Stabilization of a flexible manipulator model with passive joints

A mathematical model of a flexible manipulator consistingof an arbitrary number of links governed by the Euler-Bernoullibeam equation is derived. The first link is fixed at one end and is driven bya control torque. The last link carries a payload. Apeculiarity of the model is that the density and flexural rigidityparameters are allowed to be discontinuous but piecewise constantfunctions of the spatial coordinate. For the Galerkinapproximation of the control system considered, we derive a resulton stabilization of the equilibrium. The controller design schemeis based on explicit construction of a Lyapunov function andapplication of the invariance principle. A simulation of theclosed-loop dynamics is carried out in order to show theefficiency of the controller proposed.