Stabilization of a 2-DOF inverted pendulum by a low cost visual feedback

Abstract

This paper presents a stabilization control system of a 2-DOF inverted pendulum. The challenge is to realize a control with a contact-less feedback including a low cost CCD camera. The global control system uses two feedback loops. The first one (inner loop) includes the delayed and sampled inverted pendulum's top coordinates, obtained from the CCD camera and the second one (outer loop) concerns the cart's position in continuous time (obtained from encoders). With this feedback scheme, we propose a specific control method by choosing an optimal balancing plane at each camera's sampling instant, in view of transforming the 2-DOF pendulum problem to a 1-DOF one. Then in this balancing plane, we realize two control loops: The inner loop, relative to the pendulum's angle, is controlled by a linearization and stabilization method based on an innovative observer called piecewise continuous reduced-order Luenberger observer (PCROLO). The outer loop uses a Lyapunov function based control scheme with slower internal dynamics compared to that of the pendulum, considering that the global controlled system (cart + pendulum) is an unstable non-minimum-phase system. Numerical simulations show that the stabilization control of the inverted pendulum on an x-y robot that are strongly non linear is successful.