Innovative Control Systems for MEMS Inertial Sensors Michael Kraft Reuben Wilcock Bader Almutairi Fang Chen Pejwaak Salimi

Background and Context Accelerometer Control Systems High Order Single Loop SDM MASH SDM Control System Genetic Algorithm Design Gyroscope Control System Bandpass SDM Quadrature Cancellation SDM Conclusions

2nd order Electro-mechanical sigma-delta modulator (EMSDM) Sensing element acts as loop filter First reported by W. Henrion, et al Advantages: direct digital output (→ “smart sensors”), closed loop control, small displacements reduced non-linearity Pick- off V out Digital bitstream V f V f C(z)S/H Comp- arator 0 1 f s Compen- sator

Fully integrated chip, sampling frequency 500kHz Lemkin, M.A. Micro accelerometer design with digital feedback control. University of California, Berkeley, Ph.D. dissertation, 1997.

Sense mode embedded in a 2nd order EM  Coriolis force nulled with electrostatic feedback Problem: Bandwidth of  up to resonance frequency of gyro Ref: Xuesong, J., Seeger, J.I., Kraft, M., and Boser, B.E. A Monolithic surface micromachined Z-axis gyroscope with digital output. To be published at the Symposium on VLSI Circuits, Hawaii, USA, June 2000.

Disadvantages: Only 2nd order noise shaping Tones, deadzones, high oversampling ratio required, etc Loop dynamics rely exclusively on the sensing element High dependency on fabrication tolerances 2 nd order measurement results with zero acceleration input Tones

ParameterValue Sensitivity4.56 pF/g Natural Frequency237 Hz Overall device size7x9x0.6 mm 3 Mass of proof mass1.86 mg Proof mass area4 x 7 mm 2 Min. Feature size6 um

Applications in platform stability and tilt measurements Structural Health Monitoring Oil and Gas exploration Noise floor below under 800nG/√Hz High sensitivity 5pF/G Strategic Partnership with Mir Enterprises for commercialization

Fabrication:  60um SOI etched with DRIE  Separation of the Chips without sawing  Allows arbitrary large under-etched and freestanding areas → very large proof mass  Oxide layer etching with HF Vapour Phase Etching

Sensing Element Electronic Filter Electrostatic Force Conversation 1 Bit Quantizer Capacitive Pickoff V F D A Input Force Output bitstream fsfs Micromachined sensing element cascaded with an electronic filter and electrostatic force feedback Electro-mechanical high order Sigma-Delta Modulator Advantages: higher bandwidth, dynamic range, linearity, lower susceptibility against fabrication imperfections, Applicable to many capacitive MEMS sensors

simulated spectrum, noise floor ≈ -95dB 4 th order simulated spectrum, noise floor ≈ -130dB measured spectrum, noise floor ≈ -90dB 4 th order spectrum noise floor ≈ -110dB

Good agreement simulation - measurement Noise floor at -115dB Noise dominated by thermal, interference noise sources

No access to internal nodes of sensing element Electronic gain constants have to be optimised for stability and performance High tolerances of the mechanical sensing element parameters Usual approach is to use linear control theory  Replace quantiser by white noise and gain  Disadvantages: validity of linear model, no optimization possible

Matlab/Simulink custom made toolbox User defined parameters are optimized by a Generic Algorithm Goal functions usually are proof mass displacement and SNR Robustness analysis using Monte Carlo Analysis to test susceptibility to parameter variations Complex, (near-) optimal EM  can be designed in a day R. Wilcock and M. Kraft, “Genetic algorithm for the design of electro-mechanical Sigma Delta Modulator MEMS sensors.” MDPI Sensors J., vol. 11.

The quantization noise from the first stage is scaled by constant gains (KS, KR and K2), and then digitized by the 2nd stage. MASH is constructed by cascading a purely electronic 2nd order Ʃ ∆ Modulator. The quantization noise is cancelled by the digital filters D1 and D2.

Fully differential signal path Simple PCB implementation

MASH, 0.6G acc. signal, noise floor ≈-115dB 4 th order EMSDM, noise floor ≈-115dB MASH, 1.5G acc. signal, noise floor≈-115dB 4 th order EMSDM, unstable!

MASH, no acc. signal, noise floor ≈-100dB 4 th order EMSDM, noise floor ≈-115dB Main disadvantage of MASH is the susceptibility to parameter variations Quantisation noise leakage Possible solution: adaptive control of filter parameters Measured results for a different sensing element of the same batch (~12% parameter variation)

Sensing element is mech. resonator → Cascade with electronic resonators → electromechanical Bandpass Sigma Delta Modulator  Low noise bandwidth and low sampling frequency World‘s first Bandpass SDM Gyroscope (Dong, Y., Kraft, M., et. al. Sensors and Actuator, A, Vol. 145, pp , 2008)

Gyroscope operated in air Design of EM  using GA algorithm  Yellow parameter changed by GA

SNR as a performance criteria stable designs unstable designs

Thinning of good results for robustness analysis chosen design

Monte Carlo Analysis (2000 simulations) for chosen design Relative robust to parameter variations

Simulation result of chosen EM  design Power spectral density Proof mass displacement

Good agreement with simulated result, but thermal, interference noise dominated Measured power spectral density PCB

Good linearity between ±220°/s Linearity better than 100ppm Scale factor 22.5 mV/°/s

Clear performance improvement compared to open loop and non- optimized designs °/h for one hour long measurements

Clear bandwidth improvement compared to open loop design

Two sense mode SDM control loops  For rate signal and for quadrature error Better longer stability as conventional quadrature cancellation schemes

Two sense mode  control loop  For rate signal and for quadrature error

Clear reduction in quadrature signal obvious Power spectral density: quadrature channel Power spectral density: signal channel

Closed loop control system can be used to improve the linearity bandwidth, bias stability of MEMS physical sensors Genetic Algorithm are an effective way of designing complex EMSDM This could be even extended to include mechanical design parameters of the sensing element For gyroscopes bandpass EMSDM are a particular attractive solution These can be designed to include dynamic quadrature cancellation

Thank you!