Minimum-time design of a slewing flexible beam

This paper presents an alternative method for the "minimum-time" design for a slewing flexible beam. The two-point boundary problem involved, which incorporates nonlinearity of the rigid slew manoeuvre coupled with flexibility of the beam, is linearized and then decoupled using a mode shape based transformation. The rigid mode, which dominates the slew manoeuvre of the beam, is used to minimise the time of operation from an initial state to final desired state subject to the constrained input. A quadratic control input is suggested for the remaining flexible modes. It follows a combination of "bang-bang" and quadratic feedback control for the beam. The dynamic behaviour of the beam is handled by using a high precision integration finite element method. Numerical results show the high performance with respect to position and also the general applicability of the method.