Chaos Theory & Non-Linear Sys Analysis/Control?

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SUMMARY

The discussion centers on the evolution of aerospace vehicle control systems from linear to non-linear and probabilistic frameworks, particularly in relation to aerodynamic angle of attack (AoA). Historically, aircraft design emphasized linear AoA ranges for optimal lift, typically between 0 to 20 degrees. However, advancements have revealed the advantages of operating in non-linear regions, allowing for enhanced maneuverability. The conversation also touches on Chaos Theory and its application in designing systems that efficiently respond across both linear and non-linear domains.

PREREQUISITES
  • Understanding of aerodynamic principles, specifically angle of attack (AoA).
  • Familiarity with Chaos Theory and its relevance in system design.
  • Knowledge of non-linear dynamics in engineering applications.
  • Basic concepts of fractal embedding and wavelet analysis.
NEXT STEPS
  • Research the application of Chaos Theory in aerospace engineering.
  • Explore non-linear aerodynamic modeling techniques.
  • Study the implications of high angle of attack (AoA) on aircraft performance.
  • Investigate fractal embedding methods and their use in system optimization.
USEFUL FOR

Aerospace engineers, control system designers, and researchers interested in the intersection of Chaos Theory and non-linear dynamics in aircraft design.

RainmanAero
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Hello learned colleagues and other deep thinkers:

This question may be construed as either way too esoteric, or simply as too vague for this forum, and if deemed either of these I would agree if others find it an inappropriate topic. However...

When it comes to aerospace vehicles and the software systems that control them, I do believe the history of development has shown a marked progression from "linear and highly-predictable" systems towards an acceptance of "non-linear and more probablistic" systems. The best example I can give is aerodynamic angle of attack.

The early days of aircraft respected, honored, dare we say "worshipped" the linear angle of attack range for lift production... Generally from 0 to 18-20 degrees AOA MAX, depending upon the specific airframe/powerplant design and when its control response becomes non-linear.

We then have progressed to understanding the benefits and trade-offs of being able to maneuver aircraft at MUCH higher AoA's which are WELL into the non-linear region of aerodynamic response.

And then there is the science of Chaos Theory which bridges the worlds of linear and non-linear phenomenon with such tools as fractal embedding analytical processes (wavelets is just one of them!).

But does anyone have any references and/or citations of people who have actually used Chaos Theory as a means to design an optimal system which responds with minimum energy in both its linear and non-linear operating regions?

Thank you. I appreciate any answers or even willingness to discuss such a topic.

Rainman
 
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I am sorry rainman I cannot be of too much help here. Moreover, I want to know what do you mean with non linear aerodynamic response?. Even though my whole research goes about fluid mechanics, I am not familiar with its engineering applications to wing aerodynamics. Maybe I am too young for knowing about everything...:biggrin:
 

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