Exact controllability of a linear Euler-Bernoulli panel

Abstract

The problem of control of flexible vibrations of a flexible space structure (such as solar cell array) modelled by a thin uniform rectangular panel is considered here. The flexural vibrations of such a panel satisfies the one dimensional fourth order Petrowsky equation or Euler-Bernoulli equation. The panel is held at one end by a rigid hub and the other end is free. By attaching the hub to one side of the panel the dynamics create a non-standard hybrid system of equations. It is shown that the vibrations of the overall system can be driven to rest by means of an active boundary control force applied on the rigid hub only. Also an estimate of the minimum time of control is obtained. A closed form approximate result is constructed by Galerkin's residual technique to support and implement the method.