Nonlinear convex control of the Furuta pendulum based on its descriptor model

Abstract

This paper presents simulation and real-time results of a nonlinear control scheme for stabilization of the Furuta pendulum. Instead of the traditional state-space model, the proposal makes use of a convex exact rewriting of the nonlinear model in its descriptor form, which naturally arises in Lagrange-Euler dynamics. Convexity proves to be useful when combined with an extension of the direct Lyapunov method for singular systems, since it leads to design conditions in the form of linear matrix inequalities, which allow the use of convex programming techniques. Moreover, real-time implementation issues such as actuator saturation limits and decay rate are straightforwardly incorporated in the design. Numerical advantages of the descriptor convex model over the state-space representation are also discussed.