Steady-state, self-oscillating and chaotic behavior of a PID controlled nonlinear servomechanism by using Bogdanov-Takens and Andronov-Poincaré-Hopf bifurcations
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Title: | Steady-state, self-oscillating and chaotic behavior of a PID controlled nonlinear servomechanism by using Bogdanov-Takens and Andronov-Poincaré-Hopf bifurcations |
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Authors: | Pérez Molina, Manuel | Pérez Polo, Manuel |
Research Group/s: | Holografía y Procesado Óptico | Grupo de Control, Ingeniería de Sistemas y Transmisión de Datos |
Center, Department or Service: | Universidad de Alicante. Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal |
Keywords: | Servomechanism | Bogdanov-Takens bifurcation | Andronov-Poincaré-Hopf bifurcation | Center manifold | Chaotic behavior | PID controller |
Knowledge Area: | Física Aplicada | Ingeniería de Sistemas y Automática |
Issue Date: | 12-Mar-2014 |
Publisher: | Elsevier |
Citation: | Communications in Nonlinear Science and Numerical Simulation. 2014, Accepted Manuscript, Available online 12 March 2014. doi:10.1016/j.cnsns.2014.03.003 |
Abstract: | This paper analyzes a controlled servomechanism with feedback and a cubic nonlinearity by means of the Bogdanov-Takens and Andronov-Poincaré-Hopf bifurcations, from which steady-state, self-oscillating and chaotic behaviors will be investigated using the center manifold theorem. The system controller is formed by a Proportional plus Integral plus Derivative action (PID) that allows to stabilize and drive to a prescribed set point a body connected to the shaft of a DC motor. The Bogdanov-Takens bifurcation is analyzed through the second Lyapunov stability method and the harmonic-balance method, whereas the first Lyapunov value is used for the Andronov-Poincaré-Hopf bifurcation. On the basis of the results deduced from the bifurcation analysis, we show a procedure to select the parameters of the PID controller so that an arbitrary steady-state position of the servomechanism can be reached even in presence of noise. We also show how chaotic behavior can be obtained by applying a harmonical external torque to the device in self-oscillating regime. The advantage of achieving chaotic behavior is that it can be used so that the system reaches a set point inside a strange attractor with a small control effort. The analytical calculations have been verified through detailed numerical simulations. |
URI: | http://hdl.handle.net/10045/36160 |
ISSN: | 1007-5704 (Print) | 1878-7274 (Online) |
DOI: | 10.1016/j.cnsns.2014.03.003 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Peer Review: | si |
Publisher version: | http://dx.doi.org/10.1016/j.cnsns.2014.03.003 |
Appears in Collections: | INV - GCIST - Artículos de Revistas INV - GHPO - Artículos de Revistas |
Files in This Item:
File | Description | Size | Format | |
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2014_Perez-Molina_Perez-Polo_CNSNS.pdf | Accepted Manuscript (acceso abierto) | 1,16 MB | Adobe PDF | Open Preview |
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