Prescribed-Time State and Extended Disturbance Observer With Application to Active Vibration Isolation Systems

In this article, we present a prescribed-time state and extended disturbance observer with finite time-varying gains (PTFG-SEDO) for normal-form systems experiencing matched unknown disturbances. By extending the traditional prescribed-time state observer with finite time-varying gains (PTFG-SO), simultaneous estimation of states, disturbances, and their derivatives has been achieved. The main motivation of this article is to further improve the state estimation performance of the existing PTFG-SO by complementing it with disturbance estimation and compensation in the proposed PTFG-SEDO. Furthermore, the estimated disturbance information can be utilized in disturbance observer-based control algorithms. The proposed PTFG-SEDO is effectively integrated into an active vibration isolation system, within which a pair of absolute velocity feedback control laws, based on the PTFG-SEDO, are meticulously developed and juxtaposed with their traditional PTFG-SO-based counterparts. The experimental findings reveal that the fast and precise disturbance estimation afforded by the PTFG-SEDO facilitates the efficacious neutralization of the constant components of disturbances. Moreover, the enhanced precision in state estimation is demonstrated to contribute significantly to the refinement of the sinusoidal components of the vibrations.