| In this work we consider sensing strategies using dynamic bifurcations in MEMS resonators. We examine the statistics of jump events that occur as a result of a linear parameter sweep through a subcritical pitchfork bifurcation in a parametrically driven MEMS resonator in the presence of noise. The statistics of jump events are compared to those derived from a simple one-dimensional model and are found to have good agreement. Issues related to how system and input parameters affect these statistics are described, and sweeping strategies that lead to precise, fast estimates of the bifurcation point, as essential for these sensors, are derived. It is shown that for a typical MEMS resonator an optimal sweep rate exists, and noise may need to be added to achieve optimal sensitivity.;Next, we report the development and implementation of a new method for tracking parameters at which dynamic bifurcations occur in MEMS. The underlying theory is developed for subcritical pitchfork bifurcations that occur near the subharmonic instability experienced near parametric resonance. The method relies on observed changes in response phase and amplitude just prior to the bifurcation, and these are used to forebode the bifurcation. These precursors are then employed in a feedback control scheme to stabilize a parametrically excited MEMS device at the edge of instability, making it highly sensitive to changes in device parameters. Implementation of the controller is shown through experimental validation. A comparison with the previous method of bifurcation detection for the same device shows that the new approach offers an improvement of over three orders of magnitude for the bifurcation point acquisition rate.;Finally, feedback control based only on the root mean square of the amplitude is utilized to stabilize a device on the "edge" of instability. By using the root mean square of the amplitude, the complexity of electronics is reduced and the proposed technique is extended to a MEMS clamped clamped beam with a natural frequency near 100kHz. Sensitivity to these device parameters is explored and initial results show sensitivity of 50 ppm while vibration amplitudes are maintained near the noise floor. |
