Artificial Nonlinear Stiffness and Artificial Vacuum for Wide-Bandwidth High-Q Resonance Behavior

Abstract

This dissertation explores the use of electrostatic force feedback to generate artificial performance characteristics in a microdevice that would otherwise not be possible. As a test case, a non-vacuumed microresonator that is limited to small-amplitude linear-spring displacements and subject to thermal drift is transformed by electrostatic force feedback to behave as if it were in a vacuum and subject to highly nonlinear spring displacements that are insensitive to thermal drift. Thermal drift is the most significant challenge faced by microscale vibratory gyroscopes. A real-time performance-control technology is presented for correcting or manipulating the performance of microelectromechanical systems (MEMS) devices that are subject to process variations, temperature fluctuations, packaging stresses, or limited by manufacturing materials or geometry. This is done by using electrostatic force feedback to artificially increase or decrease the effective mass, damping, or stiffness of the MEMS device. When subject to identical excitations, process variations in the fabrication of MEMS devices cause two identically designed MEMS devices to perform differently, such as having different resonance frequencies. A shift in resonance frequency due to a variation in temperature will cause a frequency mismatch between the electrically driven excitation frequency and structural resonance frequency. This variation in temperature results in small changes in geometry, material properties, and packaging stress, causing significant drift in sensor reading from the MEMS device. For instance, readings of a three-axis vibratory MEMS gyroscope resting on a stationary table will drift by incorrectly sensing motion in the stationary table. Efforts by others to reduce drift sensitivity include using temperature-dependent drive frequency to match the drift of structural resonance frequency, creating structural designs that are less iii sensitive to temperature variations, encapsulating the MEMS in a thermal reservoir to maintain a constant temperature, etc. Applying our real-time performance-control technology to our test case, we address the abovementioned problems as follows. To ensure all identically fabricated devices can achieve identical resonance frequencies, the devices are structurally designed to have a resonance frequency that is below the desired resonance frequency. Two electrostatic force feedbacks are applied to each device. The first feedback (proportional to negative velocity) greatly narrows the bandwidth and increases the resonance amplitude, i.e. an artificial vacuum for a high-quality factor. The second feedback (proportional to cubed displacement) bends the amplitude response curve over the desired resonance frequency; i.e. an artificial nonlinear stiffness for wide bandwidth within 3dB of the preferred amplitude. Ultimately, this enables all devices to resonate precisely at the applied electronic excitation frequency and be insensitive to the process variations and thermal drift that would have overwise affected their structural resonance frequencies. This real-time performance-control technology is called performance-on-demand MEMS, or PODMEMS. Our analytical and simulation results show that the effective stiffness, quality factor, and nonlinearity of the device can be easily tuned by just changing the gain of the feedback circuit. While applying these technologies to the application of a low-cost MEMS gyroscope, the result shows that for a temperature variation of 80oC, the output amplitude of the gyro is only attenuated by 0.4dB, which is 94.4dB smaller than the gyro without the feedback control