Model based controller design for the compensation of thermally induced deformations

Abstract

Modern industries demand the production of smaller and yet more complex parts requiring the machine tool itself to fulfill increasing precision standards. Thermal stability is crucial to satisfy the producer’s and the client’s expectations regarding the product’s quality and reliability. Using high-tech materials with very low coefficients of expansion, integrating water cooling or insulation can improve the thermal stability but is not always possible due to geometric constraints. In this paper, a systematic approach is suggested to compensate the thermally induced deformations by controlling a small number of additional cooling elements. The analytic description of the thermal-mechanical behavior is derived from a Finite Element system that allows the modeling of very complex machine geometries. The Balanced Truncation method is then applied to determine a reduced order model that is used for an optimization based feed-forward controller design. It will be shown that this controller not only significantly reduces the deformations but can also be successfully applied to the original high-order model. As perfect knowledge of both the model and the disturbances can rarely be guaranteed, a feedback controller is finally introduced to improve the compensation of thermally induced deformations.