The subject of this thesis is the design of a control law for a magnetic levitation system, which in this case is the system 33-210. The method used is backstepping technique and specifically adaptive observer backstepping due to parameter uncertainties and lack of access to all the states of the system. The second state of the system, the speed of the steel ball, was estimated by a reduced order observer. The model used gave us the opportunity to estimate a parameter which in the literature is denoted virtual control coefficient. Backstepping method gives us a rather straight forward way to design the controlling unit for a system with these properties. Stabilization of the closed-loop system is achieved by incorporating a Lypapunov function, which were chose a quadratic one in this thesis. If thederivative of this function is rendered negative definite by the control law, then we achieve stability. The results of the design were evaluated in simulations and real-time measurements by testing the tracking performance of the system. The simulation results were very promising and the validations in real-time were satisfying. Note that this has been done in previous studies; the new aspect here is the limitation of the voltage input. The real-time results showed that the parameter estimation converges only locally.

Based on the Lypunov stability theorem, a design methodology of adaptive backstepping control is proposed in this thesis for a class of multi-input systems with matched and mismatched perturbations to solve regulation problems. The systems to be controlled contain blocks¡¦ dynamic equations, hence virtual input controllers are firstly designed so that the state variables of first blocks are asymptotically stable if each virtual control input is equal to the state variable of next block. The control input is designed in the last block to ensure asymptotic stability for each state even if the perturbations exist. In addition, adaptive mechanisms are embedded in each virtual input function and control input, so that the upper bound of perturbations is not required to be known beforehand. Finally, a numerical example and a practical application are given for demonstrating the feasibility of the proposed control scheme. ­^¤åºK­n(keyword)¡Gadaptive block backstepping controller, mismatched parameter uncertainty, virtual input controller, Lyapunov stability .

Based on the Lyapunov stability theorem, a design methodology of adaptive block backstepping decentralized controller is proposed in this thesis for a class of large-scale systems with interconnections to solve regulation problems. Each subsystem contains m blocks¡¦ state variables, and m- 1 virtual input controllers are designed from the first block to the (m - 1)th block. Then the proposed robust controller is designed in accordance with the last block. Some adaptive mechanisms are embedded in the backstepping controllers as well as virtual input controllers in each subsystem, so that the upper bounds of interconnections as well as perturbations are not required. Furthermore, the dynamic equations of each subsystem do not need to strictly satisfy the block strict feedback form, and the resultant controlled system can achieve asymptotic stability. Finally, a numerical and a practical examples are given for demonstrating the feasibility of the proposed control scheme.

In this thesis an adaptive backstepping control scheme is proposed for a class of multi-input perturbed systems with time-varying delays to solve regulation problems. The systems to be controlled contain n blocks¡¦ dynamic equations, hence n-1 virtual input controllers are designed from the first block to the (n-1)th block, and the backstepping controller is designed from the last block. In addition, adaptive mechanisms are embedded in each virtual input controllers and proposed controller, so that the least upper bounds of perturbations are not required to be known beforehand. Furthermore, the dynamic equations of the systems to be controlled need not satisfy strict-feedback form, and the upper bounds of the time delays as well as their derivatives need not to be known in advance either. The resultant controlled systems guarantee asymptotic stability in accordance with the Lyapunov stability theorem. Finally, a numerical example and a practical application are given for demonstrating the feasibility of the proposed control scheme.

Based on the Lyapunov stability theorem, a decentralized adaptive backstepping tracking control scheme for a class of perturbed large-scale systems with non-strict feedback form is presented in this thesis to solve tracking problems. First of all, the dynamic equations of the plant to be controlled are transformed into other equations with semi-strict feedback form. Then a decentralized tracking controller is designed based on the backstepping control methodology so that the outputs of controlled system are capable of tracking the desired signals generated from a reference model. In addition, by utilizing adaptive mechanisms embedded in the backstepping controller, one need not acquire the upper bounds of the perturbations and the interconnections in advance. The resultant control scheme is able to guarantee the stability of the whole large-scale systems, and the tracking precision may be adjusted through the design parameters. Finally, one numerical and one practical examples are demonstrated for showing the applicability of the proposed design technique.

<p>This thesis has been performed at SAAB Bofors Dynamics. The purpose was to derive a robust control design for a nonlinear missile using backstepping. A particularly interesting matter was to see how different design choices affect the robustness. Backstepping is a relatively new design method for nonlinear systems which leads to globally stabilizing control laws. By making wise decisions in the design the resulting closed loop can receive significant robustness. The method also makes it possible to benefit from naturally stabilizing aerodynamic forces and momentums. It is based on Lyapunov theory and the control laws and a Lyapunov function are derived simultaneously. This Lyapunov function is used to guarantee stability. In this thesis the control laws for the missile are first derived by using backstepping. The missile dynamics are described with aerodynamic coeffcients with corresponding uncertainties. The robustness of the design w.r.t. the aerodynamic uncertainties is then studied further in detail. One way to analyze how the stability is affected by the errors in the coeffcients is presented. To improve the robustness and remove static errors, dynamics are introduced in the control laws by adding an integrator. One conclusion that has been reached is that it is hard to immediately determine how a certain design choice affects the robustness. Instead it is at the point when algebraic expressions for the closed loop system have been obtained, that it is possible to analyze the affects of a certain design choice. The designed control laws are evaluated by simulations which shows satisfactory results.</p>

No description available.

In this thesis, analysis and comparison of different attitude control systems of a satelliteusing different reaction wheel configurations were investigated. Three different reactionwheel configurations (e.g. tetrahedron configuration, pyramid configuration, standardorthogonal 3-wheel configuration) and three control algorithms (Linear Quadratic Regulator,Sliding Mode, Integrator Backstepping) were analyzed and compared in terms of settlingtimes, power consumptions and actuator failure robustness. / <p>Validerat; 20121205 (global_studentproject_submitter)</p>

No description available.

Cette thèse concerne la conception de commandes échantillonnées pour les systèmes non-linéaires en temps continu. Les systèmes échantillonnés sont des éléments inhérents aux systèmes contrôlés par ordinateur, les systèmes hybrides ou les systèmes embarqués. La conception et le calcul des contrôleurs numériques appropriés sont des taches difficiles car ils contiennent des composants à la fois continu et en temps discret. Ce travail s'inscrit dans une activité de recherche menée par S. Monaco et D. Normand-Cyrot dans le domaine des systèmes échantillonnés non-linéaires. L'idée de base est de concevoir des contrôleurs digitaux qui permettent de récupérer certaines propriétés en temps continu qui sont généralement dégradées par l'échantillonnage. Tel est le cas de l'émulation lorsque les contrôleurs en temps continu sont mis en ouvre en utilisant des bloqueurs d'ordre zéro. Cette thèse apporte des contributions dans trois directions complémentaires. La première concerne les développements théoriques: une nouvelle conception de type ``backstepping digital" est proposée pour les systèmes en forme ``strict-feedback". Cette méthode est comparée à d'autres stratégies proposées dans la littérature. La deuxième contribution est le développement d'un logiciel pour la synthèse des contrôleurs et d'une ``boîte à outils" pour simuler (en Matlab) les systèmes échantillonnés non-linéaires et leurs contrôleurs. Cette boîte à outils inclut plusieurs algorithmes pour la synthèse de contrôleurs échantillonnés tels que: commande de type multi-échelle, reproduction entrée-sortie/Lyapunov, backstepping digital, etc. La troisième contribution concerne plusieurs études de cas menées pour mettre en évidence les performances des contrôleurs échantillonnés, calculés avec l'aide du logiciel. Des résultats expérimentaux et des simulations sont décrits pour divers exemples réels dans les domaines électriques et mécaniques. / This thesis is concerned with the sampled-data control of non-linear continuous-time systems. Sampled-data systems are present in all computer controlled, hybrid or embedded systems. The design and computation of suitable digital controllers represent unavoidable tasks since both continuous and discrete-time components interact. The basic framework of this work takes part of a wide research activity performed by S. Monaco and D. Normand-Cyrot regarding non-linear sampled-data systems. The underlying idea is to design digital controllers that recover certain continuous-time properties that are usually degraded through sampling as it is the case when continuous-time controllers are implemented by means of zero-order holder devices (emulated control). This thesis brings contributions into three different directions. The first one regards theoretical developments: a new digital backstepping-like strategy design for strict-feedback systems is proposed. This method is compared with other strategies proposed in the literature. The second contribution is the development of a control designer and of a simulation toolbox (in Matlab) for non-linear sampled-data systems. This toolbox includes different digital design strategies such as: multi-rate control, input-output/Lyapunov matching, digital backstepping design, etc. The third contribution concerns several case studies conducted to highlight the performances of the sampled-data controller designs, computed by the means of the software toolbox. Experimental and simulation results are described for various real examples especially in the area of electrical and mechanical processes. / Teza de față se concentrează asupra studiului controlului eșantionat pentru sisteme neliniare în timp continuu. Sistemele eșantionate sunt componente indispensabile oricăror sisteme de control bazate pe dispozitive de calcul, sisteme hibride sau sisteme embedded. Sinteza și calculul comenzilor digitale, potrivite pentru astfel de sisteme, devine o sarcină dificilă o dată ce presupune existența de dinamici în timp discret respectiv în timp continuu.Cadrul de bază al acestei lucrări se regăsește în activitatea de cercetare realizată de Salvatore Monaco și Dorothée Normand-Cyrot în domeniul sistemelor eșantionate neliniare. Ideea care stă la bază este de a sintetiza comenzile digitale urmărind menținerea unor proprietăți impuse în timp continuu sub eșantionare. Aceste proprietăți sunt în general degradate sub eșantionare cum este cazul comenzilor emulate, când comenzile continue sunt implementate practic cu ajutorul extrapolatoarelor de ordin 0.Această teză își aduce aportul în 3 direcții complementare. Prima adresează dezvoltările teoretice unde o nouă sinteză de tip backstepping digital este propusă pentru sisteme în formă <strict-feedback>. Această metodă, dezvoltată în două versiuni, este comparată cu alte strategii similare propuse în literatură. A doua contribuție a tezei este legată de dezvoltarea unui toolbox software pentru sinteza de controllere digitale pentru sisteme nelinare sub eșantionare. Acest toolbox include strategii diferite pentru sinteza eșantionată precum: comandă de tip multi-rate, reproducere intrare-ieșire/Lyapunov, backstepping digital și alte soluții care sunt obiectul unor noi extensii. A treia contribuție este dată de studiile de caz dezvoltate pentru a scoate în evidență performanțele comenzilor eșantionate testate și calculate cu ajutorul aplicației software. Rezultatele experimentale și de simulare sunt obținute pentru diverse exemple reale din domeniul electric și mecanic.