Amplitude control of self-excited weakly coupled cantilevers for mass sensing using nonlinear velocity feedback control

Abstract

Self-excited weakly coupled resonators are an effective way to measure a small biochemical mass in a liquid environment because such resonators can compensate for the viscosity of a measurement environment and have higher sensitivity than previous methods. Self-excitation causes the mode to change from linear to nonlinear dynamics accompanied by larger amplitudes. To prevent this deviation, an amplitude control method using the nonlinearity present in the systems is proposed for various systems. The amplitude control method for self-excited weakly coupled cantilevers has been used experimentally, but its theoretical validity has not been investigated. In the present study, we propose a nonlinear feedback method to control the amplitudes of self-excited weakly coupled cantilevers. Nontrivial steady-state amplitude control is achieved in the first mode. The relationship between the nonlinear feedback gain and the amplitudes is revealed. The validity of the proposed method is confirmed by conducting an amplitude control experiment using weakly coupled microcantilevers. These results raise the possibility of small-mass sensing using self-excited weakly coupled cantilevers in highly viscous environments.