Project Description

Figure 1: Flexible multibody system with kinematic loop.

With growing demands on energy efficiency and high movement speeds light-weight machine tools and manipulators become more and more important. This results in a tremendous decrease of the overall stiffness of such machine tools. In order to compensate for the arising deformations, modern, model-based control methods have to be applied. Especially feed-forward control methods like exact model inversion promise best possible system responses without affecting the stability properties of the system. Together with simple feedback control methods, high-precision trajectory tracking and set point changes can be realised.

This concept requires a preferably precise model of the machine tool. Due to the large working motion, which is superposed by elastic deformations, it seems likely to model such machines as a flexible multibody systems. This extension of the classical multibody system allows the consideration of elastic bodies which undergo a large, nonlinear motion.

In this project focuses on modeling and control design of flexible multibody systems with environmental contact. In the first instance, the integration of flexible machine parts into the multibody system is supposed to be investigated. The usage of finite element models, which have a huge amount of degrees of freedom, is neither feasible nor desirable. In order to keep the complexity on a low lewel, the FE models are transformed via modern model reduction techniques into models with a significantly smaller number of degrees of freedom. Therfore, the choice of the used shape functions has a wide influence on the approximation quality and on the computational time of the overall system. The floating frame of reference approach is used to include these reduced bodies in the flexible multibody system.

These models allow model-based feed-forward control designs, which offer the possibility to realize trajectory tracking. A closer attention is payed to exact model inversion. Exact model inversion implies in this context, that all dynamical effects of the model are taken into account. Therefore, the model undergoes a nonlinear coordinate transformation leading to the so-called Input-Output-Normal form, which, in case of a nonflat system, consists of a set of differentiators, an algebraic part and the so-called internal dynamics. Depending on the stability of the internal dynamics, the according feed-forward control can be computed.

Related Pages

• Flexible Multibody Systems
• Multibody Systems

Contact

• Prof. Dr.-Ing. Prof. E.h. Peter Eberhard
• Fatemeh Ansarieshlaghi, M.Sc.