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A simple noise reduction disturbance observer and Q-filter design for internal stability

The noise reduction disturbance observer is an unconventional construction of disturbance observer which has the ability of attenuating the high frequency measurement noise as well as the low frequency input disturbance. While retaining the same capabilities, this paper explores a more concise and prevailing version of the noise reduction disturbance observer with a more relaxed almost necessary and sufficient condition for the closed-loop system to be internally stable without requiring the stability of the nominal plant. Moreover, the proposed version is reduced-order compared with the classical disturbance observers in the sense that the two low-pass filters, commonly set to be identical, are now distinct and, as a result, one of them can have order less than the relative degree of the nominal plant. All of which are the direct consequence of a simplified configuration, we additionally present a design method for the two distinct low-pass filters to guarantee the internal stability of the system.