A Generalized Observer for Estimating Fast–Varying Disturbances

In this paper, a generalized disturbance observer (GDO) is proposed for estimating a broad range of disturbances including fast-varying ones. The estimation error of the proposed GDO is proven to be ultimately bounded provided that an arbitrary
$r^{\mathrm {th}}$
time derivative of disturbance is bounded. A broader range of disturbances can be estimated by the proposed GDO in comparison with the conventional disturbance observers (DO) or even recent fast-varying disturbance observers (FVDO) because conservative assumptions such as zero time-derivatives of disturbances are avoided. Furthermore, intuitive rules for gain-tuning and selecting the weighting matrices in the observer design are systematically presented. To validate the superiority of the proposed GDO to conventional FVDOs, comprehensive studies using the linear and nonlinear systems with different types of disturbances are conducted in the MATLAB/Simulink platform. In a specific application of wind energy conversion systems, the proposed GDO is employed to precisely estimate the aerodynamic torque. Then, a completed control system with a linear quadratic regulator (LQR) is designed and implemented to verify the final performance with the proposed GDO. The proposed observer-based LQR is proved to ultimately be bounded stable with superior performances to further validate the proposed GDO.