Discrete gain scheduling control approach to elliptical orbit rendezvous system with actuator saturation

This paper studies the discrete gain scheduling control design problem of elliptical orbit spacecraft rendezvous system with actuator saturation. Due to the presence of actuator saturation, the dynamic performance of the spacecraft rendezvous system degrades significantly. In order to improve the dynamic performance of the system, a discrete gain scheduling control approach is adopted to construct a group of time-invariant ellipsoidal invariant sets, which can be used to determine the switching points of the discrete gain scheduling control. By choosing some discrete parameter values, the discrete gain scheduling control is obtained from a solution of a periodic Riccati matrix differential equation. Under the control obtained, the dynamic performance of the system is much improved while accomplishing successfully the rendezvous mission of the spacecraft. Finally, a practical example is provided to show the effectiveness of the proposed control design approach

Event-triggered control for piecewise affine discrete-time systems

In the present work, we study the problems of stability analysis of piecewise-affine (PWA) discrete-time systems, and trigger-function design for discrete-time event-triggered control systems. We propose a representation for piecewise-affine systems in terms of ramp functions, and we rely on Lyapunov theory for the stability analysis. The proposed implicit piecewise-affine representation prevents the shortcomings of the existing stability analysis approaches of PWA systems. Namely, the need to enumerate regions and allowed transitions of the explicit representations. In this context, we can emphasize two benefits of the proposed approach: first, it makes possible the analysis of uncertainty in the partition and, thus, the transitions. Secondly, it enables the analysis of event-triggered control systems for the class of PWA systems since, for ETC, the transitions cannot be determined as a function of the state variables. The proposed representation, on the other hand, implicitly encodes the partition and the transitions. The stability analysis is performed with Lyapunov theory techniques. We then present conditions for exponential stability. Thanks to the implicit representation, the use of piecewise quadratic Lyapunov functions candidates becomes simple. These conditions can be solved numerically using a linear matrix inequality formulation. The numerical analysis exploits quadratic expressions that describe ramp functions to verify the positiveness of extended quadratic forms. For ETC, a piecewise quadratic trigger function defines the event generator. We find suitable parameters for the trigger function with an optimization procedure. As a result, this function uses the information on the partition to reduce the number of events, achieving better results than the standard quadratic trigger functions found in the literature. We provide numerical examples to illustrate the application of the proposed representation and methods.Ce manuscrit présente des résultats sur l’analyse de stabilité des systèmes affines par morceaux en temps discret et sur le projet de fonctions de déclenchement pour des stratégies de commande par événements. Nous proposons une représentation pour des systèmes affines par morceaux et l’on utilise la théorie de stabilité de Lyapunov pour effectuer l’analyse de stabilité globale de l’origine. La nouvelle représentation implicite que nous proposons rend plus simple l’analyse de stabilité car elle évite l’énumération des régions et des transitions entre régions tel que c’est fait dans le cas des représentations explicites. Dans ce contexte nous pouvons souligner deux avantages principaux, à savoir I) la possibilité de traiter des incertitudes dans la partition qui définit le système et, par conséquent des incertitudes dans les transitions, II) l’analyse des stratégies de commande par événements pour des systèmes affines par morceaux. En effet, dans ces stratégies les transitions ne peuvent pas être définies comme des fonctions des variables d’état. La théorie de stabilité de Lyapunov est utilisée pour établir des conditions pour la stabilité exponentielle de l’origine. Grâce à la représentation implicite des partitions nous utilisons des fonctions de Lyapunov quadratique par morceaux. Ces conditions sont données par des inégalités dont la solution numérique est possible avec une formulation par des inégalités matricielles linéaires. Ces formulations numériques se basent sur des expressions quadratiques décrivant des fonctions rampe. Pour des stratégies par événement, une fonctions quadratique par morceaux est utilisée pour le générateur d’événements. Nous calculons les paramètres de ces fonctions de déclenchement a partir de solutions de problèmes d’optimisation. Cette fonction de déclenchement quadratique par morceaux permet de réduire le nombre de d’événementsen comparaison avec les fonctions quadratiques utilisées dans la littérature. Nous utilisons des exemples numériques pour illustrer les méthodes proposées.No presente trabalho, são estudados os problemas de análise de estabilidade de sistemas afins por partes e o projeto da função de disparo para sistemas de controle baseado em eventos em tempo discreto. É proposta uma representação para sistemas afins por partes em termos de funções rampa, e é utilizada a teoria de Lyapunov para a análise de estabilidade. A representação afim por partes implícita proposta evita algumas das deficiências das abordagens de análise de estabilidade de sistemas afins por partes existentes. Em particular, a necessidade de anumerar regiões e transições admissíveis das representações explícitas. Neste contexto, dois benefícios da abordagem proposta podem ser enfatizados: primeiro, ela torna possível a análise de incertezas na partição, e, assim, nas transições. Segundo, ela permite a análise de sistemas de controle baseado em eventos para a classe de sistemas afins por partes, já que, para o controle baseado em eventos, as transições não podem ser determinadas como uma função das variáveis de estado. A representação proposta, por outro lado, codifica implicitamente a partição e as transições. A análise de estabilidade é realizada com técnicas da teoria de Lyapunov. Condi- ções para a estabilidade exponencial são então apresentadas. Graças à representação implícita, o uso de funções candidatas de Lyapunov se torna simples. Essas condições podem ser resolvidas numéricamente usando uma formulação de desigualdades matriciais lineares. A análise numérica explora expressões quadráticas que descrevem funções de rampa para verificar a postivividade de formas quadráticas extendidas. Para o controle baseado em eventos, uma função de disparo quadrática por partes define o gerador de eventos. Parâmetros adequados para a função de disparo sãoencontrados com um procedimento de otimização. Como resultado, esta função usa informação da partição para reduzir o número de eventos, obtendo resultados melhores do que as funções de disparo quadráticas encontradas na literatura. Exemplos numéricos são fornecidos para ilustrar a aplicação da representação e mé- todos propostos

Anti‐windup controller design for singularly perturbed systems subject to actuator saturation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/166157/1/cth2bf00153.pd

Recent Advances in Robust Control

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics

Robust Control

The need to be tolerant to changes in the control systems or in the operational environment of systems subject to unknown disturbances has generated new control methods that are able to deal with the non-parametrized disturbances of systems, without adapting itself to the system uncertainty but rather providing stability in the presence of errors bound in a model. With this approach in mind and with the intention to exemplify robust control applications, this book includes selected chapters that describe models of H-infinity loop, robust stability and uncertainty, among others. Each robust control method and model discussed in this book is illustrated by a relevant example that serves as an overview of the theoretical and practical method in robust control

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

Adaptive Systems: History, Techniques, Problems, and Perspectives

We survey some of the rich history of control over the past century with a focus on the major milestones in adaptive systems. We review classic methods and examples in adaptive linear systems for both control and observation/identification. The focus is on linear plants to facilitate understanding, but we also provide the tools necessary for many classes of nonlinear systems. We discuss practical issues encountered in making these systems stable and robust with respect to additive and multiplicative uncertainties. We discuss various perspectives on adaptive systems and their role in various fields. Finally, we present some of the ongoing research and expose problems in the field of adaptive control

Theoretical Approaches in Non-Linear Dynamical Systems

From Preface: The 15th International Conference „Dynamical Systems - Theory and Applications” (DSTA 2019, 2-5 December, 2019, Lodz, Poland) gathered a numerous group of outstanding scientists and engineers who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without great effort of the staff of the Department of Automation, Biomechanics and Mechatronics of the Lodz University of Technology. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our event was attended by over 180 researchers from 35 countries all over the world, who decided to share the results of their research and experience in different fields related to dynamical systems. This year, the DSTA Conference Proceedings were split into two volumes entitled „Theoretical Approaches in Non-Linear Dynamical Systems” and „Applicable Solutions in Non-Linear Dynamical Systems”. In addition, DSTA 2019 resulted in three volumes of Springer Proceedings in Mathematics and Statistics entitled „Control and Stability of Dynamical Systems”, „Mathematical and Numerical Approaches in Dynamical Systems” and „Dynamical Systems in Mechatronics and Life Sciences”. Also, many outstanding papers will be recommended to special issues of renowned scientific journals.Cover design: Kaźmierczak, MarekTechnical editor: Kaźmierczak, Mare

Vibration analysis and intelligent control of flexible rotor systems using smart materials

Flexible rotor-bearing system stability is a very important subject impacting the design, control, maintenance and operating safety. As the rotor bearing-system dynamic nonlinearities are significantly more prominent at higher rotating speeds, the demand for better performance through higher speeds has rendered the use of linear approaches for analysis both inadequate and ineffective. To address this need, it becomes important that nonlinear rotor-dynamic responses indicative of the causes of nonlinearity, along with the bifurcated dynamic states of instabilities, be fully studied. The objectives of this research are to study rotor-dynamic instabilities induced by mass unbalance and to use smart materials to stabilise the performance of the flexible rotor-system. A comprehensive mathematical model incorporating translational and rotational inertia, bending stiffness and gyroscopic moment is developed. The dynamic end conditions of the rotor comprising of the active bearing-induced axial force is modelled, the equations of motion are derived using Lagrange equations and the Rayleigh-Ritz method is used to study the basic phenomena on simple systems. In this thesis the axial force terms included in the equations of motion provide a means for axially directed harmonic force to be introduced into the system. The Method of Multiple Scales is applied to study the nonlinear equations obtained and their stabilities. The Dynamics 2 software is used to numerically explore the inception and progression of bifurcations suggestive of the changing rotor-dynamic state and impending instability. In the context of active control of flexible rotors, smart materials particularly SMAs and piezoelectric stack actuators are introduced. The application of shape memory alloy (SMA) elements integrated within glass epoxy composite plates and shells has resulted in the design of a novel smart bearing based on the principle of antagonistic action in this thesis. Previous work has shown that a single SMA/composite active bearing can be very effective in both altering the natural frequency of the fundamental whirl mode as well as the modal amplitude. The drawback with that design has been the disparity in the time constant between the relatively fast heating phase and the much slower cooling phase which is reliant on forced air, or some other form of cooling. This thesis presents a modified design which removes the aforementioned existing shortcomings. This form of design means that the cooling phase of one half, still using forced air, is significantly assisted by switching the other half into its heating phase, and vice versa, thereby equalising the time constants, and giving a faster push-pull load on the centrally located bearing; a loading which is termed ‘antagonistic’ in this present dissertation. The piezoelectric stack actuator provides an account of an investigation into possible dynamic interactions between two nonlinear systems, each possessing nonlinear characteristics in the frequency domain. Parametric excitations are deliberately introduced into a second flexible rotor system by means of a piezoelectric exciter to moderate the response of the pre-existing mass-unbalance vibration inherent to the rotor. The intended application area for this SMA/composite and piezoelectric technologies are in industrial rotor systems, in particular very high-speed plant, such as small light pumps, motor generators, and engines for aerospace and automotive application