Comment on “A Virtual Sensing Method for Tonal ANVC Systems” [C. M. Tran and S. C. Southward, 2002, J. Dyn. Syst., Meas., Control 124(1), 35–40]

In a paper by Tran and Southward (2002, J. Dyn. Syst., Meas., Control, 124(1), pp. 35–40), a virtual sensing method for tonal active noise and vibration control systems is proposed. The aim of the proposed method is to obtain accurate estimates of the virtual outputs of the dynamic system under consideration. For this purpose, a hybrid adaptive feedforward observer is designed based on an observable state-space representation of the dynamic system. In this paper, it is shown that if the number of physical sensors used in the proposed method is less than the state-space system order, the observer can converge to infinitely many solutions for which the state reconstruction errors are not equal to zero. Since accurate state estimates are required to obtain accurate estimates of the virtual sensor outputs, the suggested hybrid adaptive feedforward observer is only suitable for rejecting nonstationary disturbances at the physical sensor outputs, and not for virtual sensing purposes.