Stabilization of Uncertain Multi‐Order Fractional Systems Based on the Extended State Observer |
| |
| Authors: | Liping Chen,Gang Chen,Ranchao Wu,J.A. Tenreiro Machado,António M. Lopes,Suoliang Ge |
| |
| Affiliation: | 1. School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, China;2. School of Mathematics, Anhui University, Hefei, China;3. Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, R. Dr. António Bernardino de Almeida, 431, Porto, Portugal;4. UISPA–LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, Porto, Portugal |
| |
| Abstract: | The extended state observer (ESO) based controller has been used successfully with integer‐order systems involving large uncertainties. In this paper, the robust control of uncertain multi‐order fractional‐order (FO) systems based on ESO is investigated. First, we transform the multi‐order FO system into an equivalent system in the form of a same‐order state‐space equation. Then, the ESO for the new system is established for estimating both the state and the total disturbance. Sufficient conditions for bounded‐input and bounded‐output stability are derived, and the asymptotic stability of the closed loop system is analyzed, based on whether the states are available or not. Finally, numerical simulations are presented to demonstrate the validity and feasibility of the proposed methodology. |
| |
| Keywords: | Fractional‐order system the extended state observer 0 stabilization multi‐order |
|
|
