så kallad hjulets effektiva radie samt rollmoståndskraften som verkar på däcket. Det studerade fordonet är en hjullastare konstruerad av Volvo CE och som i nuläget är under utveckling. En hjullastare är ett overmanövrerat fordon som huvudsakligen används i låga hastigheter i bygg- och transportverksamheter. Effektivitet är ett ämne som har studerats tidigare av många tillverkare för att analysera miljörelaterade och ekonomiska förluster och vinster. Detta har gett forskarna möjligheten att studera effektivitet av olika slag. Eftersom däcket är den enda delen av ett fordon som kommer i kontakt med marken, påverkar dess karaktär fordonets dynamika beteende i helhet. Analysen visar att däckets effektivitet är direkt kopplad till slipförhållande som i sin tur är en del av det totala effektivitetsförhållandet. Studier visar att slipförhållandet bör kontrolleras på ett sådant sätt att det högsta värdet av effektivitet uppnås. Detta optimala värde är beroende av slipförhållanden hos alla fyra hjul och därför bör en strategi formuleras för att nå optimalt slipeffektivitet på alla hjul. Ytterligare analys visar att maximal slipeffektivitet i en 4WD hjullastare erhålls när fordonet går så att slipförhållandet är lika för alla hjul. I kontrollstrategin bestäms det nuvarande slipförhållandet för varje hjul. Av dessa beräknas medelvärdet som skall presentera referensvärdet av slipförhållandet. Slutligen upp-nås detta värde med motsvarande optimala momentinmatningar för varje enskilt hjul. Styralgoritmen som används för att uppnå detta mål är en Sliding mode regulator som är populär bland kontrollingenjörer för dess stabilitet, robusthet mot osäkerhet, snabbhet och enkel implementering. För en noggrann kontroll måste tillstånden av rullmotståndskraften och effektiv rull-radien observeras. De verkande krafterna på hjulet orsakar deformation på däcket som ger upphov till däckets dynamiska radie. Denna deformation är starkt beroende av vertikal spänning och däckets struktur. Vidare har hastighet, däckets lufttryck, vertikal belastning etc. också effekt på rullmotståndskraften. Rullmotstånd har stor inverkan på fordonets bränsleförbrukning och drivegenskaper. Dessa variationer av effektivradie och rullmotstånd bygger ett återkopplat system till regulatorn som i sin tur leder systemet till önskat slipförhållande. Som det visar sig, ökar slipeffektiviteten med hjälp av "equal slip" styralgoritm. Detta är emellertid mycket beroende av förhållandet av momentinmatningar mellan fram och bakhjulet.

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The present thesis employs fuzzy-polynomial control techniques in order to improve the stability analysis and control of nonlinear systems. Initially, it reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems, such as the more relevant results about polynomial and fuzzy polynomial systems. The basic framework uses fuzzy polynomial models by Taylor series and sum-of-squares techniques (semidefinite programming) in order to obtain stability guarantees. The contributions of the thesis are: ¿ Improved domain of attraction estimation of nonlinear systems for both continuous-time and discrete-time cases. An iterative methodology based on invariant-set results is presented for obtaining polynomial boundaries of such domain of attraction. ¿ Extension of the above problem to the case with bounded persistent disturbances acting. Different characterizations of inescapable sets with polynomial boundaries are determined. ¿ State estimation: extension of the previous results in literature to the case of fuzzy observers with polynomial gains, guaranteeing stability of the estimation error and inescapability in a subset of the zone where the model is valid. ¿ Proposal of a polynomial Lyapunov function with discrete delay in order to improve some polynomial control designs from literature. Preliminary extension to the fuzzy polynomial case. Last chapters present a preliminary experimental work in order to check and validate the theoretical results on real platforms in the future. / Pitarch Pérez, JL. (2013). Contributions to fuzzy polynomial techniques for stability analysis and control [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34773

Depuis l'introduction du premier système ABS par Bosch, en 1978, de nombreux algorithmes de commande pour les systèmes ABS ont été proposés dans la littérature. En général, ces algorithmes peuvent être divisés en deux catégories : ceux basés sur une logique de régulation déterminée par des seuils sur l'accélération angulaire des roues et ceux basés sur la régulation du taux de glissement. Chaque approche a ses avantages et ses inconvénients. D'une manière simplifiée, on peut dire que le point fort du premier type est sa robustesse ; tandis que ceux du deuxième type sont leur courte distance de freinage (sur les terrains secs) et leur absence de cycles limite. Au milieu de cette dichotomie industrielle/académique, en se basant sur un concept appelé extended braking stiffness (XBS), une classe complètement différente de stratégies de commande pour l'ABS a été proposée par certains chercheurs. Ce concept combine les avantages des deux approches. Néanmoins, puisque l’XBS n'est pas directement mesurable, elle introduit la question de son estimation en temps réel. La première partie de cette thèse est consacrée à l'étude de ce problème d'estimation et à une généralisation de la technique proposée à une plus grande classe de systèmes. D'un point de vue technologique, la conception des systèmes de contrôle pour l'ABS est fortement dépendante des caractéristiques physiques du système et des performances de l'actionneur. Les algorithmes de commande actuels pour l'ABS sur les véhicules, par exemple l'algorithme ABS de Bosch, sont basés sur des approches heuristiques qui sont profondément liées à la nature hydraulique de l'actionneur. Ils ne fonctionnent correctement qu'en présence d'un retard spécifique associé à la nature hydraulique de l'actionneur. Pour les systèmes de freinage qui ont un retard différent de ceux des actionneurs hydrauliques, comme les moteurs-roues électriques par exemple (un retard plus court) ou les freins pneumatiques des semi-remorques (un retard plus grand), ils ne sont plus appropriés et ont un fonctionnement déficient. Par conséquent, l'adaptation des algorithmes standards de l'ABS pour d'autres actionneurs avancés devient un objectif primordial dans l'industrie automobile. Cet objectif peut être atteint par la compensation des retards induits par les actionneurs. La deuxième partie de cette thèse se concentre sur cette question, et à la généralisation de la technique proposée à une classe particulière de systèmes non linéaires.Tout au long de cette thèse, nous utilisons deux techniques de linéarisation différentes : la linéarisation de la dynamique d'erreur dans la construction des observateurs basés sur des modèles et la linéarisation basée sur le retour d'état restreint. La première est l'une des façons les plus simples pour synthétiser un observateur pour des systèmes dynamiques avec sortie et pour analyser sa convergence. L'idée principale est de transformer le système non linéaire original via un changement de coordonnées en un système différemment formalisé, qui admette un observateur avec une dynamique d'erreur linéaire et les gains de l'observateur peuvent donc être facilement calculés pour en assurer la convergence. Cette dernière est une méthode classique pour commander des systèmes non linéaires en les convertissant en une équation d'état linéaire contrôlable via l'annulation de leurs non-linéarités. Il convient de mentionner que les résultats existants pour la synthèse des observateurs par la linéarisation de l'erreur dans la littérature ne sont appliqués que pour le cas des changements réguliers de l'échelle de temps. Cette thèse explique comment les étendre aux cas des changements singuliers de l'échelle de temps. Par ailleurs, la thèse combine la linéarisation classique par retour d'état avec une nouvelle méthode de compensation du retard de l'entrée pour résoudre le problème de suivi de la sortie pour des systèmes linéarisables par retour d'état restreint avec des retards de l'entrée. / Many control algorithms for ABS systems have been proposed in the literature since the introduction of this equipment by Bosch in 1978. In general, one can divide these control algorithms into two different types: those based on a regulation logic with wheel acceleration thresholds that are used by most commercial ABS systems; and those based on wheel slip control that are preferred in the large majority of academic algorithms. Each approach has its pros and cons [Shida 2010]. Oversimplifying, one can say that the strength of the first ones is their robustness; while that of the latter ones their short braking distances (on dry grounds) and their absence of limit cycles. At the midpoint of this industry/academy dichotomy, based on the concept of extended braking stiffness (XBS), a quite different class of ABS control strategies has been proposed by several researchers (see, e.g., [Sugai 1999] and [Ono 2003]). This concept combines the advantages from both the industrial and academic approaches. Nevertheless, since the slope of the tyre characteristic is not directly measurable, it introduces the question of real-time XBS estimation. The first part of this thesis is devoted to the study of this estimation problem and to a generalization of the proposed technique to a larger class of systems. From the technological point of view, the design of ABS control systems is highly dependent on the ABS system characteristics and actuator performance. Current ABS control algorithms on passenger cars, for instance the Bosch ABS algorithm, are based on heuristics that are deeply associated to the hydraulic nature of the actuator. An interesting observation is that they seem to work properly only in the presence of a specific delay coming from the hydraulic actuation [Gerard 2012]. For brake systems that have different delays compared to those of hydraulic actuators, like electric in-wheel motors (with a smaller delay) or pneumatic trailer brakes (with a bigger delay), they might be no longer suitable [Miller 2013]. Therefore, adapting standard ABS algorithms to other advanced actuators becomes an imperative goal in the automobile industry. This goal can be reached by the compensation of the delays induced by actuators. The second part of this thesis is focused on this issue, and to the generalization of the proposed technique to a particular class of nonlinear systems. Throughout this thesis, we employ two different linearization techniques: the linearization of the error dynamics in the construction of model-based observers [Krener 1983] and the linearization based on restricted state feedback [Brockett 1979]. The former is one of the simplest ways to build an observer for dynamical systems with output and to analyze its convergence. The main idea is to transform the original nonlinear system via a coordinate change to a special form that admits an observer with a linear error dynamics and thus the observer gains can be easily computed to ensure the observer convergence. The latter is a classical method to control nonlinear systems by converting them into a controllable linear state equation via the cancellation of their nonlinearities. It is worth mentioning that existing results for observer design by error linearization in the literature are only applied to the case of regular time scalings ([Guay 2002] and [Respondek 2004]). The thesis shows how to extend them to the case of singular time scalings. Besides, the thesis combines the classical state feedback linearization with a new method for the input delay compensation to resolve the output tracking problem for restricted feedback linearizable systems with input delays.