Event-Based Control of the Inverted Pendulum: Swing up and Stabilization
Résumé
Contrary to the classical (time-triggered) principle that calculates the control signal in a periodic fashion, an event-driven control is computed and updated only when a certain condition is satisfied. This notably enables to save computations in the control task while ensuring equivalent performance. In this paper, we develop and implement such strategies to control a nonlinear and unstable system, that is the inverted pendulum. We are first interested on the stabilization of the pendulum near its inverted position and propose an event-based control approach. This notably demonstrates the efficiency of the event-based scheme even in the case where the system has to be actively actuated to remain upright. We then study the swinging of the pendulum up to the desired position and propose a low-cost control law based on an energy function. The switch between both strategies is also analyzed. A real-time experimentation is realized and shows that a reduction of about 98% and 50% of samples less than the classical scheme is achieved for the swing up and stabilization parts respectively.Moreover, the intersampling time can be proved not to contract at the origin. More precisely, it is proved that for any initial condition within any given closed set the minimal inter-sampling time is proved to be below bounded avoiding the infinitely fast sampling phenomena. Moreover, under homogeneity assumptions the control can be proved to be smooth anywhere and the inter-sampling time bounded below for any initial condition. In that case, we retrieve a control approach previously published for continuous time stabilization of homogeneous systems.
Domaines
Automatique / Robotique
Origine : Fichiers produits par l'(les) auteur(s)
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