Linear Active Disturbance Rejection Control for Two-Mass Systems Via Singular Perturbation Approach

This article presents a linear active disturbance rejection control (LADRC) scheme for two-mass systems (TMSs) based on a singular perturbation (SP) approach. In the proposed scheme, the dynamics of TMSs are separated into a quasi-steady-state system at a slow time scale and a boundary-layer system at a fast time scale via the SP method. The quasi-steady-state model is used as the nominal model to design the LADRC, where internal model control (IMC) rules are employed for prescribed tracking performance. This not only reduces the model order but also makes the gain tuning straightforward, which is crucial for practical use. Based on the boundary-layer model, the active damping method is designed for vibration suppression, which aims at achieving a higher stable bandwidth of the IMC to better attenuate the residual disturbance of linear extended state observer such that the tracking accuracy can be improved. Stability of the full system was analyzed via the extended Tikhonov's theorem. Comparative experiments were carried out to verify the effectiveness of the proposed scheme.