Stability and perturbation analysis of a one-degree-of-freedom doubly clamped microresonator with delayed velocity feedback control

Abstract

In this paper, a study on a doubly clamped microresonator actuated by two symmetrical electrodes is carried out to investigate its dynamic properties with delayed velocity feedback control. A stability chart of the linearized system depicting delay time versus feedback gain is drawn first, which is actually nonperiodic. Moreover, stability switches do exist in this system. Then, the method of multiple scales is used to determine the existence, stability and dynamic properties of small amplitude vibration in the neighborhood of different equilibrium positions. It is shown that the stability condition via perturbation analysis overestimates the system stable region. The delayed stability condition via linearized analysis is more suitable for stability estimation. The following analytical and numerical results are presented to investigate frequency responses and frequency/damping trimming properties with various system and control parameters. Moreover, explicit formulas for optimum direct current (DC) voltage and equivalent natural frequency, corresponding to an approximate linear-like state, are deduced, respectively. Two typical design sketches depicting the initial gap width versus DC voltage are drawn with different beam lengths and thicknesses. Finally, a case study is carried out to verify the correctness of our analytical results about linear-like state prediction and frequency/damping trimming.