On relationship between time-domain and frequency-domain disturbance observers and its applications

This paper provides a generic analysis of the relationship between time/frequency-domain DOB design methodology. It is discovered that the traditional frequency-domain DOBs using a low pass filter with unity gain can only handle disturbances satisfying matching condition, while the traditional time-domain DOBs always generate an observer with a high order. A Functional Disturbance OBserver (FDOB) is proposed to improve the existing results together with its design guideline, frequency analysis and existence condition. Compared with the existing frequency-domain DOBs, the proposed FDOB can handle more classes of disturbances, while compared with the existing time-domain DOBs the proposed FDOB can generate an observer with a lower order. Numerical examples are presented to illustrate the main findings of this paper including a rotary mechanical system of nonminimum phase.