Active control of effective mass, damping and stiffness of MEMS

We propose the active control of effective stiffness, damping, and mass of MEMS by applying feedback forces that are proportional to displacement, velocity, and acceleration of its proof mass. Such control in performance is important due to the systemic variation in performance caused by process variations, packaging stresses, thermal drift, energy losses, and noise sources. Prior efforts by others have used feedback forces based on position or velocity to modify bandwidth, frequency, quality factor, and the sensitivity of resonators. What is different about our study is that it explores comprehensive control over the effective mass, damping, and stiffness simultaneously. Electrical emulations of mass, damping, and stiffness may be positive or negative, and they can be larger than their purely mechanical counterparts. We provide an analytical derivation for steady-state analysis numerical results for transient analysis. Our steady-state analysis includes signal delay, and transient simulations include both delay and noise. We find that changes in effective mass and stiffness can be increased by an order of magnitude, and damping can be increased by three orders of magnitude.