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GAO Zhiying
SHEN Yunwen
LIU Xiaoning
School of Mechatronics Engineering,
Northwestern Polytechnical University,
Xi’ an 710072, China |
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PERIODIC WINDOWS OF NONLINEAR
GEAR SYSTEM BASED ON
SYMBOLIC DYNAMICS*
Abstract:
The periodic window is researched by means of the symbolic dynamics and formal language. Firstly, the proper sampling period is taken and the orbital points of periodic motion are obtained through Poincaré mapping. Secondly, according to the method of symbolic dynamics of one-dimensional discrete mapping, the symbolic sequence describing the periodic orbit is obtained. Finally, based on the symbolic sequence, the corresponding model of minimal finite automation is constructed and the entropy is obtained by calculating the maximal eigenvalue of Stefan matrix. The results show that the orbits in periodic windows can be strictly marked by using the method of symbolic dynamics, thus a foundation for control of switching between target orbits is provided.
Key words:
Nonlinear gear system Periodic window Symbolic sequence Finite automation Entropy
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