Hidden periodic oscillations in drilling system driven by induction motor

Kiseleva, M.A.; Kondratyeva, Natalya; Kuznetsov, Nikolay; Леонов, Г. А.; Solovyeva, E.P.

doi:10.3182/20140824-6-za-1003.02449

Cited by 14 publications

(8 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the works [29,30,32,33,51,55] more complex models of drilling systems were studied. Analytical investigation of such models is a challenging task, so it is necessary to use numerical methods.…”

Section: The Set ω Contains the Point Smentioning

confidence: 99%

Theory of Differential Inclusions and Its Application in Mechanics

Kiseleva

Kuznetsov

Леонов

2017

New Perspectives and Applications of Modern Control Theory

View full text Add to dashboard Cite

The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torque characteristic is asymmetrical. Problem of sudden load chance is studied. Analytical methods of investigation of systems with such asymmetrical friction based on the use of Lyapunov functions are demonstrated. The Watt governor and Chua system are considered to show different aspects of computer modeling of discontinuous systems.

show abstract

Section: The Set ω Contains the Point Smentioning

confidence: 99%

Theory of Differential Inclusions and Its Application in Mechanics

Kiseleva

Kuznetsov

Леонов

2017

New Perspectives and Applications of Modern Control Theory

View full text Add to dashboard Cite

show abstract

“…7). In order to take into account the dynamics of the motor we write the equations in the following form [23,49,50]:…”

Section: Drilling System Actuated By Induction Motormentioning

confidence: 99%

Hidden attractors in electromechanical systems with and without equilibria

2016

View full text Add to dashboard Cite

This paper studies hidden oscillations appearing in electromechanical systems with and without equilibria. Three different systems with such effects are considered: translational oscillator-rotational actuator, drilling system actuated by a DC-motor and drilling system actuated by induction motor. We demonstrate that three systems experience hidden oscillations in sense of mathematical definition. While some of these hidden oscillations can be easily seen in natural physical experiments, the localization of others requires special efforts.

show abstract

“…Well known examples of the hidden oscillations are nested limit cycles in 16th Hilbert problem (see, e.g., [20,28]) and counterexamples to the Aizerman and Kalman conjectures on the absolute stability of nonlinear control systems [24,27,7,28]. Hidden oscillations in the models of electrical machines are discussed, e.g., in [16,15,28,29,14] the trajectory of the system after transient processes is attracted to the stable limit cycle (Figs. 14,15), i.e., vibrations are arisen in the hydropower units.…”

Section: Local Analysismentioning

confidence: 99%

“…Hidden oscillations in the models of electrical machines are discussed, e.g., in [16,15,28,29,14] the trajectory of the system after transient processes is attracted to the stable limit cycle (Figs. 14,15), i.e., vibrations are arisen in the hydropower units. Then the voltage is reduced to 0.7 of the rated voltage.…”

Section: Local Analysismentioning

confidence: 99%

A dynamical model of Sayano-Shushenskaya hydropower plant: stability, oscillations, and accident

Leonov,

Kuznetsov,

Solovyeva

2015

Preprint

View full text Add to dashboard Cite

This work is devoted to the construction and study of a mathematical model of hydropower unit, consisting of synchronous generator, hydraulic turbine, and speed governor. It is motivated by the accident happened on the Sayano-Shushenskaya hydropower plant in 2009 year. Parameters of the Sayano-Shushenskaya hydropower plant were used for modeling the system. Oscillations in zones, which were not recommended for operation, were found. The obtained results are consistent with the full-scale test results carried out for hydropower units of the Sayano-Shushenskaya hydropower plant in 1988.

show abstract

Hidden periodic oscillations in drilling system driven by induction motor

Cited by 14 publications

References 29 publications

Theory of Differential Inclusions and Its Application in Mechanics

Theory of Differential Inclusions and Its Application in Mechanics

Hidden attractors in electromechanical systems with and without equilibria

A dynamical model of Sayano-Shushenskaya hydropower plant: stability, oscillations, and accident

Contact Info

Product

Resources

About