Black-box modeling of an ultra-precision positioning system using time series analysis

It is important to construct a precise model for the ultra-precision positioning system before designing the controller. Based on the step response of the system, first the experimental data is preprocessed, such as creating a uniform sampling rate by using interpolation, removing the noise with wavelet decomposition and deconstruction; then, the experimental data is divided into two parts: the transient part and the steady-state part, and the model is identified using time series analysis in both parts. An auto-regressive with exogenous (ARX) model is constructed and validated by analyzing the residuals in the transient part. In the steady-state part, the trend of an exponential form and a triangle form is removed from the data, and then an AR model is constructed for the residuals. The conclusion is drawn that the ARX model corresponds with the original model well and some nonlinearity exists in the system.