Pulse random processes in analysis and diagnostics of nonlinear systems with dynamic chaos

The questions connected with mathematical modeling of transformation of non-Gaussian random processes, signals and noise in linear and nonlinear systems are considered and analyzed. The mathematical transformation of random processes in linear inertial systems consisting of both series and parallel connected links, as well as positive and negative feedback is analyzed. The mathematical transformation of random processes with polygamous density of probability distribution during their passage through such systems is considered. Nonlinear inertial and non-linear systems are analyzed.

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Suppression of chaotic vibrations in nonlinear systems by the example of a mechanical tachometer

Modeling of systems and processes ◽

10.12737/2219-0767-2021-14-2-73-79 ◽

2021 ◽

Vol 14 (2) ◽

pp. 73-79

Author(s):

Vladimir Shashikhin ◽

Ludmila Potapova ◽

Svetlana Budnic

Keyword(s):

Nonlinear Systems ◽

Closed System ◽

State Feedback ◽

Dynamic Chaos ◽

Characteristic Parameters ◽

Regular Motion ◽

Chaotic Vibrations ◽

Chaotic Mode

A method for controlling dynamic chaos is proposed by introducing state feedback and changing the spectrum of Lyapunov characteristic parameters of a closed system to achieve the desired result - the transition from chaotic mode to regular motion. The solution of this problem is considered on the example of stabilization of a mechanical tachometer. The parameters of the controller in the feed-back circuit are determined by the method of modal con-trol synthesis.

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Nonlinear Systems: Random Processes

Random Processes ◽

10.1109/9780470547199.ch6 ◽

2009 ◽

Keyword(s):

Nonlinear Systems ◽

Random Processes

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Stabilization of Nonlinear Systems with Dynamic Chaos

Automatic Control and Computer Sciences ◽

10.3103/s0146411621030032 ◽

2021 ◽

Vol 55 (3) ◽

pp. 213-221

Author(s):

S. V. Budnik ◽

V. N. Shashihin

Keyword(s):

Nonlinear Systems ◽

Dynamic Chaos

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Nonlinear State Monitoring With Karhunen-Loe`ve-Transform

Applied Mechanics ◽

10.1115/imece2004-60260 ◽

2004 ◽

Cited By ~ 1

Author(s):

Philipp Glo¨smann ◽

Edwin Kreuzer

Keyword(s):

Nonlinear Systems ◽

Coherent Structures ◽

Nonlinear Dynamical Systems ◽

Short Review ◽

Mathematical Concept ◽

Random Processes ◽

State Monitoring ◽

Process Data ◽

Nonlinear Dynamical ◽

Nonlinear State

Nonlinear dynamical systems often appear to have uncorrelated output. This characteristic leads to the idea of analyzing the dynamics of nonlinear systems with methods developed for random processes. The Karhunen-Loe`ve-Transform (KLT) was designed to detect coherent structures in random process data. It can also be applied for state monitoring of complex systems. This paper gives a short review on the mathematical concept of the KLT and discusses an approach to characterize the dynamics of nonlinear systems based on experimental data.

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