Innovative Control Systems for MEMS Inertial Sensors

Michael KraftReuben WilcockBader Almutairi

Fang ChenPejwaak Salimi

Overview

Background and ContextAccelerometer Control Systems

High Order Single Loop SDMMASH SDM Control SystemGenetic Algorithm Design

Gyroscope Control SystemBandpass SDM Quadrature Cancellation SDM

Conclusions

Basic Concept EMSDM

2nd order Electro-mechanical sigma-delta modulator (EMSDM)Sensing element acts as loop filterFirst reported by W. Henrion, et al. 1990Advantages: direct digital output (→ “smart sensors”), closed loop control, small displacements reduced non-linearity

Pick-off

Vout

Digital bitstream

Vf

Vf

C(z)S/H

Comp-arator

0

1

fs

Compen-sator

Fully integrated chip, sampling frequency 500kHz

sensor 1-bit ADC

1-bit DAC

x/V

V/Fel

Fel

2 - z-1

positionsense

leadcompensator

comparatordouble

integration

electrostaticactuation

main

Accelerometer EMSDM

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 EMSDMCoriolis force nulled with electrostatic feedbackProblem: Bandwidth of SDM up to resonance frequency of gyro

First EMSDM Gyroscope

Xy

Z

Digital Control Signal Circuitry

SE 2

Circuitry700m

Sensing Element 1

Sensing Element 2

4.5mm

Drive Circuitry SE1

Drive Circuitry SE2

Xy

Z

Digital Control Signal Circuitry

SE 2

Circuitry700m

Sensing Element 1

Sensing Element 2

4.5mm

Drive Circuitry SE1

Drive Circuitry SE2

Sense combs

Feedback electrodesDrive combs

FrequencyTuning

AGCControl

PositionSense

PLL

ChargeControlCircuitry

PositionSense

Compen-sation

fs=1MHz

Drive Mode Control

Sensing Mode Control

VQC

QuadratureCancellation

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.

2nd Order EMSDM

Disadvantages:Only 2nd order noise shaping

• Tones, deadzones, high oversampling ratio required, etcLoop dynamics rely exclusively on the sensing element

• High dependency on fabrication tolerances

2nd order measurement results with zero acceleration input

Tones

Accelerometer Sensing Element

Proofmass

Sensing Electrodes

Sensing Electrodes

Feedback

Electrode

Feedback

Electrode

Fee

dbac

kE

lect

rode

Fee

dbac

kE

lect

rode

Anchor Anchor

Anchor Anchor

Spring

Spring Spring

Spring

Parameter Value

Sensitivity 4.56 pF/g

Natural Frequency 237 Hz

Overall device size 7x9x0.6 mm3

Mass of proof mass 1.86 mg

Proof mass area 4 x 7 mm2

Min. Feature size 6 um

102

10-6

X: 152Y: 1.591e-006

Frequency (Hz)

Def

lect

ion

(m)

Applications in platform stability and tilt measurementsStructural Health MonitoringOil and Gas exploration

Open Loop Accelerometer

Noise floor below under 800nG/√HzHigh sensitivity 5pF/GStrategic 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

Fabrication Process

SensingElement

ElectronicFilter

Electrostatic ForceConversation

1 BitQuantizer

CapacitivePickoff

VF

D

A

InputForce

Output bitstream

fs

Higher Order EMSDM

Micromachined sensing element cascaded with an electronic filter and electrostatic force feedbackElectro-mechanical high order Sigma-Delta ModulatorAdvantages: higher bandwidth, dynamic range, linearity, lower susceptibility against fabrication imperfections, Applicable to many capacitive MEMS sensors

Lowpass delta sigma accelerometer controller - 5th order

ZOH

Switch1

1

m.s +b.s+k2

Sensor1

1

m.s +b.s+k2

Sensor Quantiser

kpo

Pickup

m

Mass

1

ts.s

Integrator3

1

ts.s

Integrator2

1

ts.s

Integrator1Input

k3

Gain3

k2

Gain2

k1

Gain1

kf3 Feedback3kf2 Feedback2kf1 Feedback1

f(u)

F/B Force -

f(u)

F/B Force +

displacement

Displacement

dispcompare

DispCompare

s+zero

s+pole

Compensator

kbst

Boost

bitstream

Bitstream

Band-LimitedWhite Noise

4th Order vs 2nd Order EMSDM

simulated spectrum, noise floor ≈ -95dB

4th order simulated spectrum, noise floor ≈ -130dB

measured spectrum, noise floor ≈ -90dB

4th order spectrum noise floor ≈ -110dB

4th Order SDM Accelerometer

Good agreement simulation - measurementNoise floor at -115dBNoise dominated by thermal, interference noise sources

Design Challenges Higher Order EMSDM

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

Genetic Algorithm for the DesignOf Higher Order EMSDM

Matlab/Simulink custom made toolboxUser defined parameters are optimized by a Generic AlgorithmGoal functions usually are proof mass displacement and SNRRobustness analysis using Monte Carlo Analysis to test susceptibility to parameter variationsComplex, (near-) optimal EMSDM can be designed in a day

Run Genetic Algoritm

0 10-50

0

50

100S

NR

5

K1 gain

2 4 6

100

90

80

70

Filtering and Thinning

K1 gain

SN

R

959085800

100

200

300

Robustness Analysis

SNR

Final Design Choice

Designed parameters:===================Pole frequency: 29.97KHzZero frequency: 769.76HzPickoff gain: 1.00MBoost gain: 834.08Gain fk1: 2.38Gain fk2: 819.01mGain fk3: 3.45Gain fk4: 1.37Feedback voltage: 11.61V

Goal(s)

Simulink Model

Parameter Constraints

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.

MASH EMSDM

Fully differential signal pathSimple PCB implementation

Electronic Implementation

MASH EM SDM Noise Shaping

MASH, 0.6G acc. signal, noise floor ≈-115dB

4th order EMSDM, noise floor ≈-115dB

MASH, 1.5G acc. signal, noise floor≈-115dB

4th order EMSDM, unstable!

MASH EMSDM Disadvantage

MASH, no acc. signal, noise floor ≈-100dB

4th order EMSDM, noise floor ≈-115dB

Main disadvantage of MASH is the susceptibility to parameter variationsQuantisation noise leakagePossible solution: adaptive control of filter parameters

Measured results for a different sensing element of the same batch (~12% parameter variation)

Gyroscope InterfaceSensing element

xC +

Coriolisforce

CV

Electrostatic feedback

force

Pick-off circuit Phasecompensator

Electronic resonators1 bit A/D

fsOutput bitstream

Elec. 1 bit D/AD

A

+

Elec. 1 bit D/AD

A

Vfb

Reference voltage

+

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. 299-305, 2008)

Gyroscope Prototype

Gyroscope Control System

Gyroscope operated in airDesign of EMSDM using GA algorithm Yellow parameter changed by GA

GA Design Process

SNR as a performance criteria

0 200 400 600 800 1000-100

-50

0

50

100

Boost gain

SN

RS

NR

Boost gain

stable designs

unstable designs

GA Design Process

Thinning of good results for robustness analysis

0 200 400 600 800 1000-100

-90

-80

-70

-60

-50S

NR

Boost gain

70

80

90

100

110

120

chosen design

GA Design Process

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

-90 -88 -86 -84 -82 -80 -78 -760

200

400

600

800

1000

1200Mean=-87.9 StDev=1.77

SNR

Quan

tity

100 98 96 94 92 90 88 860

200

400

600

800

1000

1200

Qu

an

tity

SNR

Simulation Results

Simulation result of chosen EMSDM design

1000 2000 3000 4000 5000 6000 7000 8000

-200

-150

-100

-50

0

Frequency [Hz]

Mag

nit

ud

e [d

B]

-150

-100

4200 4250 4300 4350 4400-200

-150

-100

-50

0

Frequency [Hz]

Mag

nitu

de [d

B]

-120

-100

-40

-80

-60

0

-40

-80

Quadrature Error

Input angular rate

32Hz32Hz

0 0.02 0.04 0.06 0.08 0.1-1

-0.5

0

0.5

1x 10-7

Time [s]

Dis

pla

cem

en

t [m

]

Open loopClosed loop

0.048 0.049 0.05 0.051 0.052 0.053

-5

0

5

x 10-9

Time [s]

Dis

plac

emen

t [m

]

0.03 0.032 0.034 0.036 0.038 0.047

7.5

8

8.5

9

x 10-8

Time [s]

Dis

plac

emen

t [m

]

Power spectral density

Proof mass displacement

Hardware Implementation

Good agreement with simulated result, but thermal, interference noise dominated

Measured power spectral density

PCB

-40dBVrms

-140

Mag (dB)

kHz7.2800 Hz

Pwr Spec 1X:4.24 kHz Y:-101.896 dBVX:4.304 kHz Y:-62.907 dBV

Measurement ResultsLinearity

Good linearity between ±220°/sLinearity better than 100ppmScale factor 22.5 mV/°/s

-250 -200 -150 -100 -50 0 50 100 150 200 250-6

-4

-2

0

2

4

6

Rotation Rate (°/sec)

Ou

tpu

t V

olt

age(

V)

non-optimal closed loop

optimal closed loop

open loop

Measurement ResultsAllan Variance

Clear performance improvement compared to open loop and non-optimized designs34.15 °/h for one hour long measurements

10-1

100

101

102

103

10-2

10-1

100

(s)

( )

(de

g/s

)

open loop

optimal closed loop

non-optimal closed loop

Bias stability: 89 o/h

Bias stability: 60 o/h

Bias stability: 34.15 o/h

Measurement ResultsFrequency Response

Clear bandwidth improvement compared to open loop design

0 20 40 60 80 100 1200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Bandwidth(Hz)

No

rmal

ized

Ou

tpu

t V

olt

age

open loop

optimal closed loop

3dB PointBandwidth=50Hz

3dB PointBandwidth=110Hz

Quadrature BPSDM Interface

Two sense mode SDM control loops For rate signal and for quadrature error

Better longer stability as conventional quadrature cancellation schemes

+

Fcorioles

FQuadrature M(s)X

C

Converstion of displacement to capacitive variation

Sense mode Transfer Function

CV

Readout Interface

ym

x

x

2Cos(wdt)

2Sin(wdt)

LPF

LPF

W (angular rate)

W err (quadrature error)

1

2

1

2

+-

+-

Electronic Loop Filter

Electronic Loop Filterx

x

2Cos(wdt)

2Sin(wdt)

Sense mode displacement bit stream due to Coriolis effect

Sense mode displacement bit stream due to Quadrature error

+

Kfb Kfb

--

A pair of Electronic ∑∆ Modulators

Yout

Quadrature BPSDM Interface

Two sense mode SDM control loop For rate signal and for quadrature error

ZOH1

ZOH

s+zero

s+pole

Compensator

Switch1

Multiplexer

1/m

s +Wy/Qy.s+Wy^22

Sensor1

1/m

s +Wy/Qy.s+Wy^22

Sensor

Wx.s

s +Wx^22

Resonator4

Wx.s

s +Wx^22

Resonator3

Wx.s

s +Wx^22

Resonator2

Wx.s

s +Wx^22

Resonator1

In1Out1

RZ2

In1

Ou

t1

RZ1

In1Out1

RZ

Quantiser1

Quantiser

Quadrature Drive

Quadrature Demodulator

PulseGenerator

Product3

Product2Product1

Product

kpo

Pickup Input

In1Out1

HRZ2

In1 Out1

HRZ1

In1Out1

HRZ

-K-

Gainm

-K-

Gain2*m*Wx

qkf4

qkf3

qkf2

qkf1

kf4

kf3

kf2

kf1

qfg2

FLT G 4

qfg1

FLT G 3

fg2

FLT G 2

fg1

FLT G 1

-Ffb

F/B Force-1

Ffb

F/B Force+1

Drive

displacement

Displacement

dispcompare

DispCompare

Demodulator

Coriolis

kbst

Boost

Angular rate bit-stream

Band-LimitedWhite Noise

butter

Analogue

butter

Analoguelowpass filter

lowpass filter

Quadrature BPSDM Interface

Preliminary Results

Clear reduction in quadrature signal obvious

Power spectral density: quadrature channel

Power spectral density: signal channel

Conclusions

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!