Design and Implementation of an Optimized Double Closed-Loop Control System for MEMS Vibratory Gyroscope

Abstract

This paper describes the development and experimental evaluation of a microelectromechanical system vibratory gyroscope using an optimized double closed-loop control strategy. An automatic gain control self-oscillation interface is used to resonate the gyroscope in the drive mode; the sense mode is controlled by a sixth-order continuous-time and force-feedback band-pass sigma-delta modulator. The parameters of both control loops are optimized by a genetic algorithm (GA). System level simulations show that the settling time of the drive mode self-oscillation is 125 ms, the root mean square displacement of the proof mass is in the sense mode, and the signal-to-noise ratio is 90 dB in a bandwidth of 64 Hz with a 200 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> /s angular rate input signal. The system is implemented using symmetrical and fully decoupled silicon on insulator gyroscope operating at atmospheric with the circuit implemented on printed circuit board. The measured power spectral density of the output bitstream shows an obvious band-pass noise shaping and a deep notch at the gyroscope resonant frequency. The measured noise floor is approximately -120 dBV/Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> . In the drive mode, the relative drift of the resonant frequency and amplitude is 3.2 and 10.7 ppm for 1 h measurements, respectively. The settling time, scale factor, zero bias stability, and bandwidth of the gyroscope controlled by the optimized control system are 200 ms, 22.5 mV/ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> /s, 34 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> /h, and 110 Hz, respectively. This is compared with a non-optimized system for which the corresponding values are 300 ms, 17.3 mV/ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> /s, 58 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> /h, and 98 Hz; hence, by GA optimization a considerable performance improvement is achieved.