Speed-energy optimization of electrostatic actuators based on pull-in

The speed and total energy required to accomplish pull-in switching of a generic electrostatic actuator is examined. It is found that the value of the source resistance of the voltage drive used for switching has a profound effect on both switching speed and energy requirements. The source resistance governs the charging time for the actuating capacitor. As long as this time is slower than the time required to accelerate the moving mass to maximum speed in the presence of damping, the total energy required for switching can be dramatically reduced without a significant increase in switching time. Indeed, there exists a clear optimum source-resistance value that minimizes the product of switching time and switching energy. These findings are demonstrated theoretically and then applied to specific examples from the literature. In addition, the limiting case of very large source resistance, essentially a current drive, is evaluated and compared to the voltage-driven case. It is found that for equivalent switching times, the current drive requires less total energy for a switching event.