Stabilization of Inverted Pendulum Via Gudermannian Feedback Structure

Abstract

This paper describes design of a nonlinear controller for stabilizing a single inverted pendulum using coordinate transformation based on inverse Gudermannian. Inverse Gudermannian is expressed as infinite series of pendulum position and specifically chosen to define diffeomorphism which diminishes residual nonlinearity after the coordinate transformation. The resulting feedback system possesses larger basin of attraction comparing with other approximated linearizations using so-called the center of percussion (COP) or higher order output functions. Both numerical simulations and experiments show the advantage of the design.