Force Rebalance Controller Synthesis for a Micromachined Vibratory Gyroscope Based on Sensitivity Margin Specifications

Abstract

This paper presents a design method of force rebalance control for the sense mode of a micromachined vibratory gyroscope with multiobjective. The control strategy is mainly based on constraining sensitivity margin specifications via numerical optimization approach, which embeds the sense mode in a closed-loop system to possess more robust performance. This paper also provides a quantitative methodology of configuring the system parameters to realize the functional electrostatic force feedback control for the microgyroscope in the case of nonideal coupling and external angular disturbance. Theoretical results predicted by the control loop are shown to be in close agreement with the experimental results using a practical microgyroscope, which indicated a satisfactory performance of the proposed control algorithm. The maximums of the sensitivity function and complementary sensitivity function are measured to be 4.5 and 1 dB, resulting in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GM</i> ≥ 7.84 dB and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PM</i> ≥ 35°. The gyroscope achieves a scale factor of 7.1 mV/deg/s with nonlinearity of 0.2% which is improved by one order of magnitude compared with that of the open loop. The bandwidth is extended to about 98 Hz from 30 Hz in the open loop. The quadrature error and temperature stability of the scale factor are reduced from - 10.33 to -59.22 dB and from 4858 to 646 ppm/ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> C with the force rebalance control, respectively.