A Chaotic System with Large Lyapunov Exponent: Nonlinear Observer Design and Circuit Implementation

Singh, Piyush Pratap

doi:10.1109/icepe50861.2021.9404446

Cited by 4 publications

(2 citation statements)

References 24 publications

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“…Substituting all the values in Equation ( 4), we obtain the theoretical liquid level in the tank. A dynamical system is a set of ordinary differential equations of the form shown in Equation (5).…”

Section: Computational Fluid Dynamicsmentioning

confidence: 99%

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Accurate Liquid Level Measurement with Minimal Error: A Chaotic Observer Approach

Shenoy,

Venkata

2024

Computation

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This paper delves into precisely measuring liquid levels using a specific methodology with diverse real-world applications such as process optimization, quality control, fault detection and diagnosis, etc. It demonstrates the process of liquid level measurement by employing a chaotic observer, which senses multiple variables within a system. A three-dimensional computational fluid dynamics (CFD) model is meticulously created using ANSYS to explore the laminar flow characteristics of liquids comprehensively. The methodology integrates the system identification technique to formulate a third-order state–space model that characterizes the system. Based on this mathematical model, we develop estimators inspired by Lorenz and Rossler’s principles to gauge the liquid level under specified liquid temperature, density, inlet velocity, and sensor placement conditions. The estimated results are compared with those of an artificial neural network (ANN) model. These ANN models learn and adapt to the patterns and features in data and catch non-linear relationships between input and output variables. The accuracy and error minimization of the developed model are confirmed through a thorough validation process. Experimental setups are employed to ensure the reliability and precision of the estimation results, thereby underscoring the robustness of our liquid-level measurement methodology. In summary, this study helps to estimate unmeasured states using the available measurements, which is essential for understanding and controlling the behavior of a system. It helps improve the performance and robustness of control systems, enhance fault detection capabilities, and contribute to dynamic systems’ overall efficiency and reliability.

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Section: Computational Fluid Dynamicsmentioning

confidence: 99%

“…"Chaos" refers to the irregular and unpredictable behavior observed in a deterministic system [5]. Chaos theory suggests that in a deterministic system, even a tiny alteration in the initial conditions can result in significant and unforeseeable outcomes if the equation governing its behavior is nonlinear.…”

Section: Introductionmentioning

confidence: 99%