Mass sensing using a virtual cantilever virtually coupled with a real cantilever

Abstract

Mass measurements based on the eigenmode shift of coupled cantilevers provide much higher sensitivity than the method based on the natural frequency shift of a single cantilever. The essence of the former method is that the two cantilevers are identical and are weakly coupled. However, in practical coupled cantilevers, these requirements cannot be satisfied completely because of the limitations of machining accuracy. To realize the advantages of this method fully, we propose the concepts of a “virtual cantilever” and “virtual coupling.” In the proposed method, one of the real cantilevers is replaced with a virtual cantilever that is virtually coupled with the remaining real cantilever. The virtual cantilever dynamics and the effect of coupling on the real cantilever are thus calculated in real-time using a digital computer, and the real cantilever is also actuated in real-time based on the coupling effect obtained. By adjusting the virtual cantilever's physical parameters to match those of the real cantilever while tuning the virtual coupling stiffness to be low in the digital scheme, identical real and virtual cantilevers and the weak coupling required can be realized. Additionally, to produce self-excitation with a steady-state amplitude, we apply the linear and nonlinear velocity feedback control technique that was proposed in our previous study for the above system. We confirm the validity of the virtual cantilever and virtual coupling concepts proposed for mass sensing experimentally using a real single macrocantilever and a virtual cantilever virtually coupled with the real cantilever as a prototype.