Nonlinear Robust Adaptive Multi-Modal Vibration Control of Bi-Electrode Micro-Switch with Constraints on the Input.

Micro functionally graded material (FGM) structures are able to have proper functions in vast environments. In this paper, nonlinear governing equations of the size-dependent micro-switch are derived using modified couple stress theory. Effective external forces including fringing field of electrostatic force and Casimir force are considered. Two electrodes cooperate to track the in-plane motions of the micro continuous system by tuning the supply voltages of the electrostatic force. An adaptive projection law is proposed to compensate for the effect of error in the initial estimates of system parameters. To achieve more reliability, a robust active vibration strategy is presented to withstand external disturbances. At any time, just one electrode is operational, and optimization is performed to decrease the controller gains. The highly nonlinear inputs have a singularity in the dynamics of the system, which are known as pull-in instability, so for safety, the controller gains are chosen such that the pull-in voltage is avoided. The dynamic response of the system is simulated using a single mode or multiple modes to validate the effectiveness of the presented vibration control approaches. The effects of error of the initial estimate of system parameters, the effect of impulse and the influences of various volume fractions are studied.