Using model order reduction for disturbance feed forward control based on transient thermal finite element models

Abstract

Today's developments in production processes lead towards higher and higher precision requirements and demand an improved stability of the machine towards thermally induced errors. Often, an analytical description of the thermal behavior is impossible due to complex geometries and the Finite Element Method (FEM) is applied to simulate the system numerically, e.g. in ANSYS. The FEM formulation leads to very large sparse matrices that allow for the analysis of the system but can not be used for the design of methods to compensate the analyzed errors. In this paper, methods on modeling and model order reduction (MOR) are applied in combination with a feed forward controller to an exemplary transient thermal system. The Balanced Truncation (BT) method is used to significantly reduce the original system order and still conserving the most significant behavior. Based on the reduced system a disturbance feed forward controller is designed and successfully applied to the full-size model in order to compensate the known heat sources.