Adaptive Control Strategies for MEMS Gyroscopes

This dissertation presents adaptive control strategies for MEMS z-axis gyroscopes. Specifically, a unified methodology is proposed for designing and analyzing the performance of control algorithms that can identify and, in an adaptive fashion, compensate for most fabrication defects and perturbations affecting the behavior of a MEMS z-axis gyroscope.
Dynamic analysis of typical MEMS gyroscopes shows that fabrication imperfections are a major factor limiting the performance of the gyroscope. Thus, the main purpose of gyroscope control should be to null out these imperfections and cross-couplings effectively during the operation of the gyroscope. However, the motion of a conventional mode-matched z-axis gyroscope does not have sufficient persistence of excitation and, as a result, all major fabrication imperfections cannot be identified and compensated for in an on-line fashion. Moreover, some types of fabrication imperfections, which can be modeled as cross-damping terms, produce inherent zero-rate output (ZRO).
An off-line self-calibration scheme is proposed in this dissertation for estimating fabrication defects and enhance the performance of a gyroscope operating in open-loop mode. This scheme can be implemented during the initial calibration stage when the gyroscope is turned on, or at regular calibration sessions, which may be performed periodically. An adaptive add-on control scheme is also proposed for a closed-loop mode of operation. This scheme is realized by adding an outer loop to a conventional force-balancing system which includes a parameter estimation algorithm. This parameter adaptation algorithm estimates the angular rate, identifies and compensates the quadrature error, and may permit on-line automatic mode tuning.
An analysis technique for identifying z-axis gyroscope operating conditions, which permit the on-line compensation of fabrication imperfections and self-calibration, was developed. It showed that the motion of a mode-unmatched gyroscope, in which the resonance frequency of the x-axis is different from that of the y-axis, has sufficient persistence of excitation to permit the identification of all major fabrication imperfections as well as "input" angular rate. Based on this analysis, new operation strategies were formulated for MEMS gyroscopes with two un-matched oscillatory modes. A new adaptive control algorithm with velocity estimation was developed, which operates with only measurements of the x and y positions of the proof mass. The parameter adaptation algorithm (PAA) in the adaptive controller simultaneously estimates the component of the angular velocity vector, which is orthogonal to the plane of oscillation of the gyroscope (the z-axis) and the linear damping and stiffness model coefficients. A discrete time version of the observer based adaptive control system, which can be readily implemented using digital processors, was also developed.
The convergence and resolution analysis presented in this dissertation showed that the proposed adaptive controlled scheme offers several advantages over conventional modes of operation. These advantages include a larger operational bandwidth, absence of zero-rate output, self-calibration and a large robustness to parameter variations, which are caused by fabrication defects and ambient conditions.  A simulation study using the preliminary design data of the MIT-SOI MEMS gyroscope was conducted, to test the analytical results derived in this dissertation and to verify the predicted performance of the different proposed controlled schemes. Simulation results were in strong agreement with the analytically derived predicted results and performance estimates.
Sungsu Park
Roberto Horowitz
Publication date: 
December 31, 2000
Publication type: 
Ph.D. Dissertation
Park, S. (2000). Adaptive Control Strategies for MEMS Gyroscopes. United States: University of California, Berkeley.

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