An equivalent control based second order sliding mode observer using robust differentiators

In this paper a sliding-mode observer for a class of non-linear systems is proposed. The observer is based on the equivalent control method. The mathematical tools required to design such an observer are also presented. The proposed scheme can ensure finite time convergence of the observer and the reduction of chattering effect due to relay- type correction terms. Several examples are presented to illustrate the proposed method.ColcienciasCinvestavUniversidad Nacional de Colombi

Robust exact differentiators with predefined convergence time

The problem of exactly differentiating a signal with bounded second derivative is considered. A class of differentiators is proposed, which converge to the derivative of such a signal within a fixed, i.e., a finite and uniformly bounded convergence time. A tuning procedure is derived that allows to assign an arbitrary, predefined upper bound for this convergence time. It is furthermore shown that this bound can be made arbitrarily tight by appropriate tuning. The usefulness of the procedure is demonstrated by applying it to the well-known uniform robust exact differentiator, which the considered class of differentiators includes as a special case

On the Discretization of a Class of Homogeneous Differentiators

This paper proposes explicit and implicit discrete-time realizations for a class of homogeneous sliding-mode-based differentiators. The proposed approach relies on the exact discretization of the continuous differentiator. Also, it is demonstrated that the proposed implicit discretization always exists, is non-anticipative and unique. A numerical simulation shows the better performance of the implicit scheme over the proposed and the referenced explicit implementations.ITESO, A.C

Application of homogeneous observers with variable exponent to a mechatronic system

International audiencePreventive maintenance becomes nowadays more and more essential in many industrial applications. In fact, researchers are always looking for new techniques and analysis tools to monitor the dynamic behavior of their machines. In this context, firstly, we deal with the modeling of an electromechanical system which is accounted for by a hybrid model obtained by assembling the mechanical model of a gear element and the electrical model of an asynchronous motor. Secondly, we use Sliding Mode Observers to supervise the gear dynamic behavior. The observers parameters are suitably chosen to ensure rapid and accurate convergence between the real and the estimated system quantities. 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 ones