Term of Award
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department of Mathematical Sciences
Committee Member 1
Committee Member 2
Adel El Shahat
In this thesis, we study the stability of Active Disturbance Rejection Control (ADRC) applied to controlling the Lorenz system. The Lorenz system is a nonlinear dynamical system that we attempt to control. In fact, the system is used to model convection flow such as that found in thermosyphons, electric circuits, and lasers. We are stabilizing the Lorenz system along with a few disturbances. Thus, to stabilize this chaotic system, a robust controller is required. The ADRC system is known as as effective method to stabilize a dynamical system. With the help of the Extended State Observer (ESO), the system can be stabilized with the least information about the disturbances. In particular, when the model of the plant is given the system converges asymptotically. Since most physical plants are highly uncertain in the real world, we also establish a second case. When the dynamics of the plant is largely unknown, the errors of the ADRC Controlled Lorenz system is bounded by the observer gains and feedback control gains, which is Lyapunov stable.
C. Park. "ADRC based control of nonlinear dynamical system with multiple sources of disturbance and multiple inputs." Georgia Southern University, 2017.
Research Data and Supplementary Material