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Convergent Polishing: A Simple, Rapid, Full Aperture Polishing Process of High Quality Optical Flats & Spheres
Published on: December 1, 2014
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Transient chaotic behavior of fuzzy controlled polishing processes
1Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest 1111, Hungary.
Chaos (Woodbury, N.Y.)
|October 1, 2022
Summary
This study analyzes fuzzy controlled polishing machines, revealing chaotic dynamics due to temporal sampling. Algebraic expressions were derived for transient chaotic motion, aiding in understanding system stability and performance.
Area of Science:
- Engineering
- Control Systems
- Nonlinear Dynamics
Background:
- Polishing processes are critical in manufacturing for achieving precise surface finishes.
- Understanding the dynamic behavior of automated systems is essential for optimizing performance and preventing failures.
- Fuzzy control offers a robust approach to managing complex system dynamics, but temporal sampling effects require careful consideration.
Purpose of the Study:
- To investigate the dynamic behavior of a fuzzy controlled polishing machine.
- To analyze the influence of temporal sampling on the machine's dynamics.
- To characterize chaotic and transient chaotic behaviors within the system.
Main Methods:
- Utilizing fuzzy control theory to model the polishing machine.
- Incorporating temporal sampling effects into the dynamic model.
- Analyzing system behavior through simulation and mathematical analysis to identify chaotic regimes.
Main Results:
- Chaotic and transient chaotic dynamics were observed for specific control parameter combinations.
- Closed-form algebraic expressions were derived for the expected value of the kickout number during transient chaotic motion.
- The standard deviation corresponding to the kickout number was also determined algebraically.
Conclusions:
- Temporal sampling significantly impacts the dynamics of fuzzy controlled polishing machines, potentially leading to chaotic behavior.
- The derived algebraic expressions provide valuable tools for quantifying and predicting system behavior under transient chaotic conditions.
- This research contributes to a deeper understanding of nonlinear dynamics in automated manufacturing processes, enabling improved control strategies.
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