Abstract
This paper presents a study of the effect of a time-delay feedback controller on the dynamics of a Microelectromechanical systems (MEMS) capacitor actuated by DC and AC voltages. It is shown that negative time-delay feedback control gain can lead to an unstable system, even if AC voltage is relatively small compared to DC voltage. Perturbation method is utilized to present analytically the nonlinear dynamic characteristics of the MEMS capacitor. Agreements among the results of a shooting technique, long-time integration, basin of attraction analysis with the perturbation method are achieved.
Highlights
Delay in MEMS devices is a very common phenomenon, which can be introduced into the system unavoidably or by design
This paper presents a study of the effect of a time-delay feedback controller on the dynamics of a Microelectromechanical systems (MEMS) capacitor actuated by DC and AC voltages
It is shown that negative time-delay feedback control gain can lead to an unstable system, even if AC voltage is relatively small compared to DC voltage
Summary
Delay in MEMS devices is a very common phenomenon, which can be introduced into the system unavoidably or by design. Wang & Hu [2] applied several singular perturbation methods, such as methods of multiple scales and averaging, to model a controlled Duffing oscillator with delayed velocity feedback. They applied other methods including the Lyapunov function for stability combined with averaging, the energy analysis, and pseudo-oscillator analysis [3]. Alsaleem and Younis [5] investigated theoretically the dynamics of MEMS resonators using shooting technique and basin of attraction analysis and verified their results experimentally. We use a single-freedom model to investigate the dynamics of electrostatic MEMS resonators with the delayed feedback controller of [1]. The results are verified using long-time integration, shooting techniques, and basin of attraction analysis
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