Simulation and feed-forward control of a flexible parallel manipulator

The importance of lightweight constructions are steady increasing since they promise a low energy consumption together with higher movement speeds. However these demand modern, model-based feed-forward control designs. Especially the undesired vibrations due to the reduced overall stiffness of such manipulators have to be taken into account. A convenient way to model the dynamical behavior of systems that perform large, nonlinear motions superposed with small, elastic deformations is the floating frame of reference approach in a flexible multibody system. The application of the Newton-Euler-Formalism together with D'Alembert's principle to parallel manipulators results in a set of differential-algebraic equations. Therefore, the consideration of the trajectory tracking problem with so-called servo constraints appears to be promising. In case of a non-flat system, the arising set of differential-algebraic equations, which consists of the system dynamics, the holonomic loop closing constraint equations and the servo constraints embodies nontrivial dynamics. With an oblique projection, the embedded set of ordinary differential equations describing the internal dynamics can be obtained. The stability properties of these dynamics determines the complexity of the feed-forward control design, as two-point boundary value problems might have to be solved. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)