STABILIZATION OF THE PROGRAMMED MOTIONS OF A RIGID-BODY WITH UNCERTAINTY IN THE PARAMETERS OF THE EQUATIONS OF DYNAMICS

A control scheme is proposed to guarantee the asymptotic stability of a given programmed motion of a rigid body rotating about a fixed point . The body is controlled by means of a couple of reactive forces, or t he control action is created by rotating flywheels. The inertial param eters and angular momentum of the system rue estimated while the motio n is in progress. The control is synthesized by expressing the equatio ns of dynamics in a form that is linear in the parameter vector and by using the passivity property of the dynamical object. A law is propos ed for the control and for adjusting the parameters that guarantees th e asymptotic stability of the motion and, for programmed motions that satisfy the condition of non-vanishing action, guarantees the converge nce of the vector of adjusted parameters to its true value. The domain in phase space for which exponential stabilization is achieved is det ermined. (C) 1997 Elsevier Science Ltd. All rights reserved.