Disturbance Rejection-Guarded Learning for Vibration Suppression of Two-Inertia Systems

TL;DR

The paper tackles disturbances in vibration suppression for multi-inertia systems by embedding a learning-enabled disturbance rejection framework within an Extended State Observer (ESO). It introduces three ESO variants—model-free (MF-ESO), model-based (MB-ESO), and a Learning-Enabled ESO (L-ESO) that combines online regression for feedforward disturbance estimation with ESO-based feedback correction, producing a total disturbance estimate $\hat{f}=\hat{f}_L+\Delta\hat{f}$. Through simulations on a two-mass-spring benchmark and hardware tests on a torsional two-mass plant, L-ESO demonstrates superior disturbance rejection and tracking performance, achieving robust control with lower bandwidth requirements than MF-ESO, and matching or exceeding MB-ESO when learning is effective. The approach is modular and real-time capable, offering a practical disturbance-rejection enhancement for vibration suppression in complex, uncertain systems, with potential applicability to broader robotic and mechatronic platforms.

Abstract

Model uncertainty presents significant challenges in vibration suppression of multi-inertia systems, as these systems often rely on inaccurate nominal mathematical models due to system identification errors or unmodeled dynamics. An observer, such as an extended state observer (ESO), can estimate the discrepancy between the inaccurate nominal model and the true model, thus improving control performance via disturbance rejection. The conventional observer design is memoryless in the sense that once its estimated disturbance is obtained and sent to the controller, the datum is discarded. In this research, we propose a seamless integration of ESO and machine learning. On one hand, the machine learning model attempts to model the disturbance. With the assistance of prior information about the disturbance, the observer is expected to achieve faster convergence in disturbance estimation. On the other hand, machine learning benefits from an additional assurance layer provided by the ESO, as any imperfections in the machine learning model can be compensated for by the ESO. We validated the effectiveness of this novel learning-for-control paradigm through simulation and physical tests on two-inertial motion control systems used for vibration studies.

Figures (7)

• Figure 1: The proposed framework in this paper, where the red and the blue blocks represent the L-ESO and the disturbance rejection tracking controller, respectively. Once the total disturbance is estimated, the tracking controller will be able to reject disturbance.
• Figure 2: Two-mass-spring system with uncertain parameters
• Figure 3: Tracking performance for MB-ESO, MF-ESO, L-ESO plotting from 120s.
• Figure 4: Control signal for MB-ESO, MF-ESO, L-ESO plotting from 120s.
• Figure 5: ECP Model 205 torsional testbed

Theorems & Definitions (5)

• Remark 1
• Theorem 1
• Remark 2
• Remark 3
• Remark 4