[en] Mechatronics deals with the integrated design of a mechanical system and its control system. Moreover, a large number of mechatronic systems may have their natural frequencies and mode shapes dependent on their spatial configuration, which inevitably affects the performance and the stability of the control system. In particular, mechatronic systems, such as machine tools and pick-and-place robots, can be classified as systems with configuration-dependent dynamics, since the relative motion between their flexible components can lead to time-varying boundary conditions. A parametric model able to capture this behavior is proposed using finite element based flexible multibody method. A global modal parameterization is applied for model-order reduction. A linear parameter varying model is derived from these reduced models and can be used in a control design scheme.
This methodology is applied to a pick-and-place assembly robot with a gripper carried by a flexible beam (Fig. 1a). Vibrations, which depend on the beam length, decrease the throughput of the machine (Fig. 1b). Linear time invariant and linear parameter varying control strategies are evaluated using the derived linear parameter varying model.
