Article
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Controlling Chaos – Forced Lorenz System
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Version 1
: Received: 29 December 2022 / Approved: 4 January 2023 / Online: 4 January 2023 (10:35:26 CET)
How to cite: Kuck, E.; Sands, T. Controlling Chaos – Forced Lorenz System. Preprints 2023, 2023010077. https://doi.org/10.20944/preprints202301.0077.v1 Kuck, E.; Sands, T. Controlling Chaos – Forced Lorenz System. Preprints 2023, 2023010077. https://doi.org/10.20944/preprints202301.0077.v1
Abstract
Chaotic systems are systems whose results are sensitive to the initial conditions. Chaotic systems generally have nonlinearities that can be difficult to model. One example of a chaotic system with nonlinearities is the Lorenz system. The Lorenz system can be used to model weather, wind disturbances, and electronic circuit design, among other applications. In this manuscript, the Lorenz system is modeled and various control methods are applied in an effort to dictate the system’s state and rate trajectories. The combination of the linear feedback and nonlinear feedforward controllers can show over an 80% improvement in state trajectory errors when compared to the baseline run. However, the improved state trajectory performance comes at a cost of as much as 1800% error in the rate trajectories.
Keywords
chaos; linear feedback control; Lorenz system; nonlinear feedforward control; oscillator; sinusoidal forcing
Subject
Engineering, Control and Systems Engineering
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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