Stabilization and Robustness Analysis for a Chain of Saturating Integrators Arising in the Visual Landing of Aircraft

International audienceWe study a chain of saturating integrators with imprecise output measurements. Using a recent backstepping approach that leads to pointwise delays in the control and a dynamic extension, we provide an input-to-state stability result using a bounded control of arbitrarily small amplitude. We apply the result to a problem in the visual landing of aircraft

On output-based accelerated stabilization of a chain of integrators: Implicit Lyapunov-Krasovskii functional approach

International audienceThe problem of output accelerated stabilization of a chain of integrators is considered. Proposed control law nonlinearly depends on the output and its delayed values, and it does not use an observer to estimate the unmeasured components of the state. It is proven that such a nonlinear delayed control law ensures practical output stabilization with rates of convergence faster than exponential. The effective way of computation of feedback gains is given. It is shown that closed-loop system stability does not depend on the value of artificial delay, but the maximum value of delay determines the width of stability zone. The efficiency of the proposed control is demonstrated in simulations

Backstepping for Uncertain Nonlinear Systems with a Delay in the Control

International audienceThe recent new backstepping control design strategy based on the introduction of artificial delays and/or dynamic extensions is adapted to a family of systems. That way, globally asymptotically stabilizing control laws for fundamental systems which cannot be handled by other techniques are determined

Systems and control : 21th Benelux meeting, 2002, March 19-21, Veldhoven, The Netherlands

Book of abstract

Feedback Systems: An Introduction for Scientists and Engineers

This book provides an introduction to the basic principles and tools for the design and analysis of feedback systems. It is intended to serve a diverse audience of scientists and engineers who are interested in understanding and utilizing feedback in physical, biological, information and social systems.We have attempted to keep the mathematical prerequisites to a minimum while being careful not to sacrifice rigor in the process. We have also attempted to make use of examples from a variety of disciplines, illustrating the generality of many of the tools while at the same time showing how they can be applied in specific application domains. A major goal of this book is to present a concise and insightful view of the current knowledge in feedback and control systems. The field of control started by teaching everything that was known at the time and, as new knowledge was acquired, additional courses were developed to cover new techniques. A consequence of this evolution is that introductory courses have remained the same for many years, and it is often necessary to take many individual courses in order to obtain a good perspective on the field. In developing this book, we have attempted to condense the current knowledge by emphasizing fundamental concepts. We believe that it is important to understand why feedback is useful, to know the language and basic mathematics of control and to grasp the key paradigms that have been developed over the past half century. It is also important to be able to solve simple feedback problems using back-of-the-envelope techniques, to recognize fundamental limitations and difficult control problems and to have a feel for available design methods. This book was originally developed for use in an experimental course at Caltech involving students from a wide set of backgrounds. The course was offered to undergraduates at the junior and senior levels in traditional engineering disciplines, as well as first- and second-year graduate students in engineering and science. This latter group included graduate students in biology, computer science and physics. Over the course of several years, the text has been classroom tested at Caltech and at Lund University, and the feedback from many students and colleagues has been incorporated to help improve the readability and accessibility of the material. Because of its intended audience, this book is organized in a slightly unusual fashion compared to many other books on feedback and control. In particular, we introduce a number of concepts in the text that are normally reserved for second-year courses on control and hence often not available to students who are not control systems majors. This has been done at the expense of certain traditional topics, which we felt that the astute student could learn independently and are often explored through the exercises. Examples of topics that we have included are nonlinear dynamics, Lyapunov stability analysis, the matrix exponential, reachability and observability, and fundamental limits of performance and robustness. Topics that we have deemphasized include root locus techniques, lead/lag compensation and detailed rules for generating Bode and Nyquist plots by hand. Several features of the book are designed to facilitate its dual function as a basic engineering text and as an introduction for researchers in natural, information and social sciences. The bulk of the material is intended to be used regardless of the audience and covers the core principles and tools in the analysis and design of feedback systems. Advanced sections, marked by the “dangerous bend” symbol shown here, contain material that requires a slightly more technical background, of the sort that would be expected of senior undergraduates in engineering. A few sections are marked by two dangerous bend symbols and are intended for readers with more specialized backgrounds, identified at the beginning of the section. To limit the length of the text, several standard results and extensions are given in the exercises, with appropriate hints toward their solutions. To further augment the printed material contained here, a companion web site has been developed and is available from the publisher’s web page: http://press.princeton.edu/titles/8701.html The web site contains a database of frequently asked questions, supplemental examples and exercises, and lecture material for courses based on this text. The material is organized by chapter and includes a summary of the major points in the text as well as links to external resources. The web site also contains the source code for many examples in the book, as well as utilities to implement the techniques described in the text. Most of the code was originally written using MATLAB M-files but was also tested with LabView MathScript to ensure compatibility with both packages. Many files can also be run using other scripting languages such as Octave, SciLab, SysQuake and Xmath. The first half of the book focuses almost exclusively on state space control systems. We begin in Chapter 2 with a description of modeling of physical, biological and information systems using ordinary differential equations and difference equations. Chapter 3 presents a number of examples in some detail, primarily as a reference for problems that will be used throughout the text. Following this, Chapter 4 looks at the dynamic behavior of models, including definitions of stability and more complicated nonlinear behavior. We provide advanced sections in this chapter on Lyapunov stability analysis because we find that it is useful in a broad array of applications and is frequently a topic that is not introduced until later in one’s studies. The remaining three chapters of the first half of the book focus on linear systems, beginning with a description of input/output behavior in Chapter 5. In Chapter 6, we formally introduce feedback systems by demonstrating how state space control laws can be designed. This is followed in Chapter 7 by material on output feedback and estimators. Chapters 6 and 7 introduce the key concepts of reachability and observability, which give tremendous insight into the choice of actuators and sensors, whether for engineered or natural systems. The second half of the book presents material that is often considered to be from the field of “classical control.” This includes the transfer function, introduced in Chapter 8, which is a fundamental tool for understanding feedback systems. Using transfer functions, one can begin to analyze the stability of feedback systems using frequency domain analysis, including the ability to reason about the closed loop behavior of a system from its open loop characteristics. This is the subject of Chapter 9, which revolves around the Nyquist stability criterion. In Chapters 10 and 11, we again look at the design problem, focusing first on proportional-integral-derivative (PID) controllers and then on the more general process of loop shaping. PID control is by far the most common design technique in control systems and a useful tool for any student. The chapter on frequency domain design introduces many of the ideas of modern control theory, including the sensitivity function. In Chapter 12, we combine the results from the second half of the book to analyze some of the fundamental trade-offs between robustness and performance. This is also a key chapter illustrating the power of the techniques that have been developed and serving as an introduction for more advanced studies. The book is designed for use in a 10- to 15-week course in feedback systems that provides many of the key concepts needed in a variety of disciplines. For a 10-week course, Chapters 1–2, 4–6 and 8–11 can each be covered in a week’s time, with the omission of some topics from the final chapters. A more leisurely course, spread out over 14–15 weeks, could cover the entire book, with 2 weeks on modeling (Chapters 2 and 3) — particularly for students without much background in ordinary differential equations — and 2 weeks on robust performance (Chapter 12). The mathematical prerequisites for the book are modest and in keeping with our goal of providing an introduction that serves a broad audience. We assume familiarity with the basic tools of linear algebra, including matrices, vectors and eigenvalues. These are typically covered in a sophomore-level course on the subject, and the textbooks by Apostol [10], Arnold [13] and Strang [187] can serve as good references. Similarly, we assume basic knowledge of differential equations, including the concepts of homogeneous and particular solutions for linear ordinary differential equations in one variable. Apostol [10] and Boyce and DiPrima [42] cover this material well. Finally, we also make use of complex numbers and functions and, in some of the advanced sections, more detailed concepts in complex variables that are typically covered in a junior-level engineering or physics course in mathematical methods. Apostol [9] or Stewart [186] can be used for the basic material, with Ahlfors [6], Marsden and Hoffman [146] or Saff and Snider [172] being good references for the more advanced material. We have chosen not to include appendices summarizing these various topics since there are a number of good books available. One additional choice that we felt was important was the decision not to rely on a knowledge of Laplace transforms in the book. While their use is by far the most common approach to teaching feedback systems in engineering, many students in the natural and information sciences may lack the necessary mathematical background. Since Laplace transforms are not required in any essential way, we have included them only in an advanced section intended to tie things together for students with that background. Of course, we make tremendous use of transfer functions, which we introduce through the notion of response to exponential inputs, an approach we feel is more accessible to a broad array of scientists and engineers. For classes in which students have already had Laplace transforms, it should be quite natural to build on this background in the appropriate sections of the text. Acknowledgments: The authors would like to thank the many people who helped during the preparation of this book. The idea for writing this book came in part from a report on future directions in control [155] to which Stephen Boyd, Roger Brockett, John Doyle and Gunter Stein were major contributors. Kristi Morgansen and Hideo Mabuchi helped teach early versions of the course at Caltech on which much of the text is based, and Steve Waydo served as the head TA for the course taught at Caltech in 2003–2004 and provided numerous comments and corrections. Charlotta Johnsson and Anton Cervin taught from early versions of the manuscript in Lund in 2003–2007 and gave very useful feedback. Other colleagues and students who provided feedback and advice include Leif Andersson, John Carson, K. Mani Chandy, Michel Charpentier, Domitilla Del Vecchio, Kate Galloway, Per Hagander, Toivo Henningsson Perby, Joseph Hellerstein, George Hines, Tore Hägglund, Cole Lepine, Anders Rantzer, Anders Robertsson, Dawn Tilbury and Francisco Zabala. The reviewers for Princeton University Press and Tom Robbins at NI Press also provided valuable comments that significantly improved the organization, layout and focus of the book. Our editor, Vickie Kearn, was a great source of encouragement and help throughout the publishing process. Finally, we would like to thank Caltech, Lund University and the University of California at Santa Barbara for providing many resources, stimulating colleagues and students, and pleasant working environments that greatly aided in the writing of this book

Fault tolerant control for nonlinear aircraft based on feedback linearization

The thesis concerns the fault tolerant flight control (FTFC) problem for nonlinear aircraft by making use of analytical redundancy. Considering initially fault-free flight, the feedback linearization theory plays an important role to provide a baseline control approach for de-coupling and stabilizing a non-linear statically unstable aircraft system. Then several reconfigurable control strategies are studied to provide further robust control performance:- A neural network (NN)-based adaption mechanism is used to develop reconfigurable FTFC performance through the combination of a concurrent updated learninglaw. - The combined feedback linearization and NN adaptor FTFC system is further improved through the use of a sliding mode control (SMC) strategy to enhance the convergence of the NN learning adaptor. - An approach to simultaneous estimation of both state and fault signals is incorporated within an active FTFC system.The faults acting independently on the three primary actuators of the nonlinear aircraft are compensated in the control system.The theoretical ideas developed in the thesis have been applied to the nonlinear Machan Unmanned Aerial Vehicle (UAV) system. The simulation results obtained from a tracking control system demonstrate the improved fault tolerant performance for all the presented control schemes, validated under various faults and disturbance scenarios.A Boeing 747 nonlinear benchmark model, developed within the framework of the GARTEUR FM-AG 16 project “fault tolerant flight control systems”,is used for the purpose of further simulation study and testing of the FTFC scheme developed by making the combined use of concurrent learning NN and SMC theory. The simulation results under the given fault scenario show a promising reconfiguration performance

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

Modeling diversity by strange attractors with application to temporal pattern recognition

This thesis belongs to the general discipline of establishing black-box models from real-word data, more precisely, from measured time-series. This is an old subject and a large amount of papers and books has been written about it. The main difficulty is to express the diversity of data that has essentially the same origin without creating confusion with data that has a different origin. Normally, the diversity of time-series is modeled by a stochastic process, such as filtered white noise. Often, it is reasonable to assume that the time series is generated by a deterministic dynamical system rather than a stochastic process. In this case, the diversity of the data is expressed by the variability of the parameters of the dynamical system. The parameter variability itself is then, once again, modeled by a stochastic process. In both cases the diversity is generated by some form of exogenous noise. In this thesis a further step has been taken. A single chaotic dynamical system is used to model the data and their diversity. Indeed, a chaotic system produces a whole family of trajectories that are different but nonetheless very similar. It is believed that chaotic dynamics not only are a convenient means to represent diversity but that in many cases the origin of diversity stems actually from chaotic dynamic. Since the approach of this thesis explores completely new grounds the most suitable kind of data is considered, namely approximately periodic signals. In nature such time-series are rather common, in particular the physiological signal of living beings, such as the electrocardiograms (ECG), parts of speech signals, electroencephalograms (EEG), etc. Since there are strong arguments in favor of the chaotic nature of these signals, they appear to be the best candidates for modeling diversity by chaos. It should be stressed however, that the modeling approach pursued in this thesis is thought to be quite general and not limited to signals produced by chaotic dynamics in nature. The intended application of the modeling effort in this thesis is temporal signal classification. The reason for this is twofold. Firstly, classification is one of the basic building block of any cognitive system. Secondly, the recently studied phenomenon of synchronization of chaotic systems suggests a way to test a signal against its chaotic model. The essential content of this work can now be formulated as follows. Thesis: The diversity of approximately periodic signals found in nature can be modeled by means of chaotic dynamics. This kind of modeling technique, together with selective properties of the synchronization of chaotic systems, can be exploited for pattern recognition purposes. This Thesis is advocated by means of the following five points. Models of randomness (Chapter 2) It is argued that the randomness observed in nature is not necessarily the result of exogenous noise, but it could be endogenally generated by deterministic chaotic dynamics. The diversity of real signals is compared with signals produced by the most common chaotic systems. Qualitative resonance (Chapter 3) The behavior of chaotic systems forced by periodic or approximately periodic input signals is studied theoretically and by numerical simulation. It is observed that the chaotic system "locks" approximately to an input signal that is related to its internal chaotic dynamic. In contrast to this, its chaotic behavior is reinforced when the input signal has nothing to do with its internal dynamics. This new phenomenon is called "qualitative resonance". Modeling and recognizing (Chapter 4) In this chapter qualitative resonance is used for pattern recognition. The core of the method is a chaotic dynamical system that is able to reproduce the class of time-series that is to be recognized. This model is excited in a suitable way by an input signal such that qualitative resonance is realized. This means that if the input signal belongs to the modeled class of time-series, the system approximately "locks" into it. If not, the trajectory of the system and the input signal remain unrelated. Automated design of the recognizer (Chapters 5 and 6) For the kind of signals considered in this thesis a systematic design method of the recognizer is presented. The model used is a system of Lur'e type, i.e. a model where the linear dynamic and nonlinear static part are separated. The identification of the model parameters from the given data proceed iteratively, adapting in turn the linear and the nonlinear part. Thus, the difficult nonlinear dynamical system identification task is decomposed into the easier problems of linear dynamical and nonlinear static system identification. The way to apply the approximately periodic input signal in order to realize qualitative resonance is chosen with the help of periodic control theory. Validation (Chapter 7) The pattern recognition method has been validated on the following examples — A synthetic example — Laboratory measurement from Colpitts oscillator — ECG — EEG — Vowels of a speech signals In the first four cases a binary classification and in the last example a classification with five classes was performed. To the best of the knowledge of the author the recognition method is original. Chaotic systems have been already used to produce pseudo-noise and to model signal diversity. Also, parameter identification of chaotic systems has been already carried out. However, the direct establishment of the model from the given data and its subsequent use for classification based on the phenomenon of qualitative resonance is entirely new

Sensorless Commissioning and Control of High Anisotropy Synchronous Motor Drives

L'abstract è presente nell'allegato / the abstract is in the attachmen