Application of homogeneous observers with variable exponent to a mechatronic system

Abstract

Monitoring of mechatronic systems is one of the essential issues in the industries. In this context, we firstly deal with the modeling of an electro-mechanical system obtained by assembling a mechanical model, which is a single stage of a gear element and an electrical model that is an asynchronous motor. Secondly, we use homogeneous sliding mode observers in order to supervise the gear dynamical behavior. The observers' parameters are suitably chosen to ensure rapid and accurate convergence between the real and the estimated system states. Finally, a comparative study between three simulations is presented in order to illustrate the observers performances and the influence of the mechanical dynamics on the electrical states.

Fault diagnosis via a dynamical sparse recovery method and application to a gearbox system

“…Another particularity of the SRD method is that all algorithms (corresponding to the optimization problem given by equation ( 30) and to the observer equations, see, for instance, García and Frank (1997), Besançon (2007) and Derbel et al (2019b)) are solved in a continuous process (i.e. in the same iteration loop) and with the same computation step.…”

“…whereÿ 1 ,ÿ 2 ,ÿ 3 , andÿ 4 are estimated using differentiators (see Derbel et al (2019b) where a sliding mode differentiator is applied to a single stage of gears). It must be noted that differentiators can be implemented because system (41) verifies the observability property explained in Assumption 1.…”

“…Following (17), we deduce the measurement vector χ containing the available information about the system (recall that χ denotes the difference between the derivatives of the outputs and the healthy operating dynamics of the system)where ÿ 1 , ÿ 2 , ÿ 3 , and ÿ 4 are estimated using differentiators (see Derbel et al (2019b) where a sliding mode differentiator is applied to a single stage of gears). It must be noted that differentiators can be implemented because system (41) verifies the observability property explained in Assumption 1.…”

“…It must be noted that differentiators can be implemented because system (41) verifies the observability property explained in Assumption 1. Algorithms very similar to those of Derbel et al (2019b) are used for the two-stage gear (in particular, the differentiator parameters that have to be suitably chosen to ensure rapid and accurate convergence between the real and the estimated system states have the same order of magnitude as those of Derbel et al (2019b)) and we do not present them here.…”

Dynamic System Fault Diagnosis Under Sparseness Assumption

“…These reported works all avoid state-space representation of the monitored system, and their results are either strongly relying on massively available data or with limited physical interpretation. On the other hand, state-space systems are considered in [32], [33]. In these works, hidden state variables are eliminated through numerical differentiation of sensor signals.…”