Modelling and flatness-based motion planning for an interconnected flexible beam structure

Transient shape control is considered for a tip interconnected flexible beam structure with embedded piezoelectric actuators. Based on the distributed-parameter mathematical model of the beam structure flatness-based motion planning is developed taken into account a Galerkin approximation of the equations of motion. The approach is complicated by the tip interconnection, which results in an algebraic constraint by means of a Lagrange multiplier. To address model uncertainties and disturbances the feedforward control is combined with an output error feedback controller realizing a two-degree-of-freedom control (2DOF) concept. Experimental results confirm the applicability of the approach and its tracking performance to achieve rest-to-rest motion.