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1997 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Constructive Nonlinear Control

verfasst von: Dr R. Sepulchre, Dr M. Janković, P. V. Kokotović

Verlag: Springer London

Buchreihe : Communications and Control Engineering

Enthalten in: Professional Book Archive

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Über dieses Buch

Constructive Nonlinear Control presents a broad repertoire of constructive nonlinear designs not available in other works by widening the class of systems and design tools. Several streams of nonlinear control theory are merged and directed towards a constructive solution of the feedback stabilization problem. Analysis, geometric and asymptotic concepts are assembled as design tools for a wide variety of nonlinear phenomena and structures. Geometry serves as a guide for the construction of design procedures whilst analysis provides the robustness which geometry lacks. New recursive designs remove earlier restrictions on feedback passivation. Recursive Lyapunov designs for feedback, feedforward and interlaced structures result in feedback systems with optimality properties and stability margins. The design-oriented approach will make this work a valuable tool for all those who have an interest in control theory.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
Control theory has been extremely successful in dealing with linear time-invariant models of dynamic systems. A blend of state space and frequency domain methods has reached a level at which feedback control design is systematic, not only with disturbance-free models, but also in the presence of disturbances and modeling errors. There is an abundance of design methodologies for linear models: root locus, Bode plots, LQR-optimal control, eigenstructure assignment, H-infinity, µ-synthesis, linear matrix inequalities, etc. Each of these methods can be used to achieve stabilization, tracking, disturbance attenuation and similar design objectives.
Dr R. Sepulchre, M. Janković, P. V. Kokotović
Chapter 2. Passivity Concepts as Design Tools
Abstract
Only a few system theory concepts can match passivity in its physical and intuitive appeal. This explains the longevity of the passivity concept from the time of its first appearance some 60 years ago, to its current use as a tool for nonlinear feedback design. The pioneering results of Lurie and Popov, summarized in the monographs by Aizerman and Gantmacher [3], and Popov [88], were extended by Yakubovich [121], Kalman [51], Zames [123], Willems [120], and Hill and Moylan [37], among others. The first three sections of this chapter are based on these references from which we extract, and at times reformulate, the most important concepts and system properties to be used in the rest of the book.
Dr R. Sepulchre, M. Janković, P. V. Kokotović
Chapter 3. Stability Margins and Optimality
Abstract
For stabilization of an unstable system, feedback is a necessity. With uncertainties in the operating environment, and in system components, feedback is needed to preserve stability and improve performance. However, feedback can also be dangerous. A tighter feedback loop, instead of achieving better performance, may cause instability. To guard against such dangers, the quantitative concepts of gain and phase stability margins were among the frequency domain tools of the classical Nyquist-Bode designs.
Dr R. Sepulchre, M. Janković, P. V. Kokotović
Chapter 4. Cascade Designs
Abstract
With this chapter we begin the presentation of feedback stabilization designs which exploit structural properties of nonlinear systems. In Section 4.1 we introduce a class of cascade structures formed of two subsystems, with the subsystem states z and ξ, as illustrated in Figure 4.1.
Dr R. Sepulchre, M. Janković, P. V. Kokotović
Chapter 5. Construction of Lyapunov functions
Abstract
Several designs in the preceding chapters require the knowledge of Lyapunov functions which need to be constructed during the design. This construction is a crucial part of the design and is the main topic of this chapter
Dr R. Sepulchre, M. Janković, P. V. Kokotović
Chapter 6. Recursive designs
Abstract
Feedback passivation designs, which have been successful for the cascade structures in Chapters 4 and 5, will now be extended to larger classes of nonlinear systems. The common idea of the two main recursive procedures in this chapter, backstepping and forwarding, is to apply a passivation design to a small part of the system, and then to reapply it step-by-step by augmenting the sub-system at each step. The design is completed when the augmentations recover the whole system.
Dr R. Sepulchre, M. Janković, P. V. Kokotović
Backmatter
Metadaten
Titel
Constructive Nonlinear Control
verfasst von
Dr R. Sepulchre
Dr M. Janković
P. V. Kokotović
Copyright-Jahr
1997
Verlag
Springer London
Electronic ISBN
978-1-4471-0967-9
Print ISBN
978-1-4471-1245-7
DOI
https://doi.org/10.1007/978-1-4471-0967-9