Observer Design for a Class of Nonlinear Discrete Time Systems: Real Time Application to the One-link Flexible Joint Robot

Abstract

This paper demonstrates the observer design for large class of nonlinear discrete time systems. The use of the differential mean value theorem (DMVT) allows transforming the nonlinear error dynamics into a linear parameter varying (LPV) system. This has the advantage of introducing a general condition on the nonlinear functions. To ensure asymptotic stability, sufficient conditions are expressed in terms of linear matrix inequalities (LMIs). For comparison, an observer based on the use of the one-sided Lipschitz condition is introduced. High performances are shown through real time implementation of the one-link flexible joint robot to ARDUINO MEGA 2560 device. General TermsNonlinear Observers, ARDUINO MEGA 2560

Robust Observer Design for Uncertain Lipschitz Nonlinear Systems Based on Differential Mean Value Theorem: Application to Induction Motors

“…The observer gain matrices are obtained by solving optimization problems with LMI constraints. In the recent literature, the problem of observer design using DMVT has been successfully studied in some practical applications, such as PMSM drive (Hamidani et al 2019), Vascular Microrobot (Sadelli et al 2017), secure communication problem (Messaoud 2019), one-link flexible joint robot (Thabet and Gasmi 2018) and etc. In the same context, other works have also been focused on the application of the same concept to induction motor, which is the subject of this paper.…”