Optimal Real-Time Control of Flexible Rack Feeders Using the Method of Integrodifferential Relations

Rack feeders are of high practical importance as automated conveying systems. In this paper, control-oriented models are derived for an experimental setup representing the structure of a typical high bay rack feeder. On the basis of these models, feedforward control strategies are designed. The rack feeder is a viscoelastic structure consisting of two identical flexible beams which are attached to a horizontally movable carriage. The beams are rigidly connected at their tip by a pulley block which is necessary for the vertical positioning of a payload. To develop a real-time applicable control algorithm, a frequency analysis is performed for the original double-beam structure. As a consequence, a simplified Bernoulli beam model is derived with specific boundary conditions. The control objective under consideration is the positioning of the flexible beam structure at a desired position in such a way that the terminal mechanical energy stored in the beam is minimized. A modification of the Galerkin method which is based on an integrodifferential approach and a suitable finite element technique are employed to describe the viscoelastic structural vibrations and to design optimal control strategies. Results of numerical simulations are presented and compared with measured data.