A Large-Stroke Electrostatic Micro-Actuator
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Parallel-plate electrostatic actuators driven by a voltage difference between two electrodes suffer from an operation range limited to 30% of the gap that has significantly restrained their applications in Microelectromechanical systems (MEMS). In this thesis, the travel range of an electrostatic actuator made of a micro-cantilever beam electrode above a fixed electrode is extended quasi-statically to 90% of the capacitor gap by introducing a voltage regulator (controller) circuit designed for low frequency actuation. The developed large-stroke actuator is valuable contribution to applications in optical filters, optical modulators, digital micro-mirrors and micro-probe based memory disk drives. To implement the low-frequency large-stroke actuator, the beam tip velocity is measured by a vibrometer, the corresponding signal is integrated in the regulator circuit to obtain the displacement feedback, which is used to modify the input voltage of the actuator to reach a target location. The voltage regulator reduces the total voltage, and therefore the electrostatic force, once the beam approaches the fixed electrode so that the balance is maintained between the mechanical restoring force and the electrostatic force that enables the actuator to achieve the desired large stroke. A mathematical model is developed for the actuator based on the mode shapes of the cantilever beam using experimentally identified parameters that yields good accuracy in predicting both the open loop and the closed loop responses. The low-frequency actuator also yields superharmonic resonances that are observed here for the first time in electrostatic actuators. The actuator can also be configured either as a bi-stable actuator using a low-frequency controller or as a chaotic resonator using a high-frequency controller. The high-frequency controller yields large and bounded chaotic attractors for a wide range of excitation magnitudes and frequencies making it suitable for sensor applications. Bifurcation diagrams reveal periodic motions, softening behavior, period doubling cascades, one-well and two-well chaos, superharmonic resonances and a reverse period doubling cascade. To verify the observed chaotic oscillations, Lyapunov exponents are calculated and found to be positive. Furthermore, a chaotic resonator with a quadratic controller is designed that not only requires less voltage, but also produces more robust and larger motions. Another metric of chaos, information entropy, is used to verify the chaotic attractors in this case. It is found that the attractors have a common information entropy of 0.732 independent of the excitation amplitude and frequency.