Model parameter identification for CNC machine tool feed drive using robust recursive least squares with non-temporal adaptive weight filter

Abstract

The identification result of system model parameters determines the model accuracy and its applications, such as dynamic system prediction and task performance improvement. The recursive least squares (RLS) methods are widely used for online identification because of the low computational load and high performance. However, the conventional RLS-based algorithms have limitations in improving the identification of time-invariant parameters by adjusting parameter update size, since it is challenging to make the measured system data non-temporally weighted. In addition, the user-defined factors significantly affect the identification accuracy. This requires an additional process for selecting optimal factors, leading to decreased identification efficiency. To address these limitations, this study proposes a non-temporally weighted RLS algorithm that improves the identification of time-invariant parameters with an adaptive weight filter based on the Lyapunov stability theory. The proposed algorithm is derived from a generalized parametric decoupled cost function, which allows applying multiple variable weights while making the measured system data non-temporally weighted throughout the identification process. To compute optimal weights at each step, a weight determination rule is derived from the Lyapunov stability theory, guaranteeing the identification stability. The effect of user-defined factors on the identification is eliminated by the Lyapunov stability theory-based adaptive weight filter and the property that the proposed algorithm updates parameters considering both weights and the parameter identification error at each step. The validation against conventional algorithms using simulation of feed drive model parameter identification and experiment using a commercial CNC machine tool confirms that the proposed method improves the online model parameter identification with high robustness against the user-defined factor and high identification accuracy.