Acta Scientific Computer Sciences

Research Article Volume 4 Issue 11

Low-pass Equivalent Dynamics and Control in Systems with Nonlinear Coupling of Linear Oscillators

Nikolaos I Xiros1-5*

1Dipl. Eng., Electrical and Computer Engineering, National Technical University of Athens, 1995, Greece
2M.Sc., Mathematics, University of New Orleans, 2017, USA
3M.Sc., Applied Physics, University of New Orleans, 2019, USA
4Dr. Eng., Naval Architect and Marine Engineer, National Technical University of Athens, 2001, Greece
5Boysie Bollinger School of Naval Architecture and Marine Engineering at the University of New Orleans, UNO Campus, New Orleans, USA

*Corresponding Author: Nikolaos I Xiros, Boysie Bollinger School of Naval Architecture and Marine Engineering at the University of New Orleans, UNO Campus, New Orleans, USA

Received: February 15, 2022; Published: October 31, 2022

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Abstract

Control theory of nonlinear systems receives continuously increasing attention. System nonlinearity occurs when at least one subsystem is nonlinear. Classical methods used for linear systems, particularly superposition, are not applicable to the nonlinear systems. It is necessary to use other methods to study the control of these systems. For a wide class of nonlinear systems, a rather important feature is the strong coupling nonlinearity between spectrally decoupled parts. Even in the case of low frequencies, where lumped models can still be employed the nonlinear coupling between parts of the system requires specific treatment, using advanced mathematical tools. A frequency domain approach is employed for systems with linearly decoupled but nonlinearly coupled subsystems. The Hilbert transform is appropriately introduced for obtaining two low-pass subsystems that form an equivalent description of the essential overall system dynamics. The nonlinear coupled dynamics is investigated systematically by partitioning the coupled system state vector in such a way as to fully exploit the low-pass and the band-pass intrinsic features of free dynamics. In particular, by employing the Hilbert Transform, a low-pass equivalent system is derived. Then, a typical case is investigated via numerical simulation of the original coupled low and band-pass, real-state-variable system and the low-pass-equivalent, complex-state-variable derived one. The nonlinear model equations considered here enable a systematic investigation of nonlinear feedback control options to operate mechatronic transducers in energy harvesting, sensing or actuation modes.

Keywords: Dynamics and Control; Feedback Linearization; Mechatronics; MEMS; Nonlinear Control; Nonlinear Systems

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Citation

Citation: Nikolaos I Xiros. “Low-pass Equivalent Dynamics and Control in Systems with Nonlinear Coupling of Linear Oscillators". Acta Scientific Computer Sciences 4.11 (2022): 56-70.

Copyright

Copyright: © 2022 Nikolaos I Xiros. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.




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