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 fiel d-oriented control of induction motors allows us to provide simple sol utions to the problems of global regulation and tracking for the nonho lonomic double integrator. Two controllers are proposed, one motivated by the well-known direct field-oriented motor control, which is a sim ple continuous static-state feedback that guarantees exponential conve rgence for all initial conditions in R-3 - {X-1 = X-2 = 0}. To overcom e 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 indirec t held oriented motor control. In view of the well-known Brockett's co ndition we obviously do not ensure Lyapunov stability. (C) 1998 Elsevi er Science Ltd. All rights reserved.