Parameter optimization for a high-order band-pass continuous-time sigma-delta modulator MEMS gyroscope using a genetic algorithm approach

This paper describes a novel multiobjective parameter optimization method based on a genetic algorithm (GA) for the design of a sixth-order continuous-time, force feedback band-pass sigma-delta modulator (BP-ΣΔM) interface for the sense mode of a MEMS gyroscope. The design procedure starts by deriving a parameterized Simulink model of the BP-ΣΔM gyroscope interface. The system parameters are then optimized by the GA. Consequently, the optimized design is tested for robustness by a Monte Carlo analysis to find a solution that is both optimal and robust. System level simulations result in a signal-to-noise ratio (SNR) larger than 90 dB in a bandwidth of 64 Hz with a 200° s−1 angular rate input signal; the noise floor is about −100 dBV Hz−1/2. The simulations are compared to measured data from a hardware implementation. For zero input rotation with the gyroscope operating at atmospheric pressure, the spectrum of the output bitstream shows an obvious band-pass noise shaping and a deep notch at the gyroscope resonant frequency. The noise floor of measured power spectral density (PSD) of the output bitstream agrees well with simulation of the optimized system level model. The bias stability, rate sensitivity and nonlinearity of the gyroscope controlled by an optimized BP-ΣΔM closed-loop interface are 34.15° h−1, 22.3 mV °−1 s−1, 98 ppm, respectively. This compares to a simple open-loop interface for which the corresponding values are 89° h−1, 14.3 mV °−1 s−1, 7600 ppm, and a nonoptimized BP-ΣΔM closed-loop interface with corresponding values of 60° h−1, 17 mV °−1 s−1, 200 ppm.

[1]  Y. Manoli,et al.  Modulated electro-mechanical continuous-time lowpass sigma-delta-modulator for micromachined gyroscopes , 2011, 2011 16th International Solid-State Sensors, Actuators and Microsystems Conference.

[2]  William Redman-White,et al.  Force feedback linearization for higher-order electromechanical sigma-delta modulators , 2006 .

[3]  F. Ayazi,et al.  High Performance Matched-Mode Tuning Fork Gyroscope , 2006, 19th IEEE International Conference on Micro Electro Mechanical Systems.

[4]  B. Boser,et al.  A monolithic surface micromachined Z-axis gyroscope with digital output , 2000, 2000 Symposium on VLSI Circuits. Digest of Technical Papers (Cat. No.00CH37103).

[5]  F. Ayazi,et al.  A 0.1°/HR bias drift electronically matched tuning fork microgyroscope , 2008, 2008 IEEE 21st International Conference on Micro Electro Mechanical Systems.

[6]  M. Kraft,et al.  High Order Bandpass Sigma Delta Interface for Vibratory Gyroscopes , 2005, IEEE Sensors, 2005..

[7]  T. Akin,et al.  A single-crystal silicon symmetrical and decoupled MEMS gyroscope on an insulating substrate , 2005, Journal of Microelectromechanical Systems.

[8]  K. Najafi,et al.  A HARPSS polysilicon vibrating ring gyroscope , 2001 .

[9]  P. Pelin,et al.  A digitally controlled MEMS gyroscope with 3.2 deg/hr stability , 2005, The 13th International Conference on Solid-State Sensors, Actuators and Microsystems, 2005. Digest of Technical Papers. TRANSDUCERS '05..

[10]  Wouter Olthuis,et al.  A sensitive differential capacitance to voltage converter for sensor applications , 1999, IEEE Trans. Instrum. Meas..

[11]  S. E. Alper,et al.  High-Performance SOI-MEMS Gyroscope with Decoupled Oscillation Modes , 2006, 19th IEEE International Conference on Micro Electro Mechanical Systems.

[12]  Michael Kraft,et al.  A high-performance accelerometer with a fifth-order sigma–delta modulator , 2005 .

[13]  Q. Shen,et al.  Micromachined inertial measurement unit fabricated by a SOI process with selective roughening under structures , 2011 .

[14]  T. Rahkonen,et al.  A fully automated flowgraph analysis tool for Matlab , 2005, Proceedings of the 2005 European Conference on Circuit Theory and Design, 2005..

[15]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[16]  Michael Kraft,et al.  Higher Order Noise-Shaping Filters for High-Performance Micromachined Accelerometers , 2007, IEEE Transactions on Instrumentation and Measurement.

[17]  B.E. Boser,et al.  A fourth-order /spl Sigma//spl Delta/ interface for micromachined inertial sensors , 2004, IEEE Journal of Solid-State Circuits.

[18]  Tayfun Akin,et al.  A low-cost rate-grade nickel microgyroscope , 2006 .

[19]  Yiannos Manoli,et al.  Drive and sense interface for gyroscopes based on bandpass sigma-delta modulators , 2010, Proceedings of 2010 IEEE International Symposium on Circuits and Systems.

[20]  S. E. Alper,et al.  A Compact Angular Rate Sensor System Using a Fully Decoupled Silicon-on-Glass MEMS Gyroscope , 2008, Journal of Microelectromechanical Systems.

[21]  M. Kraft,et al.  A High-Resolution Silicon-on-Glass $Z$ Axis Gyroscope Operating at Atmospheric Pressure , 2010, IEEE Sensors Journal.

[22]  M. Kraft,et al.  Micromachined Vibratory Gyroscopes Controlled by a High-Order Bandpass Sigma-Delta Modulator , 2007, IEEE Sensors Journal.

[23]  Pieter Rombouts,et al.  An Unconstrained Architecture for Systematic Design of Higher Order $\Sigma\Delta$ Force-Feedback Loops , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  P. Rombouts,et al.  A Closed-Loop Digitally Controlled MEMS Gyroscope With Unconstrained Sigma-Delta Force-Feedback , 2009, IEEE Sensors Journal.

[25]  Farrokh Ayazi,et al.  Micromachined inertial sensors , 1998, Proc. IEEE.

[26]  K. Halonen,et al.  Readout Electronics with Bandpass Delta-Sigma A/D Converter for a Bulk Micromachined Capacitive Gyroscope , 2005, 2005 IEEE Instrumentationand Measurement Technology Conference Proceedings.

[27]  Zhenchuan Yang,et al.  MEMS gyroscope control system using a band-pass continuous-time sigma-delta modulator , 2010 .

[28]  Bernhard E. Boser,et al.  17.6 A Fourth-Order Σ∆ Interface for Micromachined Inertial Sensors , 2004 .

[29]  Honglong Chang,et al.  Integrated Behavior Simulation and Verification for a MEMS Vibratory Gyroscope Using Parametric Model Order Reduction , 2010, Journal of Microelectromechanical Systems.

[30]  Michael Kraft,et al.  Genetic Algorithm for the Design of Electro-Mechanical Sigma Delta Modulator MEMS Sensors , 2011, Sensors.

[31]  R. Schreier,et al.  Delta-sigma data converters : theory, design, and simulation , 1997 .

[32]  R.K. Curey,et al.  Proposed IEEE inertial systems terminology standard and other inertial sensor standards , 2004, PLANS 2004. Position Location and Navigation Symposium (IEEE Cat. No.04CH37556).

[33]  Yiannos Manoli,et al.  Excess Loop Delay compensated Electro-Mechanical Bandpass Sigma-Delta Modulator for Gyroscopes , 2009 .

[34]  Tayfun Akin,et al.  A high-performance silicon-on-insulator MEMS gyroscope operating at atmospheric pressure , 2007 .

[35]  Jian Luo,et al.  A new design methodology for electro-mechanical Sigma- Delta-Modulators , 2009, 2009 4th IEEE International Conference on Nano/Micro Engineered and Molecular Systems.