Simulations and Analysis of ADRC/Controlled Lorenz System
Location
Room 2903
Session Format
Paper Presentation
Research Area Topic:
Natural & Physical Sciences - Mathematics
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 annihilating 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 state trajectories. In particular, we first prove the asymptotic stability of the ESO of the y-state in the sense of Lyapunov. We then establish the asymptotic stability of the y-state controlled by an ADRC controller. This leads to the global stability of all three states of the Lorenz system. In addition to the analysis of ADRC, we will also provide simulations for regulation control and tracking control.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Presentation Type and Release Option
Presentation (Open Access)
Start Date
4-16-2016 4:00 PM
End Date
4-16-2016 5:00 PM
Recommended Citation
Espe, Zachary, "Simulations and Analysis of ADRC/Controlled Lorenz System" (2016). GS4 Georgia Southern Student Scholars Symposium. 110.
https://digitalcommons.georgiasouthern.edu/research_symposium/2016/2016/110
Simulations and Analysis of ADRC/Controlled Lorenz System
Room 2903
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 annihilating 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 state trajectories. In particular, we first prove the asymptotic stability of the ESO of the y-state in the sense of Lyapunov. We then establish the asymptotic stability of the y-state controlled by an ADRC controller. This leads to the global stability of all three states of the Lorenz system. In addition to the analysis of ADRC, we will also provide simulations for regulation control and tracking control.
