Honors College Theses

Publication Date

2019

Major

Mathematics (B.S.)

Document Type and Release Option

Thesis (open access)

Faculty Mentor

Yan Wu

Abstract

This study addresses the control of chaotic dynamic systems represented by three coupled Lorenz systems. In application, Lorenz systems are commonly used to describe the one-dimensional motion of fluids in a tube when heated below and cooled above. This system, in particular, reflects the fluid motion in a coupled triple-loop thermosyphon system. The goal is to derive a system of nonlinear differential equations to help us study various flow patterns governed by such a high-dimensional nonlinear model numerically. Once the driving parameter (Rayleigh number) values are identified corresponding to the chaotic regime, a minimal number of proportional controllers are designed that only depend on the measurable states, which serve as perturbations to the system, so that the system trajectories are stabilized at its equilibrium point even though the Rayleigh numbers are significantly large. The stability property of the control system is then investigated over a large range of the parameter values through simulations. Furthermore, the stability bounds on the controller gains obtained via the Lyapunov Stability Theorem are tested for its feasibility in practice.

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