Rejection of time-varying frequency sinusoidal disturbance using refined observer for a class of uncertain systems

The time-varying frequency disturbance rejection problem is addressed for a class of nonlinear uncertain system. A novel refined disturbance observer (RDO) is developed composed of auxiliary observer and calibration observer. At first, the disturbance is redescribed using auxiliary observer after coordinate transformation, which contains a parametric form about frequency and a decay term. The derivative of frequency and system uncertain are absorbed in the decay term, furthermore, the correlation between disturbance frequency and disturbance can be derived. Then the key parameter, i.e. frequency factor is estimated by calibration observer characteristic with two-degree-freedom, the decay term associated with derivative of frequency can be attenuated in feedback control loop. Thus, the composite controller including a refined disturbance observer (RDO) and a robust feedback controller is designed, which inherits the elegant feature of disturbance observer based control (DOBC). The H∞ index performance can be guaranteed to attenuate the estimation error driven by disturbance time-varying frequency together with system uncertainty.