Event-Based Control of the Inverted Pendulum: Swing up and Stabilization

Abstract

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 allows 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 firstly propose to apply an event-based approach previously developed in Marchand et al. (2011, 2013) for the stabilization of the pendulum near its inverted position. We then study the swinging of the pendulum up to the desired position and especially design a (low computational cost) control law for this second case, based on an energy function. The switch between both strategies is also analyzed for stability reason. A real-time experimentation is realized and notably demonstrates the efficiency of the event-based schemes, even in the case where the system has to be actively actuated to remain upright. A reduction of about 98% and 50% of samples less than the classical scheme is achieved for the swing up and stabilization parts respectively, whereas the system performance remains the same (in terms of balancing and stabilizing time or control amplitude).