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A mechanism consisting of a horizontally moving cart that carries an erected flexible beam with a point mass -as occurring in placement machines or stacker cranes -is considered. An explicitly parametrized feed-forward control law is designed using a flatness-based approach. Nominally, this control law allows one to perform fast placement motions although avoiding residual oscillations at the arrival. The efficiency of this approach and sensitivity with respect to parametric uncertainties are investigated numerically using both finite element and finite difference models. An experimental set-up is presented and some experimental results demonstrate the usefulness of the approach.

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Today increasing the speed of moving machines with the same or even better precision can often only be realized if flexibilities are taken into account. In order to avoid a stiffer and therefore heavier structure, the flexibility must be considered in the control design. Numerical optimization approaches as well as an analytical feed forward control for linearly actuated robots like placement machines or stacker cranes are presented. These methods help to reduce the time required for positioning in dynamic automation scenarios where the structure's elasticity is essential for achieving high positioning precision in a minimum of time. Backlash in the gear limits standard closed loop active damping controller's capabilities in respect to the achievable damping constant. Therefore, feedforward trajectories avoiding residual vibrations are desirable to reduce the positioning time to a structural given limit.Key words: flatnessbased trajectory planning, distributed parameter system, elastic robot, residual vibrations, numerical optimization Schlüsselworte: flachheitsbasierte Trajektorienplanung, verteilt parametrisches System, elastischer Roboter, Nachschwingungen, numerische Optimierung MotivationStructural flexibilities in systems like placing machines, x-y plotters and stacker cranes, can often be well modelled using the EULER-BERNOULLI beam assumptions [5]. For achieving high performance positioning both a well planned feedforward trajectory and a well designed controller for active damping are required. Thus, the overall performance of the device can be increased without the essential need for more sensors or high computation power. In order to design appropriate trajectories, a flatness based algorithm is proposed within the presented work. Today, this closed analytic planning approach is limited to scenarios with a non moving payload. Therefore two different actuator parametrizations are proposed and subjected to a numerical optimization for trajectory generation. A multi-body simulation is established as reference model and to perform numeric optimizations of the control design.