Regulation and tracking of the nonholonomic double integrator: A field-oriented control approach

In this paper we show how a slight modification to the well-known field-oriented control of induction motors allows us to provide simple solutions to the problems of global regulation and tracking for the nonholonomic double integrator. Two controllers are proposed, one motivated by the well-known direct field-oriented motor control, which is a simple continuous static-state feedback that guarantees exponential convergence for all initial conditions in R-3 - {X-1 = X-2 = 0}. To overcome the latter restriction we add a dynamic extension to transfer this (initial conditions) singularity to the controller state, hence making the stability global. This controller is a direct outgrowth of indirect held oriented motor control. In view of the well-known Brockett's condition we obviously do not ensure Lyapunov stability. (C) 1998 Elsevier Science Ltd. All rights reserved.