Assessment of Transient Stability of Nonlinear Dynamic Systems by the Method of Tangent Hyperplanes and the Method of Tangent Hypersurfaces

1989 ◽  
Vol 111 (3) ◽  
pp. 540-541
Author(s):  
A. M. Eskiciogˇlu
Keyword(s):  
Asymptotic Stability ◽  
Dynamic System ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Transient Stability ◽  
Stability Boundary ◽  
Direct Methods ◽  
Nonlinear Dynamic System ◽  
Nonlinear Dynamic Systems ◽  
Stability Assessment

Two direct methods, the method of tangent hyperplanes and the method of tangent hypersurfaces, are applied to an elementary nonlinear dynamic system for transient stability assessment. The former method is based on the approximation of the asymptotic stability boundary by hyperplanes at a certain class of unstable singular points in the state-space, and the latter replaces hyperplanes by hypersurfaces. The applicability and accuracy of both methods are evaluated through a comparison of results.

Methods of Identification of Definite Degenerated and Nonlinear Dynamic System Using Specially Programmed Nonharmonic Enforce

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Miroslaw Bocian ◽  
Krzysztof Jamroziak ◽  
Mariusz Kosobudzki ◽  
Maciej Kulisiewicz
Keyword(s):  
Energy Balance ◽  
Dynamic System ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Nonlinear Dynamic System ◽  
Dynamic Structure ◽  
Dynamic Loads ◽  
Nonlinear Dynamic Systems ◽  
Wide Range

The paper presents the new way of identification of complex nonlinear dynamic systems. The method has been explained with the use of a dynamic structure (degenerated one) with 1.5 degrees-of-freedom and some nonlinear restitution force. The applied method allows for the assessment of the dynamic behavior of material in a wide range of dynamic loads. The equation of energy balance when oscillations are set harmonic is applicable to the solution. It is possible when the loading force is adjustable. The method has been computer verified using a system with cubic spring characteristic.

scholarly journals Orbital stability analysis of trajectories of highly nonlinear dynamic systems with feedback coupling

2021 ◽  
Vol 2131 (3) ◽  
pp. 032038
Author(s):  
G K Annakulova
Keyword(s):  
Dynamic System ◽  
Dynamic Systems ◽  
Limit Cycles ◽  
Nonlinear Dynamic ◽  
Phase Plane ◽  
Orbital Stability ◽  
Nonlinear Dynamic System ◽  
Phase Pattern ◽  
Highly Nonlinear ◽  
Complete Study

Abstract Orbital stability and qualitative study of the oscillations of a highly nonlinear dynamic system with feedback coupling are considered. For a highly nonlinear dynamic system with feedback coupling that satisfies Liénard’s theorem (on the existence and uniqueness of a periodic solution), a complete study of the phase pattern of the system is conducted. Applying the Poincaré criterion, the conditions for the existence of limit cycles and their Lyapunov stability are determined. The diagrams of phase trajectories are constructed numerically using the Mathcad 15 software package. Limit cycles are established, which are consistent with the limit cycles obtained by the Poincaré method. The behavior of trajectories outside the limit cycles is investigated. Recurrent homogeneous Pfaff equations are obtained, which determine the behavior of the systems “at infinity”. It was determined that the infinitely distant point of the horizontal axis is the only singular point for these equations. Linear approximations of recurrent homogeneous equations are obtained, which make it possible to determine the nature of the singular points. It was found that the trajectories then wind like a spiral on the limit cycles. Images of trajectories on the phase plane outside the limit cycles for the cases of degrees of nonlinearity under consideration are constructed.

On the Control and Stability of One Class of Biped Locomotion Systems

1970 ◽  
Vol 92 (2) ◽  
pp. 328-332 ◽  
Author(s):  
M. Vukobratovic´ ◽  
D. Juricˇic´ ◽  
A. A. Frank
Keyword(s):  
Nonlinear Systems ◽  
Dynamic System ◽  
Dynamic Systems ◽  
Lower Limb ◽  
Nonlinear Dynamic ◽  
Point Mass ◽  
Nonlinear Dynamic Systems ◽  
Biped Locomotion ◽  
Gait Stability ◽  
Stability Properties

The control and stability properties of a “simplified dynamic system” representing a particular biped gait are discussed. The simplified dynamic system consists of an algorithmically controlled lower limb system and a movable point mass. The concepts of repeatability and cyclicity are introduced by means of this model. These concepts provide the basis for control considerations in this class of systems. They lead to conditions which guarantee the maintenance of a gait. Stability of such nonlinear systems cannot be considered by classical techniques. To study stability, the concept of disturbance to nonlinear dynamic systems is introduced. This concept leads to a measure of stability by a quantity termed an “index of capability.” A method of computation for this index for this class of machines is shown.

Model Checking Control Software for Nonlinear Dynamic Systems

2008 ◽  
Author(s):  
James Kapinski ◽  
Alexandre Donze ◽  
Flavio Lerda ◽  
Hitashyam Maka ◽  
Edmund Clarke ◽  
...  
Keyword(s):  
Model Checking ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Systems ◽  
Control Software

Emulation of Ensembles of Nonlinear Dynamic Systems in Ultrawideband Active Wireless Direct Chaotic Networks

2018 ◽  
Vol 7 (3) ◽  
pp. 38-49
Author(s):  
Yu.V. Andreyev ◽  
◽  
M.Yu. Gerasimov ◽  
A.S. Dmitriev ◽  
R.Yu. Yemelyanov ◽  
...  
Keyword(s):  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Systems
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