Identification for Precision Mechatronics: An Auxiliary Model-Based Hierarchical Refined Instrumental Variable Algorithm

When the physical properties of mechanical systems align with the structure of the model, the continuous-time (CT) systems can be effectively represented by an interpretable and parsimonious additive formal models. This article addresses the parameter estimation challenges of additive CT autoregressive moving average (ACTARMA) systems. Based on the maximum likelihood principle, the optimality conditions for the proposed identification algorithms are formulated for ACTARMA systems. Additionally, an auxiliary model-based hierarchical refined instrumental variable (AM-HRIV) iterative algorithm and an AM-HRIV recursive algorithm are developed by means of the hierarchical identification principle and the auxiliary model identification idea. These algorithms establish a pseudo-linear regression relationship involving optimal prefilters derived from a unified autoregressive moving average model. The effectiveness of the proposed methods is demonstrated by numerical simulation, and the performance of AM-HRIV iterative method in identifying modal representations is verified by experimental data.