Computation of a compact state space model for an adaptive spindle head configuration with piezo actuators using balanced truncation

Finite Element models of machine tools or their building blocks are usually very large and thus do not allow for fast simulation or application in controller design. Especially when algebraic constraints come into play the models become differential algebraic equations and therefore are even more difficult to handle in the application. In this contribution we propose a method based on modern system theoretic model order reduction algorithms that allows to generate a first order standard state space reduced order model for a structural model of an adaptive spindle support (ASS) that is of second order index 1 differential algebraic form due to the piezo actuation applied. The accuracy of the method is demonstrated by a numerical frequency domain error analysis