MEMS ACCELEROMETERS, PRINCIPLES OF OPERATION, ERROR ANALYSIS

8/19/2019 MEMS ACCELEROMETERS, PRINCIPLES OF OPERATION, ERROR ANALYSIS

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WARSAW UNIVERSITY OF TECHNOLOGY

FACULTY OF POWER AND AERONAUTICAL ENGINEERING

ATTITUDE AND NAVIGARION SYSTEMS

Topic of project:

MEMS ACCELEROMETERS, PRINCIPLES OF

OPERATION, ERROR ANALYSIS

SUPERVISOR

ANTONI KOPYT, M. Sc., Eng

DONE BY

OLEH SHULIMOV, student

280738

WARSAW 2016


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CONTENT

1. INTRODUCTION ..................................................................................................... 4

2. BASIC THEORETICAL INFORMATION ............................................................. 5

2.1 MEMS Accelerometers Implementation ............................................................. 52.2 Architecture and operational principle of MEMS accelerometers ...................... 7

2.3 Error and noise analysis ..................................................................................... 10

3. CONCLUSION ....................................................................................................... 11

4. PROBLEM DESCRIPTION AND METHOD OF SOLUTION ............................ 12

4.1 Input and output representation .......................................................................... 18

5. CONCLUSION ....................................................................................................... 26

6. REFERENCES ........................................................................................................ 27

APPENDIX A ......................................................................................................... 28

APPENDIX B ......................................................................................................... 31


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LIST OF SYMBOLS AND ABBREVIATIONS

a – acceleration

F – force to compress or extend spring

m – mass of the proof mass

k – spring stiffness constant

x – displacement of the proof mass

– roll angle of the proof mass

– pith angle of the proof mass

g – normalized accelerometer data

V – velocity of the proof mass


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1. INTRODUCTION

MEMS it is abbreviation that means “microelectromechanical systems”. These

are miniature devices that contain microelectronic and micromechanical components.

Daily we use variety of devices that are based on MEMS technology. The simplestexample of microelectromechanical systems is an accelerometer that is used in all

modern smart phones, gaming consoles and hard drives. At present MEMS

accelerometer has became important part of many systems. Its solution is used in the

automotive industry, military industry, medicine and particularly in aerospace

industry. [1]

The aim of this project is considerable learning of MEMS accelerometers,

including knowledge acquisition relating its spheres of implementation, operational

principle, consideration of error and noise appearance.


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2. BASIC THEORETICAL INFORMATION

2.1 MEMS Accelerometers Implementation

Technologies have been advanced daily. To combine small size of

accelerometer and its effectiveness people started to invent something absolutely new

using microelectronics field. In 1979 at Stanford University there was developed

MEMS (micro electro-mechanical systems) accelerometer. Today MEMS

accelerometers revolutionized and uses in variety of technologies spheres to simplify

our routine life. This type of accelerometers is highly potential from technological

and commercial point of view. Less power – more efficiency. This is great advantage

of MEMS accelerometers over others. Also it has more benefits. Firstly, it has chip

and easy maintenance. Secondly, comparing with average electromechanical

accelerometer, it three times cheaper than price, for example, of piezoelectric

accelerometer. Similar, it has 1/100 size. Lastly, all electronic situates on the one chip

that gives high portability for users. [2]

Fig. 2.1 Evolution of accelerometers

The most common device in MEMS technology is a MEMS accelerometer. As

mentioned above, the scope of its use is extremely broad. It covers mobile phones,

laptops, game consoles as well as more serious devices such as automobiles, aircraft

and rockets. The main purpose of the accelerometer is to measure the acceleration. In

the case of mobile phones, it is used for many goals. For example, it is used for

change of screen orientation or performance of some functions during the “shaking”

of the device. However, the main area of implementation of MEMS accelerometers in


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smart phones is game industry. Nowadays it is difficult to imagine smart phone

without installed accelerometer. By the way, first time it was installed in the mobile

phone Nokia 5500. It used as a pedometer. On the whole, interest in MEMS began to

grow with the development of platforms iOS and Android. Also accelerometers are

also available in variety of controllers, game consoles. For example, it can be used in

ordinary gamepad or in motion controllers. Especial importance MEMS

accelerometers have in laptops, precisely in its hard disks. It is known that hard disk

is brittle device that can be damaged easily. During the drop of laptop accelerometer

fixes sharp change in acceleration and sends command to parking of the head of a

hard disk preventing the damage of device and the losses of data. On a similar

principle accelerometer affects the car DVR. During hard acceleration, braking and

vehicle rebuild videotape marked with a special marker, which protects it from

erasing and rewriting, which greatly facilitates further parsing of road accidents.

In general, the largest and most promising market for accelerometers and other

MEMS is the automotive industry. In contrast to the market and mobile gaming

devices, where the accelerometers are used for entertainment purposes, in

automobiles any security system based on accelerometer working. With its help,

operating system of airbags deployment, anti-lock brakes, stability, adaptive cruise

control, adaptive suspension, Traction Control system. Taking into account that car

manufacturers are paying particular attention to safety, the number of employed

accelerometers and other MEMS will only grow. In mechanics and aerospace

industry, MEMS accelerometers is used to measure the level of vibrations of separate

parts. For example, in aviation this type of accelerometer is used for measurement the

level of engine vibration. Also it is actively implemented in aircraft control systems

and navigation. [1]


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2.2 Architecture and operational principle of MEMS accelerometers

Design of the MEMS accelerometer. There are several types of devices

depending on their architectures. The work of the accelerometer can be based on the

capacitor principle. The movable part of such a system is a proof mass which shiftsdepending on the inclination of the device. The capacitance changes because of shift

of proof mass and then change the voltage appears. From these data, it is possible to

obtain displacement of the proof mass and desired acceleration.

Fig. 2.2 Structure of capacitor MEMS accelerometer [1]

The most common type of accelerometer is piezoelectric system

accelerometers. Just as in the capacitor accelerometers, they are based on proof mass,

pressure of which acts on the piezoelectric crystal. Under the pressure it generates an

electric current that allows calculating the required acceleration, knowing the

parameters of the entire system. There is another type of accelerometer that is

fundamentally different from the capacitor and the piezoelectric accelerometer. These

accelerometers are called thermal. Their architecture involves the use of an air

bubble. During the acceleration the bubble is deflected from its initial position and

accelerometer fixes it. Knowing how much shifted bubble motion, the acceleration

can be calculated. [1]

Simple mass spring system is the main key principle of MEMS accelerometerworking. Hooke’s law physically controls spring movement inside an accelerometer.


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“Hooke's law is a principle of physics that states that the force needed to extend or

compress a spring by some distance is proportional to that distance. That is: where is

a constant factor characteristic of the spring, its stiffness .”[3]. Mathematically

Hooke’s law has a form:

where

[ ] – stiffness of spring, its constant factor characteristic, N/m;

[ ] – displacement of spring, m;

[ ] – force to compress or extend spring, N;

Another very important physical rule that underlies working of MEMS

accelerometer is Newton’s second law. It states that force acting on the accelerated

mass will produce the force with magnitude. Mathematically Newton’s second law

looks like:

where

[ ] – mass of the proof mass, g;

[ ] – acceleration m/s2;

Fig. 2.3 Mass-spring system [4]

Figure 2.2.2 demonstrates the mass connected to the spring. In accordance to

the Newton’s second law, if this system will be accel erated resulting force will

appear and will equal . This force causes expanding or compression of the massunder the constraint that


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Consequently, acceleration a will cause displacement of the proof mass that

can be expressed as:

Similarly, if we observe displacement that using following expression it is possible to find acceleration:

This simple mathematical method solves a problem that relates to acceleration

finding using change of displacement of proof mass connected to the spring.

However, this system responds only along length of spring. Other words, it is

possible to measure acceleration only along one axis. To receive acceleration along

desirable axes, this system should be installed along each axis: [4]

where

[ , – acceleration and displacement along axis x respectively;

[ ] – acceleration and displacement along axis y respectively;

[ – acceleration and displacement along axis z respectively.

Fig. 2.4 Capacitive MEMS accelerometer operation [5]


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2.3 Error and noise analysis

However, MEMS accelerometers contain set of errors that can reduce its

accuracy of measurement. It is possible to characterize and divide errors into two

groups, deterministic and stochastic.Deterministic errors are characterized by misalignment configurations. These

problems are possible to divide into two groups, external and internal. External

misalignment may appear during 2D MEMS accelerometers usage. Problem with

nonperpendicularity between two accelerometers may be present. Internal

misalignment occurs due to the manufacturing process. Also deterministic errors

include quantization errors. During digitalization for the convenience of processingand information transmission, discrete signal can contain quantization errors.

Generally stochastic errors in accelerometer is caused by some amount of noise

and created by thermal and mechanical fluctuations inside the accelerometer. Each

axis of accelerometer has different level of noise. It is explained by different

construction of each orientation of accelerometer. There are two basic types of noise,

namely white noise and random walk. White noise is created by means of random

charge motion made by the thermal agitation. Random walk, called drift, is

characterized by long-term noise that makes true values of samples not accurate. This

type of noise is not so significant for accelerometers with constant movement and fast

rate of sampling. However, accelerometers with long-term averaged measurements

suffer from influence of this type of noise. [6]


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3. CONCLUSION

MEMS technology has been advanced with time. One of the popular MEMS

technology device accelerometer has became important part of modern life. Although

first accelerometers were constructed for industrial and automotive purposes, today itevolved to use for personal goals. Our ordinary devices use MEMS accelerometer

technology to make a lot of things easier and improve it. Moreover, scientists plan to

implement it more and more in the near future. Therefore, research in this topic is

very actual at present.

There was considered main areas of implementation of MEMS accelerometer,

its design and basic principle of operation. Possible errors and noise factor duringMEMS accelerometer usage were regarded.


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4. PROBLEM DESCRIPTION AND METHOD OF SOLUTION

Project includes modeling of real data from MEMS accelerometer and its

simulation during addition of noise and filtration.

The main idea of the project is to provide visualization of MEMSaccelerometer operation in real-time conditions and present the method of solution of

the problems that can appear during MEMS accelerometer exploitation.

After all computations and modeling of the results it is expected to gain the

true, noised and filtered trajectory of proof mass displacement in three-dimensional

area; true, noised and filtered acceleration along three coordinates; velocity along

coordinate of movement and angle of change in real-time during movement ofaccelerometer. It is expected to perform rotation of MEMS accelerometer along two

axes that demonstrates changes in pitch and roll angles. Before the start of

experiment it was decided to change both angles approximately to 60 degrees during

above 5 seconds. The main difference between two experiments it is not only change

in different angles. During the first experiment just upward movement will be

realized, while second experiment implies upward movement and then downward

coming back to initial position.

The practical part of the project is based on measurements of real-time data

using built-in 3-axis MEMS accelerometer of Samsung Galaxy Tab 4 tablet. To

measure input data there was downloaded from Play Market special application that

is called Accelerometer. To model and simulate the inputs and outputs programming

software Matlab was used. Following diagram demonstrates algorithm of program:


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Fig. 4.1 Algorithm of program

Basic part of the experiment was to move physically the tablet. This movement

caused displacement of accelerometer proof mass and acceleration was occurred.

During experiment there was decided to move tablet changing its pitch and roll

angles. Following pictures represent initial and final position of tablet during both

experiments:

2

1

3

4

5

6

7

8

9

Input data extraction.Input of optimized parameters.

Gaussian white noiseaddition to measured

acceleration along each axis

Calculation of proof

mass displacement

Calculation of roll and pitch angles of proof mass

changed during displacement

Calculation of velocityof proof mass

Calculation of proofmass displacement with

Gaussian white noise

Filtration of accelerationwith added noise

Calculation of proofmass displacement using

filtered acceleration

Plotting of graphs


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Fig. 4.2 Initial and final position of the tablet during first experiment

Graphically it looks like:

Fig. 4.3 Graphical representation of pitch angle change

Θ

X Y

Z


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Fig. 4.4 Initial and final position of the tablet during second experiment

Graphically it looks like:

Fig. 4.5 Graphical representation of roll angle change

Than the data including acceleration along each of the axes and time of

displacement was recorded to tablet in txt format. Following steps describes process

in details:

1. The data was put to the laptop and extracted using functions of Matlab

software.

X Y

Z

φ


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2. After the data were extracted, along each axis displacement of proof mass

was calculated using optimized design parameters of capacitive MEMS

accelerometer such as spring constant and mass of the proof mass. Optimized data

were taken from one of the scientific articles [7]. Displacement along each of axis

was calculated from equation:

3. Using accelerometer, it is possible to find roll and pitch angles which a

change during some period of time. It was achieved using following formulas: [8]

where,

[ , [ – roll and pitch angles respectively;[ [ – normalized data of accelerometer.

4. Also the velocity along axis X was found using integration of acceleration

along axis X:

5. Using special function in Matlab, there was added Gaussian white noise to

measured acceleration. The signal-to-noise ratio per sample is 30 dB.

6. Then displacement with some error was computed. Method of calculation

remained the same as on step number 2.

7. To minimize the appearance of noise during the measurements, Gaussian

low pass filter with equiripple single-rate or multirate FIR filter design was applied. It

was used with some specifications such as frequency at the start of the pass band

equal 100 Hz, frequency at the end of the stop band equal 220 Hz, amount of ripple


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allowed in the pass band is 60 dB and attenuation in the stop band is 0.5 dB. After it

implementation acceleration data along each axis were filtered.

8. In this step displacement in accordance to the filtered acceleration was

received. Method was used as on the previous steps.9. Finally, after all computations graphs were built.


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4.1 Input and output representation

Following figures demonstrates results of the first experiment:

Fig. 4.6 Displacement of proof-mass along X,Y,Z axis (NED frame)

Fig. 4.7 Velocity on time dependence along X axes

-5 0 5 10 15 20x 10

-7-1

-0.50

0.5

1

x 10-7

1

1.5

2

2.5

x 10-6

Y, m

X, m

Z ,

m

Measured displacement of massMeasured displacement of mass with added noise

Filtered displacement of mass by Gaussian low pass filter

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-2

0

2

4

6

8

10

12

Time, s

V e

l o c

i t y , m

/ s


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Fig. 4.8 Pitch angle of proof mass on time dependence

Fig. 4.9 Roll angle of proof mass on time dependence

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-60

-50

-40

-30

-20

-10

0

10

Time, s

P i t c

h a n g

l e ,

d e g

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10

-8

-6

-4

-2

0

2

4

6

8

10

Time, s

R o

l l a n g

l e ,

d e g


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Fig. 4.10 Acceleration on time dependence along X axis

Fig. 4.11 Acceleration on time dependence along Y axis

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1

0

1

2

3

4

5

6

7

8

Time, s

A c c e

l e r a

t i o n ,

m / s

. 2

Measured accelerationMeasured acceleration with added noiseFiltered acceleration by Gaussian low pass filter

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Time, s

A c c e

l e r a

t i o n ,

m / s

. 2



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Fig. 4.12 Acceleration on time dependence along Z axis

Following figures demonstrates results of the second experiment:

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 54

5

6

7

8

9

10

11

12

13

Time, s

A c c e

l e r a

t i o n ,

m / s

. 2



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Fig. 4.13 Displacement of proof-mass along X,Y,Z axis (NED frame)

Fig. 4.14 Velocity on time dependence along X axes

-15-10

-50

5x 10-8

-3-2

-10

1

x 10-6

0.5

1

1.5

2

2.5

3

x 10-6

Y, mX, m

Z ,

m

Measured displacement of massMeasured displacement of mass with added noiseFiltered displacement of mass by Gaussian low pass filter

0 2 4 6 8 10 120

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Time, s

V e

l o c

i t y ,

m / s


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Fig. 4.15 Pitch angle of proof mass on time dependence

Fig. 4.16 Roll angle of proof mass on time dependence

0 2 4 6 8 10 12-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Time, s

P i t c

h a n g

l e ,

d e g

0 2 4 6 8 10 12-70

-60

-50

-40

-30

-20

-10

0

10

20

Time, s

R o

l l a n g

l e ,

d e g


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Fig. 4.17 Acceleration on time dependence along X axis

Fig. 4.18 Acceleration on time dependence along Y axis

0 2 4 6 8 10 12

-0.5-0.4

-0.3

-0.2

-0.1

0

0.1

0.20.3

0.4

0.5

Time, s

A c c e

l e r a

t i o n ,

m / s

. 2


0 2 4 6 8 10 12-10

-8

-6

-4

-2

0

2

4

Time, s

A c c e

l e r a

t i o n ,

m / s

. 2



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Fig. 4.19 Acceleration on time dependence along Z axis

0 2 4 6 8 10 120

2

4

6

8

10

12

Time, s

A c c e

l e r a

t i o n ,

m / s

. 2



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4. CONCLUSION

During performance of the project all expected parameters were received. Set

up value of angle and time of rotation during experiment were realized. Different

graphs were built. Results of all computations were displayed using simulation andvisualization method.

Using this computer program it is possible to analyze desired movement of

MEMS accelerometer and to get goal values.


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5. REFERENCES

1. http://www.ferra.ru/ru/techlife/review/mems-part-1/#.VmBkhnYvfIW

2. Matej Andrejaśić, MEMS accelerometers , pp. 2-3, March 2008

3. https://en.wikipedia.org/wiki/Hooke%27s_law

4. http://soundlab.cs.princeton.edu/learning/tutorials/sensors/node9.html

5. http://www.globalspec.com/learnmore/sensors_transducers_detectors/acceler

ation_vibration_sensing/accelerometers

6. http://www.phidgets.com/docs/Accelerometer_Primer

7. Kanchan Sharma, Isaac G. Macwan, Linfeng Zhang, Lawrence Hmurcik,

Xingguo Xiong, Design Optimization of MEMS Comb Accelerometer , p.8

8. Der-Ming Ma, Jaw-Kuen Shiau, I.-Chiang Wang and Yu-Heng Lin, Attitude

Determination Using a MEMS-Based Flight Information Measurement Unit , p.5,

2012


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%calculation of displacement with noise along x,y,zx11=(m*a11/k);y11=(m*a12/k);z11=(m*a13/k);%Gaussian low pass filter design and filtration

d = fdesign.lowpass( 'Fp,Fst,Ap,Ast' ,100,220,60,0.5,1000);Hd = design(d, 'equiripple' );axf = filter(Hd,a11);ayf = filter(Hd,a12);azf = filter(Hd,a13);

xf=(m*axf/k);yf=(m*ayf/k);zf=(m*azf/k);

figure

plot3(x,y,z, '--' )hold on plot3(x11,y11,z11, '--g' )hold on plot3(xf(5:123),yf(5:123),zf(5:123), 'r' )grid on xlabel( 'X, m' )ylabel( 'Y, m' )zlabel( 'Z, m' )legend( 'Measured displacement of mass' , 'Measured displacementof mass with added noise' , 'Filtered displacement of mass by

Gaussian low pass filter' )

figureplot(tx1,Vx)grid onxlabel( 'Time, s' )ylabel( 'Velocity, m/s' )

figureplot(tx1,pitch)grid on

xlabel( 'Time, s' )ylabel( 'Pitch angle, deg' )

figureplot(ty1,roll)grid on axis([0 5 -10 10])xlabel( 'Time, s' )ylabel( 'Roll angle, deg' )

figureplot(tx1, ax1)hold on


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plot(tx1,a11, 'g' )hold on plot(tx1,axf, 'r' )grid on xlabel( 'Time, s' )ylabel( 'Acceleration, m/s.^2' )

legend( 'Measured acceleration' , 'Measured acceleration withadded noise' , 'Filtered acceleration by Gaussian low passfilter' )

figureplot(tx1, ay1)hold on plot(tx1,a12, 'g' )hold on plot(tx1,ayf, 'r' )grid on

xlabel( 'Time, s' )ylabel( 'Acceleration, m/s.^2' )legend( 'Measured acceleration' , 'Measured acceleration withadded noise' , 'Filtered acceleration by Gaussian low passfilter' )

figureplot(tx1, az1)hold on plot(tx1,a13, 'g' )hold on

plot(tx1,azf, 'r' )grid on xlabel( 'Time, s' )ylabel( 'Acceleration, m/s.^2' )legend( 'Measured acceleration' , 'Measured acceleration withadded noise' , 'Filtered acceleration by Gaussian low passfilter' )


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APPENDIX B

Block scheme of the computer program

Begin

m=0.42e-6k=1.784a1=textread( 'D:\1\mmm_x.txt' );a2=textread( 'D:\1\mmm_y.txt' );a3=textread

( 'D:\1\mmm_z.txt' );

ax1=ax(1:2:length(ax));ay1=ay(1:2:length(ay));az1=az(1:2:length(az));tx1=tx(1:2:length(tx));ty1=ty(1:2:length(ty));tz1=tz(1:2:length(tz));

x=(m*ax1/k);y=(m*ay1/k);z=(m*az1/k);

r=atan(ay1./az1);p=atan((-ax1.*cos(r))./az1);roll=r.*180./3.14;

pitch=p.*180./3.14;

Vx=cumtrapz(tx1,ax1);Vy=cumtrapz(ty1,ay1);Vz=cumtrapz(tz1,az1);

1


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figureplot3(x,y,z, '--' )

hold on plot3(x11,y11,z11, '--g' )hold on plot3(xf(5:123),yf(5:123),zf(5:123), 'r' )figureplot(tx1,Vx)grid onfigureplot(tx1,pitch)grid on figureplot(ty1,roll)grid on figureplot(tx1, ax1)hold on plot(tx1,a11, 'g' )hold on plot(tx1,axf, 'r' )figureplot(tx1, ay1)hold on plot(tx1,a12, 'g' )hold on plot(tx1,ayf, 'r' )grid on figureplot(tx1, az1)hold on plot(tx1,a13, 'g' )hold on plot(tx1,azf, 'r' )grid on

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MEMS ACCELEROMETERS, PRINCIPLES OF OPERATION, ERROR ANALYSIS

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