Synchronization of Chaotic Gyros Based on Robust Nonlinear Dynamic Inversion

Abstract

A robust nonlinear dynamic inversion (RNDI) technique is proposed in order to synchronize the behavior of chaotic gyros subjected to uncertainties such as model mismatches and disturbances. Gyro is a crucial device that measures and maintains the orientation of a vehicle. By Leipnik and Newton in 1981, chaotic behavior of a gyro under specific conditions was established. Hence, controlling and synchronizing a gyro that shows irregular (chaotic) motion are very important. The proposed synchronization method is based on nonlinear dynamic inversion (NDI) control. NDI is a nonlinear control technique that removes the original system dynamics into the user-defined desired dynamics. Since NDI removes the original dynamics directly, it does not need linearizing and designing gain-scheduled controllers for each equilibrium point. However, achieving perfect cancellation of the original nonlinear dynamics is impossible in real applications due to model uncertainties and disturbances. This paper proposes the robustness assurance method of NDI based on sliding mode control (SMC). Firstly, similarities of the conventional NDI control and SMC are provided. And then the RNDI control technique is proposed. The feasibility and effectiveness of the proposed method are demonstrated by numerical simulations.