  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.
