Stability preserving maps for finite-time convergence: Super-twisting sliding-mode algorithm

• Autores: Picó, J.; Picó Marco, E.; Vignoni, A.; de Battista, Hernan
• Año de publicación: 2013
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Stability Analysis; Convergence Analysis; Sliding Mode; Stability Preserving Maps; Super-Twisting Algorithm
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

The super-twisting algorithm (STA) has become the prototype of second-order sliding mode algorithm. It achieves finite time convergence by means of a continuous action, without using information about derivatives of the sliding constraint. Thus, chattering associated to traditional sliding-mode observers and controllers is reduced. The stability and finite-time convergence analysis have been jointly addressed from different points of view, most of them based on the use of scaling symmetries (homogeneity), or non-smooth Lyapunov functions. Departing from these approaches, in this contribution we decouple the stability analysis problem from that of finite-time convergence. A nonlinear change of coordinates and a time-scaling are used. In the new coordinates and time–space, the transformed system is stabilized using any appropriate standard design method. Conditions under which the combination of the nonlinear coordinates transformation and the time-scaling is a stability preserving map are given. Provided convergence in the transformed space is faster than O(1/τ )—where τ is the transformed time— convergence of the original system takes place in finite-time. The method is illustrated by designing a generalized super-twisting observer able to cope with a broad class of perturbations.
Fil: Picó, J.. Universidad Politecnica de Valencia; España
Fil: Picó Marco, E.. Universidad Politecnica de Valencia; España
Fil: Vignoni, A.. Universidad Politecnica de Valencia; España
Fil: de Battista, Hernan. Universidad Nacional de la Plata. Facultad de Ingenieria. Departamento de Electrotecnia. Laboratorio de Electronica Ind., Control E Instrumentac.; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina