Experimental modeling of hysteresis in stage systems: A Maxwell–Iwan approach

Dynamic links of high-precision stage systems consist of wires and hoses that are used for example to transport electrical current to the actuators and sensors or cooling liquids to the stages. During stage motion, these dynamic links typically express complex hysteretic behavior due to internal friction and viscoelastic properties. As such, dynamic links give rise to unwanted disturbances acting on the high-precision stage systems. This paper presents a simple but accurate physics-based and experimental modeling procedure. The generalized Maxwell model and a modification of the Iwan model are combined in parallel to capture both frequency dependencies by viscoelastic effects and amplitude dependencies by friction-based effects. The modified and physically meaningful Iwan model is shown to be equivalent to the well-known Bouc–Wen model. A so-called normalized dissipation factor is introduced to quickly recognize frequency and/or amplitude dependent behavior using measured data. Using this information, a well-founded choice for an (initial) model structure to be identified can be made. Subsequently, an identification procedure is proposed to estimate values of the model parameters again using the measured data. A simulated experiment is used to show the use of the normalized dissipation factor and validate the identification procedure. Finally, the validity and usefulness of the Maxwell–Iwan modeling approach is demonstrated by experimental results obtained from an industrial wafer stage system.