Term of Award

Summer 2016

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Department

Department of Mathematical Sciences

Committee Chair

Yan Wu

Committee Member 1

Yi Hu

Committee Member 2

Shijun Zheng

Abstract

In this work, we study the stability property of a chaotic Lorenz system stabilized by an ADRC (Active Disturbance Rejection Control) controller. The Lorenz system is known as a benchmark nonlinear dynamical system, which is widely seen in many applications such as thermosyphon and lasers. In practice, the disturbances to the system are usually ignored during the modeling process. Higher order terms are dropped due to simplification. All these factors contribute to the so-called uncertainties associated with the system. A robust controller should take the uncertainties into consideration. An ADRC controller is shown to be effective in adaptation to the unmodeled components of the system while regulating the flow pattern. An ADRC controller consists of an ESO (extended state observer), which is designed to approximate the uncertainties, and an annihilator along with a PI-controller used to cancel the disturbances and stabilize the system. We consider the case where the systems dynamics are largely unknown and discover that the observer error is bounded by a constant depending on the observer gain parameter. Next, we prove the asymptotic stability of the ESO of the y-state in the sense of Lyapunov. Then, we establish the asymptotic stability of a single state controlled by an ADRC controller leading to global asymptotic stability of all three states.

Research Data and Supplementary Material

No

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