studying of a tunneling accelerometer with piezoelectric actuation and fuzzy controller

8/8/2019 Studying of a Tunneling Accelerometer with Piezoelectric Actuation and Fuzzy Controller

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Sensors & Transducers Journal (ISSN 1726-5479) is a peer review international journal published monthly online by International Frequency Sensor Association (IFSA).Available in electronic and CD-ROM. Copyright 2007 by International Frequency Sensor Association. All rights reserved.


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SS ee nn ss oo rr ss && TTrraa nn ss dd uu cc ee rrss JJ oo uu rrnn aa ll

CC oo nn ttee nn tt ss Volume 89Issue 3March 2008

www.sensorsportal.com ISSN 1726-5479

Research Articles

Use of Smart Sensors in the Measurement of Power QualityA. Moreno-Muoz, and J. J. G. de la Rosa ........................................................................................ 1

A Multi-Channel, High-Precision Sensor Interface for Low-Power Applications ZMD21013Marko Mailand .................................................................................................................................... 10

Studying of a Tunneling Accelerometer with Piezoelectric Actuation and Fuzzy ControllerAhmadali Tahmasebi Moradi, Yousef Kanani, Behrouz Tousi, Asadollah Motalebi,and Ghader Rezazadeh ..................................................................................................................... 17

Control of Neutralization Process Using Soft ComputingG. Balasubramanian, N. Sivakumaran and T. K. Radhakrishnan...................................................... 30

Artificially Controlling the Limb Movement of Robotic Arm Using Machine Interface withEMG SensorGovind Singh Patel, Amrita Rai and Dr. S. Prasad............................................................................ 39

Active Vibration Control of a Flexible Structure Using Piezoceramic ActuatorsJ. Fei ................................................................................................................................................... 52

Analysis and Implementation of Nonlinear Transducer Response over a Wider ResponseRangeSheroz Khan, AHM Zahirul Alam, Syed Masrur Ahmmad, TIJANI I. B., Muhammad Asraful Hasan,Lawal Wahab Adetunji, Salami Femi Abdulazeez, Siti Hana Mohammad Zaini, Siti Aminah Othman, Saman S. Khan.................................................................................................................... 61

Leak Detection and Model Analysis for Nonlinear Spherical Tank Process UsingConductivity SensorP. Madhavasarma, S. Sundaram ....................................................................................................... 71

Analytical and Fundamental Study of EMATs SystemA. Doniavi, M. Eskandarzade, J. Malekani......................................................................................... 77

A Modified Design of an Anemometric Flow TransducerS. C. Bera and N. Mandal................................................................................................................... 83

A Novel Hybrid Binary Reconstruction Algorithm for Ultrasonic TomographyM. H. Fazalul Rahiman and R. Abdul Rahim...................................................................................... 93

Authors are encouraged to submit article in MS Word (doc) and Acrobat (pdf) formats by e-mail: [email protected]

Please visit journals webpage with preparation instructions: http://www.sensorsportal.com/HTML/DIGEST/Submition.htm

International Frequency Sensor Association (IFSA).


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Sensors & Transducers Journal, Vol. 89, Issue 3, March 2008, pp. 17-29

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SSS eee nnn sss ooo rrr sss &&& TTT rrr aaa nnn sss ddd uuu ccc eee rrr sss ISSN 1726-5479 2008 by IFSA

http://www.sensorsportal.com

Studying of a Tunneling Accelerometer with PiezoelectricActuation and Fuzzy Controller

1Ahmadali Tahmasebi Moradi, 2Yousef Kanani, 3Behrouz Tousi,4Asadollah Motalebi, and 5Ghader Rezazadeh

1,2,5 Mech. Eng. Dept. Urmia University, Urmia, Iran4Mech. Eng. Dept. Khoy Azad University, Khoy, Iran

3Elec. Eng. Dept. Urmia University, Urmia, Iran5E-mail: [email protected]

Received: 10 February 2008 /Accepted: 17 March 2008 /Published: 24 March 2008

Abstract: This report demonstrates the design of closed-loop micro accelerometer sensor. Proposedsensor consists of a polysilicon cantilever micro beam as a proof mass and uses the extreme sensitivityof electron tunneling to variations in electrode separation as sensing element of the sensor. The modeluses piezoelectric forces as an actuating element to control the separation between the tunnelingelectrodes with a low voltage due to large piezoelectric constant. In order to have a proper responsetime a Fuzzy controller is considered which can be very useful, fast, and reliable. The inputs for thementioned controller are tunneling current error, gradient of the tunneling current and the summationof errors. And the output is the piezoelectric voltage. Due to the simulation and its results, it is seenthat the proposed micro accelerometer have high linearity and dynamic range and also have good

respond to the step and sinusoidal acceleration. Copyright 2008 IFSA.

Keywords: Micro acceleration, Piezoelectric, Tunneling current, Fuzzy controller

1. Introduction

Miniaturization has been one of the most important technological trends in the last decades.Microminiaturization of mechanical components was started from the microfabricated sensors and wasfollowed by microfabricated parts, such as beams and membranes, and microactuators. In recent yearsthe integration of microelectronics, micromechanisms, microsensors and microactuators intomicrosystems has become one of the most prominent research areas all over the world.


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One kind of micro sensors is micro accelerometers. Accelerometers measure acceleration, vibrationand shock. Commonly there is a proof mass in accelerometers that acceleration affects it, and withrespect to its movement and its mass, acceleration will be measured. The difference betweenaccelerometers comes from its structure and method of sensing and actuating corresponding withacceleration. At the heart of MEMS accelerometer is the micro-mechanical structure which, due to theacceleration, alters its stiffness, mass or shape. Micro-mechanical elements are typically attached to the

substrate, e.g. with supporting beams or tethers [1, 2].

There are various kinds of measurement mechanisms of the accelerometers, like capacitive,piezoelectric, piezoresistive, tunneling current and so on. One of the most sensitive and recentaccelerometers are based on the variation of tunneling current. Tunneling accelerometer has threeadvantages: one is the super sensitivity caused by the exponential relation between the tunnelingcurrent and the distance. The second is that its sensitivity reduction due to the volume reduction is lessthan capacitive devices because the sensitive area is smaller than 21 m . The third is that the feedback

circuit is simpler than that of a capacitive accelerometer [3-14].

MEMS accelerometers are founded in open-loop and close-loop mode. For static/low frequencyapplications, which do not require a high degree of accuracy, they can be used in open-loop(compensated or uncompensated) but for higher precision applications, negative feedback must beused to increase linearity, bandwidth and dynamic range. Nowadays researches in close-loopaccelerometer are focused on increasing the dynamic range and bandwidth and decreasing noiseeffects, and designing better controller that have good response to different external accelerations suchas step and sinusoidal acceleration. For the closed-loop accelerometer, it has to be noted that anactuation mechanism is needed. These mechanisms are mainly based on electrostatic, magnetic,thermal or piezoelectric actuation.

The preponderance of MEMS literature utilizes electrostatic actuation of flexural structures.

Electrostatics is relatively easy to implement, and offers the possibility of large amplitude actuation,though typically at the cost of large driving voltages and substantial hysteresis. Current-basedactuation approaches, such as those utilized in many thermal and magnetically driven devices,typically require high power to operate, and in some cases are inherently slow (e.g. due to thermal timeconstants). In contrast, the piezoelectric effect can be utilized to drive large displacements in MEMSstructures at modest voltages, low powers, and with low hysteresis. Piezoelectricity shows goodscaling with size. That is, the energy density available for actuation remains high, even as device sizesdrop. The piezoelectric materials have ability to provide electrical signals to drive or sense the device.However, the researches on using piezoelectric materials to enhance the controlling or improvement of MEMS structures behaviors such as pull-in voltage are considered recently [15].

Closed loop accelerometers are mostly based on the PID controllers, since using of Fuzzy controllersor combination of common controllers corresponding with Fuzzy controller arent attracted muchattention from the scientific community. The Fuzzy Logic Control uses the qualitative aspects of thehuman decision process to construct the control algorithm. The Fuzzy Logic Control achieved all thegoals that the PID and sliding mode control are normally used to achieve. For the last 20 years, FuzzyControl Theory has emerged as a fruitful approach to a wide variety of control problems. Fuzzy logicwas first proposed by Lotfi A. Zadeh of the University of California at Berkeley in a 1965 paper[16] ;he elaborated on his ideas in a 1973 paper that introduced the concept of "linguistic variables" [17]. Inhis approach, a Fuzzy implication is defined as a Fuzzy Cartesian product. Based on Zadeh's definitionof implication, Mamdani built the first fuzzy logic controller [18]. Such controller may be used invarious mechanisms, for instance it can be used in micro accelerometer.

Fuzzy controllers use the linguistic rules for controlling systems, so it is quite suitable for the unknownor non-linear systems that could not be controlled easily with classical control approach like PID


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controller to achieving desired purpose. Fuzzy controllers also have better performance from othercontrol methods, if well designed. Combining Fuzzy controllers with other classical method lead torobustness controller such as PID-Fuzzy controller.

In this paper a new closed-loop micro accelerometer with a pair of piezoelectric layers is presentedwhich has the characteristic of low actuation voltage to the piezoelectric layers, high sensitivity due to

the tunneling measurement, and high linear range to measure the acceleration by means of the closed-loop mechanism. The accelerometer is modeled into a lump model. Piezoelectric layers is used toapply a oppose moment to control the displacement of the micro accelerometer which cause toincrease the range of the measurement corresponding to low actuation voltage. The PID-Fuzzycontroller is applied in order to control the actuation voltage to the piezoelectric layers. The obtainedresults prove the characteristics of the proposed micro accelerometer are highly acceptable.

2. Electromechanical Behavior of Micro accelerometer

2.1. Model Description and Assumptions

As it is shown in the Fig. 1, assume a beam with thickness h , width w , length L , density andisotropic with Youngs modulus E that has piezoelectric layers bonded on its top and bottom surfaces.The piezoelectric layers are located throughout the beam length. And have thickness 1h , density 0 ,

Youngs modulus P E and equivalent piezoelectric coefficient for one-dimensional problem 31e .Suppose that y is the coordinate along the length of the beam with its origin at the left end, and )( yu isthe deflection of the beam, defined to be positive downward.

Fig.1. Schematic of the micro accelerometer.

Microbeams are usually modeled as continuous and prismatic straight beams, made of elastic andhomogeneous material [19], with principal axes of elasticity equally directed for all sections. Theabove assumption allows uncoupling flexural, torsional and axial behaviors. Since the flexuralbehavior is here mainly considered, transverse displacement and rotation are suitable to writeequilibrium equations.

2.2. Mathematical Model for Micro Accelerometer

For preliminary analysis, as it is shown in Fig. 2 a low-order model is considered by assimilating themicro accelerometer to a system with lumped parameters.


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Fig. 2. Lumped electromechanical model.

The dynamic equation for the micro accelerometer can be written as:

maF withF F kx xb xm a pa ==++ &&& , (1) whereas m is the proof mass, b is the damping coefficient, k is the equivalent stiffness, a is theexternal acceleration impose to the system and pF is the equivalent force of the piezoelectric layers.

2.2.1. Equivalent Stiffness

Without considering shear strain of the beam, based on the Euler-Bernoulli beam theory, the equivalent stiffness for a cantilever beam can be written as:

3

3 L EI

k = , (2)

where 12

3wh I = is the moment of inertia of the cross-sectional area. For a wide beam, for which

hw 5 , the effective modulus E ~ can be approximated by the plate modulus)1( 2

E , otherwise E

~is

the Young's modulus E where is the Poissons Ratio.

2.2.2. Equivalent Mass

With considering the first mode for the vibration of the micro cantilever beam, the equivalent mass canbe expressed as:

dy y A Lm L

)(21

2

)( 20

2

&&

= , (3) where is the first mode shape of a cantilever beam, A is the cross sectional area and is the beamdensity.


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2.2.3. Damping Coefficient

There are two sources of mechanical damping: the structural damping: and the viscous damping by gasflow. The damping in the high Q materials (i.e. CMOS MEMS) is very low. Thus, damping in mainlyMEMS devices caused by viscous flow gas of surrounding the micro structures.

Damping coefficient can be varies with mechanical properties and dominate pressure in accelerometer.The dominant damping mechanism in lateral accelerometer is squeeze-film damping. For rectangularplate, the damping coefficient is based on the evaluations by [20], namely:

( )304396

xg

w Lb

=

, (4)

where 0g is the initial Gap or initial distance between plate and the ground and is the viscosity of

the gas.

2.2.4. Equivalent Piezoelectric Force

The stress in the piezoelectric layer accounting for electro-mechanical effects can be expressed as [21]:

eP y E edy

ud z E 312

2

= , (5)

where the over-bar represents the parameters in the piezoelectric layer and e E is the electric field in

the piezoelectric layer which is PPe hV E / = . In this model, two piezoelectric layers are bounded topand bottom through out the length of the beam. The forces in the piezoelectric layers are opposed toeach other direction due to the difference direction of applied voltage to the each piezoelectric layers

pV . The applied force by piezoelectric layers as pointed out by [21] can be written as:

+

=

+

+

=

2 /

2 / 312

2

2 /

2 /

2 /

2 / 312

2

2

2

0) / (

) / (

h

hh PPP

h

h

hh

h PPP

p

p

bdzhV edy

ud z E

bdzhV edy

ud z E bdz

dyud

EzP

, (6)

+

+

= 2 /

0

2 /

2 / 312

2

2

2

) / (22h hh

h PPP y

p

bdzhV edy

ud z E zbdz

dyud

Ez z M , (7)

By integrating of the Eq. (7), we have:

pPP y M dy

ud I E

dy

ud I E M += 2

2

2

2~

, (8)


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whereas )(31 pPP hhbV e M += and ))2(

12(2 2

3P

PP

P

hhbh

bh I

++= . Therefore, the bending moment can be

written as follow:

p y M dy

yud M +=

2

2 )( , (9)

whereas PP I E I E +=

~ . To determine the equivalent piezoelectric force, the other forces on the beam

are neglected. This can be written as: 0 = y M . Thus the equivalent piezoelectric force which isaccounted for the lump model can be expressed as:

)( Luk F p = , (10) where )( Lu is the tip displacement of the micro accelerometer due to the piezoelectric moment.

2.3. Sensing Approach and Operating Principle

Tunneling current ( t I ) is a reference for sensing beam deflection. The relationship between t I anddistance between tunneling tip and conductive surface is given by:

( )= sV I I bt exp , with xgs = 0 (11) where bV is tunneling bias across electrode gap,

5.01025.1 = eV A I o

is a constant , s is tunneling gap

and is the effective height of the tunneling barrier. According to experimental results, the effectivebarrier height is considered as: 1685.0= [22].

Sensor measures acceleration with respect to variation of tunneling current. A Controller has beendesigned to make beam position zero, this can be achieved with applying voltage to piezoelectriclayers. This voltage is the sensor output which is used to calculate input acceleration. The gain thatmust be multiplied to piezoelectric voltage to calculate the input acceleration can be obtained fromsensor simulation and tests. The block diagram of the closed-loop system is shown in the Fig. 3:

Fig. 3. Block diagram of the closed-loop system.

2.4. Design of Fuzzy Controller

Fuzzy controller is developed to control the beam deflection about its static position, and increase thesensor measuring range. The fuzzy control system generates the control action from a set of rules


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representing the heuristic knowledge about the plant to be controlled [23]. Fuzzy controller consists off three steps:

1- Fuzzification2- Rule base decision3- Defuzzification

A crisp data as input is converted to degree of membership for any linguistic condition by a look up inone or several membership functions. Decision makes by rule base part that includes IF-THEN rulecreated by expert knowledge. And defuzzification gives a crisp data for output from fuzzy outputs.

The input of the designed controller is based on tunneling current, gradient of tunneling current andsummation of errors and the piezoelectric voltage is the output. The input and output membershipfunctions are shown in Fig. 4. and Fig. 5, respectively. Tunneling current changes exponentially due tothe tunneling gap, so this sensor has different behavior for positive and negative acceleration. For theequal negative and positive acceleration, if the controller rules are the same for those accelerations,larger deflection would be obtained for the negative acceleration than the positive one. Therefore, inthis design has been tried to have a better performance for the negative acceleration, so currentmemberships designed exact symmetric to beam deflection not to tunneling current .

10 -1 100 101 10 2

0

0.2

0.4

0.6

0.8

1

current (nA)

D e g r e e o

f m e m

b e r s

h i p

NL NS ZO PS PL

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

0

0.2

0.4

0.6

0.8

1

current's derivate *10 7

D e g r e e o

f m e m

b e r s

h i p

NL NS ZO PS PL

-2 -1 0 1 2 3 4 5

0

0.2

0.4

0.6

0.8

1

integral of c urrent errors

D e g r e e o

f m e m

b e r s

h i p

NL NS ZO PS PL

Fig. 4. Input membership functions.


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-6 -4 -2 0 2 4 6

x 10 -3

0

0.2

0.4

0.6

0.8

1

piezoelectric's voltage

D e g r e e o

f m e m

b e r s

h i p

NH NL NS ZO PS PL PH

-0.01 -0.008 -0.006 -0.004 -0.002 0 0.002 0.004 0.006 0.008 0.01

0

0.2

0.4

0.6

0.8

1

piezoelectric's voltage

D e g r e e o

f m e m

b e r s

h i p

NL NS ZO PS PL

(a) (b)

Fig. 5. Output membership functions, a) for PD controller Output, b) for D and I controllers.

Labels NH, NL, NS, ZO, PS , PL and PH represent the negative huge, negative large, negative small,zero, positive small, positive large and positive huge respectively.

The fuzzy logic rules are similar the below example:

IF (P, D) THEN V,

where P and D are fuzzy sets for current and gradient of the current as inputs and V is output fuzzy setto determine output voltage.

PID Fuzzy controller designed as three separate controllers, that output voltage for piezoelectric comesfrom summation of this controllers. It has been in this way to have a good adjustment for the fuzzycontroller to achieve best performance. First is a D controller for removing oscillation, second is PDcontroller, cause to minimizing deflection and third is I controller to make deflection about zero.

To achieve desired voltage, the rules of D, PD, and I controller are shown in Table 1, 2 and 3. PDcontroller uses the min intersection operator and all controllers use centroid method fordefuzzification.

Table 1. D FUZZY Control Rules.

dI NL NS ZO PS PLV NL NS ZO PS PL

Table 2. PD FUZZY Control Rules.

I dI NL NS ZO PS PL

NL PL PL ZO ZO ZO NS PL PS ZO NS NS

ZO PS PS ZO NS NSPS PS PS ZO NS NLPL ZO ZO ZO NL NL


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Table 3. I FUZZY Control Rules.

)( 0 I I NL NS ZO PS PLV NL NS ZO PS PL

Defuzzifier factors, K D , K PD and K I were used to easily tune the effect of each controller.

4. Numerical Results and Discussion

For this simulation, quality factor is considered 1. The geometrical and material properties of usedmodel and defuzzifier factors are listed in Table 4 as:

Table 4. Geometrical and material properties of the MEM actuator and piezoelectric layers.

MEM Actuator Piezoelectric layer (PZT-4)Length 270 m 270 mWidth 60 m 60 mHeight 2 m 0.01 mYoungs modulus 190 (GPa) 78.6 (GPa)

Poissons ratio 0.06 0.3Mass density 2331 (Kg/m 3) 7500 (Kg/m 3)

31e - -9.29 ( )mvolt N . 0g (initial gap) 1.5 m

(Permittivity of air) 8.854187 10 -12 (F/m) Defuzzifier

factors

K D = 0.9 K PD = 0.3 K I = 0.5

Step response of sensor for applied acceleration 5 g and -5 g shows in Fig. 6. As it can be seen, sensorresponses are different for the positive and negative acceleration, although have a robust behavior innegative acceleration. Deflection is very small (about 1

o

A ) and Response time is about 25 s.

Controller's outputs are shown in Fig. 7 for applied acceleration 5g, and -5g, respectively .

Behavior of system due to harmonic accelerations simulated with maximum acceleration of 5 g for30 KHz and 50 g for 1 KHz. As can be seen, this sensor has good results in harmonic acceleration withconsidering its relative lower deflection (Fig.8-11).


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26

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10 -4

-4

-2

0

2

4

6

8

10x 10 -11 deflection of beam for st ep acceleration input

time

d e

f l e c

t i o n

+5g-5g

Fig. 6. S tep response for applied acceleration 5g and -5g.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10 -4

-2

-1.5

-1

-0.5

0

0.5

1

1.5x 10 -4 pizoeelectric voltage

time

p i z e o e

l e c

t r i c v o

l t a g e

[ V ]

5g-5g

Fig. 7. Piezoelectric voltage for applied acceleration 5g and -5g.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-4

-4

-2

0

2

4

6

8x 10 -11 deflection of beam for step acceleration input

time

d e

f l e c

t i o n

Fig. 8. Deflection vs. time for 5g 30 KHz.


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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10 -4

-1.5

-1

-0.5

0

0.5

1


time

p i z e o e

l e c

t r i c v o

l t a g e

[ V ]

Fig. 9. Piezoelectric voltage vs. time for 5 g 30 KHz.

0 0.5 1 1.5 2 2.5

x 10 -3

-8

-6

-4

-2

0

2

4

6x 10 -11 deflection of beam for s tep acceleration input

time

d e

f l e c

t i o n

Fig. 10. Deflection vs. time for 50g 1 KHz.

0 0.5 1 1.5 2 2.5

x 10 -3

-1.5

-1

-0.5

0

0.5

1


time

p i z e o e

l e c

t r i c v o

l t a g e

[ V ]

Fig. 11. Piezoelectric voltage vs. time for 50 g 1 KHz.


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As it is shown in Fig. 12, the Linearity of the designed sensor is about


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[10]. C. -H. Liu, et al., Characterization of a high-sensitivity micromachined tunneling accelerometer withmicro-g resolution, J. Microelectromech. Syst ., 7, 1998, pp. 235245.

[11]. C. Yeh, K. Najafi, A low-voltage tunneling-based silicon microaccelerometer, IEEE Trans. Electr. Devices , 44, 1997, pp. 18751882.

[12]. C. Yeh, K. Najafi, CMOS interface circuitry for a low-voltage micromachined tunneling accelerometer, J. Microelectromech. Syst ., 7, 1998, pp. 616.

[13]. J. Wang, et al., Synthesis of the modeling and control systems of a tunneling accelerometer using theMatlab simulation, Micromech. Microeng ., 12, 2002, pp. 730735.[14]. T. W. Kenney, et al., Micromachined silicon tunnel sensor for motion detection, Appl. Phys. Lett ., 58,

1991, pp. 100103.[15]. Gh. Rezazadeh, A. Tahmasebi and Mikhail Zubtsov, Application of Piezoelectric Layers in Electrostatic

MEM Actuators: Controlling of Pull-in Voltage, Journal of Microsystem Technologies , Vol. 12, No. 12,2006, pp. 1163-1170.

[16]. Zadeh, L. A., Fuzzy Sets and Systems. In Fox, J., ed., Proceedings Symposium on System Theory,Polytechnic Institute of Brooklyn , April 1965, pp. 29-37.

[17]. L. A. Zadeh, Outline of a new Approach to the Analysis of Complex Systems and Decision Process, IEEE Transactions on Systems , Man and Cybernetics, Vol. 3, 1973, pp. 28-44.

[18]. E. H. Mamdani, Fuzzy Sets for Man - Machine Interaction, IEEE Transactions on Computer , Vol. 26,1977, pp. 1182-1191.

[19]. G. Genta, Vibration of Structures and Machines, SpringerVerlag , 2000.[20]. Philip W. Barth, et al, A Monolithic Silicon Accelerometer With Integral Air Damping and Overange

Protection, IEEE Solid-State Sensor and Actuator Workshop , June 1988, pp. 35- 38.[21]. E. F. Crawley and J. de Luis, Use of Piezoelectric Actuators as Elements of Intelligent Structures, AIAA

Journal , 25, 10, 1987, pp. 1373-1385.[22]. Tianhong Cui and Jing Wang, Polymer-Based Wide-Bandwidth and High-Sensitivity Micromachined

Electron Tunneling Accelerometers Using Hot Embossing, Journal of Microelectromechanical Systems ,Vol. 14, No. 5, October 2005.

[23]. Liu, Y., Gordaninejad, F., Evrensel, C. A., Hitchcock, G., Wang, X., Variable Structure System BasedFuzzy Logic Control of Bridge Vibration Using Fail-Safe Magneto-Rheological Fluid Dampers,

Proceedings of SPIE Conference on Smart Materials and Structures, San Diego, March 2002.

___________________

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studying of a tunneling accelerometer with piezoelectric actuation and fuzzy controller

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