Modelling and Trajectory Tracking Control of A 2-DOF Vision Based Inverted Pendulum

This paper presents a new modelling and trajectory tracking control system of a 2-DOF inverted pendulum using a contactless feedback with a low cost CCD camera. The proposed modelling method transforms the 2-DOF problem into a 1-DOF one by choosing a new balancing plane for the pendulum at each camera sampling instant. For a given plane, two feedback loops are considered. The first one, which is an observation loop, processes the delayed and sampled angle information delivered by the artificial vision system so as to set up a stable linear model of the pendulum and to estimate its continuous state by means of a specific observer called Piecewise Continuous Observer. The second loop, which is a stabilization loop, realizes a Lyapunov function based control to stabilize the cart-pendulum system. Simulation results illustrate the performances of the proposed approach.