[PDF] A Stability Study Of Nonlinear Sampled Data Systems eBook

Author : Toshimitsu Nishimura
Publisher :
Page : 250 pages
File Size : 41,87 MB
Release : 1961
Category : Discrete-time systems
ISBN :

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The fundamental equation that describes limit cycles in nonlinear sampled-data systems was derived. The equivalence of limit cycles with finite pulsed systems having a periodically varying sampling-rate was observed, and the methods of analysis applied to the latter were extended to obtain these limit cycles with the aid of final value theorem. This fundamental equation is modified and simplified under certain assumptions as it can be applied to systems both with and without integrators. The limitation on the longest period of saturated and unsaturated oscillation is investigated and the critical gain for their existence is derived, starting from the modified fundamental equation. Also, the stability of limit cycles and the equilibrium point is considered, based on Neace's method. Various kinds of non-linearities, namely, pulse-width modulation, relay saturating amplifier with linear zone and quantized level amplifier are discussed. Self-excited oscillations are mainly examined, as well as the possible existence and stability of limit cycles, however, the method can be extended to forced oscillations.

Author : Iasson Karafyllis
Publisher : Springer Science & Business Media
Page : 401 pages
File Size : 48,91 MB
Release : 2011-04-02
Category : Technology & Engineering
ISBN : 0857295136

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Recently, the subject of nonlinear control systems analysis has grown rapidly and this book provides a simple and self-contained presentation of their stability and feedback stabilization which enables the reader to learn and understand major techniques used in mathematical control theory. In particular: the important techniques of proving global stability properties are presented closely linked with corresponding methods of nonlinear feedback stabilization; a general framework of methods for proving stability is given, thus allowing the study of a wide class of nonlinear systems, including finite-dimensional systems described by ordinary differential equations, discrete-time systems, systems with delays and sampled-data systems; approaches to the proof of classical global stability properties are extended to non-classical global stability properties such as non-uniform-in-time stability and input-to-output stability; and new tools for stability analysis and control design of a wide class of nonlinear systems are introduced. The presentational emphasis of Stability and Stabilization of Nonlinear Systems is theoretical but the theory’s importance for concrete control problems is highlighted with a chapter specifically dedicated to applications and with numerous illustrative examples. Researchers working on nonlinear control theory will find this monograph of interest while graduate students of systems and control can also gain much insight and assistance from the methods and proofs detailed in this book.

Author : Mangalore Anantha Pai
Publisher :
Page : 226 pages
File Size : 36,77 MB
Release : 1961
Category : Data transmission systems
ISBN :

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Various techniques are available for the analysis of nonlinear sampled-data systems. Most of these methods use either the phase plane approach or the describing function technique. Since the performance of such a system is described, at sampling instants, by means of a difference equation, an approach based on the difference equation would seem to be both natural and direct. The principle of complex convolution for a transform is explained and its geometrical interpretation is given. It is shown how the application of the convolution transform is both direct and simple with respect to solving nonlinear difference equations when the equation is given in scalar form. Dependence of the convergence of the solution on the initial value and the degree of nonlinearity is pointed out. It is concluded that for difference equations of second order and higher, this method involves too much laborious computation to justify its use. A simple method is presented for examining free oscillations in a sampled-data system containing either relay or a saturating amplifier. In addition, a certain analytical technique, analogous to that for differential equations, is developed to investigate the stability of forced oscillations for certain types of nonlinear difference equations. (Author).

Author : S. Kodama
Publisher :
Page : 26 pages
File Size : 27,6 MB
Release : 1960
Category : Asymptotic theory
ISBN :

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With regard to the asymptotic stability in the large of nonlinear autonomous sampled-data control systems, the following conjecture has frequently appeared and been used as a criterion for system design in the literature. Namely, "if the linearized system is stable for all points of the state space, the original nonlinear system is asymptotically stable in the large (henceforth abbreviated a.s.i.l.)." This paper shows by counter examples that the statement is not true in general. Both total and incremental linearization are considered and in both cases the conjecture is false. Finally, a sufficient condition for a.s.i.l. is estabilished.