Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback

Area of Science:

• Nonlinear Dynamics
• Microelectromechanical Systems (MEMS)

Background:

• MEMS actuators with flexible beams and shuttle masses exhibit complex nonlinear behaviors.
• Time-delay feedback is a potential control strategy for these systems.

Purpose of the Study:

• Investigate nonlinear jumping and bifurcation conditions in electrostatically-driven MEMS actuators.
• Analyze the impact of time-delay feedback on system stability and dynamics.

Main Methods:

• Derivation of partial differential equations for a comb-driven MEMS actuator.
• Application of the method of multiple scales to obtain a slow flow.
• Stability and bifurcation analysis, including Hopf and saddle-node bifurcations.

Main Results:

• Time-delay feedback improves resonance frequency and system stability.
• The Hopf bifurcation discriminant is derived, allowing for stable branches.
• Theoretical expressions for parameter space and monostable vibration amplitude are deduced.

Conclusions:

• Time-delay feedback offers enhanced control over MEMS actuator dynamics.
• Stable operation and predictable vibration amplitudes can be achieved through appropriate time-delay control.
• The disappearance of global bifurcation points leads to monostable vibration, crucial for device design.