Amplitude control of parametric resonances for mass sensing

A new approach for real-time vapor mass sensing at atmospheric pressure by tracking frequency shifts of parametrically excited fixed-fixed micro-beams is presented. A robust control designed with the Glover-McFarlane H∞ loop-shaping procedure is implemented on a field-programmable gate array (FPGA). Constant amplitude is maintained on the stable branch of the super-critical pitchfork bifurcation inside the Arnold tongue. Previous work has utilized sweep-based and phase noise-based methods to track frequency shifts. The new method actively controls the constant amplitude at a high gradient on the stable branch to achieve faster acquisition and higher sensitivity. Experimental results show the capability of the amplitude control method for mass sensing applications. System parameters are identified from curve fitting, good agreement between dynamical modeling and experimental results is achieved. The acquisition rate using amplitude control tracking is improved by four to five orders of magnitude when compared with sweep-based bifurcation tracking. This novel approach enables microsecond frequency tracking and femtogram mass sensitivity. Higher mass sensitivity is deemed possible utilizing amplitude control on MHz devices.