Controlled Lagrangians with gyroscopic forcing: an experimental application

This paper describes an experimental implementation of a feedback control law derived using the method of controlled Lagrangians. This technique, which was developed to stabilize underactuated mechanical systems, involves shaping a system´s total energy through feedback and introducing fictitious gyroscopic forces in the closed-loop system. The experimental application is the classic problem of stabilizing an inverted pendulum on a servo-actuated cart. In the absence of damping, the control law provides asymptotic stability in a region that contains all states for which the pendulum is inclined above horizontal. Even with linear damping, stabilizing control parameter values exist and simulations suggest that the region of attraction remains quite large. Although the nonlinear controller provides asymptotic stability within a large region of attraction, the controller´s local performance is poor when compared to that of a well-tuned linear controller. To obtain good performance both regionally and locally, a Lyapunov-based switching strategy is employed.