Wafer Stage Modal Model Identification by Modified Vector Fitting Method

Abstract

Vector fitting is modified in this study for the parametric identification of a model with an undamped rigid body mode in the frequency domain. The modal model of a six-degree-of-freedom (6DOF) wafer stage is identified using the modified vector fitting method. The modal model is typically fitted from the matrix fraction description (MFD) form of the transfer function, which increases the cost function. The vector fitting in frequency domain provides an approach to fitting the modal model directly from frequency response functions(FRFs) via a partial rational basis function, the poles of which can be obtained by pole relocation technology. The traditional vector fitting method is not applicable in identifying systems containing rigid body modes. The method is reformulated here and effectively applied for wafer stage identification. The accuracy of the fitted model is validated by control loop simulation.