The objective of this paper is the design of smooth differentiator estimators for noise-free signals. A new class of differentiator estimators, with gains adaptively adjusted, is proposed. The algorithms allow ultimately uniformly bounded convergence of the estimators, and circumvent the unknown bounds of the second derivative of the original signal. Simulation results are led using different signal shapes to validate the efficiency of the proposed techniques, and to compare their performances to existing estimators depicted from literature.

In this article, new nonlinear differentiator estimators for noise-free signals, with gains adaptively adjusted, are proposed. The algorithms allow finite time convergence of the differentiator estimation, and circumvent the unknown bounds of the second derivative of the original signal. Simulation results are led using different signal shapes to validate the efficiency of the proposed techniques, and to compare their performances to existing estimators depicted from literature.

In this paper, we discuss the application of a recently proposed adaptive sliding mode control (ASMC) design with a novel switching gain dynamics, called integral/exponential adaptation law, to a five-link robot manipulator with uncertain dynamics. The proposed design does not require a priori knowledge of the upper bounds of perturbations. Robust stability with finite time convergence (FTC) is obtained with low chatter on control action and fast transient performance. The simulation results demonstrate the effectiveness of the proposed design.

Based on recent results on adaptive sliding mode control (ASMC) design for nonlinear systems with uncertainties, we propose some lemmas and theorems to discuss finite time convergence (FTC) and alternative approaches to smoothen the adaptation tuning algorithm of the ASMC design. These modifications are proposed to enhance accuracy without overestimation of the uncertainty magnitude and to suppress the chattering phenomenon. In fact, the new adaptation laws are designed in ways to assign a minimum admissible value to the switching gain. The robustness is proven using the Lyapunov stability criterion combined with an intuitive analysis of the control behavior. Simulation results are performed to demonstrate the effectiveness of the proposed algorithm. Part I introduces the new designs for ideal ASMC while the real case design will be shown in Part II.

Based on new results on ideal adaptive sliding mode control (ASMC) design for nonlinear systems with uncertainties discussed in Part I of the present contribution, we extend the new designs to the real case in this paper (Part II) by using boundary layer method and filtered rate of the sliding variable. These modifications are proposed to enhance accuracy without overestimation of the uncertainty magnitude and to suppress the chattering phenomenon, often magnified within real measured signals. In fact, the new adaptation laws are designed in ways to assign a minimum admissible value to the switching gain. The robustness is proven using the Lyapunov stability criterion combined with an intuitive analysis of the control behavior. Simulation results are performed to demonstrate the effectiveness of the proposed algorithm.

This paper deals with an extended output- feedback positioning tracking of a servo-system with friction based on generalized Maxwell-slip (GMS) friction observer dynamics with fixed model parameters. We succeed in designing a linear time invariant (LTI) compensator which ensures exponential stabilization and additional multi-objective features (e.g. closed-loop pole location). These conditions are expressed in terms of linear matrix inequalities (LMIs). Numerous simulations results illustrate the effectiveness of the proposed compensator and state a comparison with the similar LuGre closed-loop friction compensator.