research article a tent map based conversion circuit for ...tent map on the initial value (the...

Hindawi Publishing CorporationJournal of SensorsVolume 2013 Article ID 624981 5 pageshttpdxdoiorg1011552013624981

Research ArticleA Tent Map Based 119860119863 Conversion Circuit forRobot Tactile Sensor

Jianxin Liu1 Xuan Zhang2 Zhiming Li2 and Xuling Li2

1 NARI Technology Development Limited Company Nanjing 210061 China2 Experiment amp Verification Center State Grid Electric Power Research Institute Nanjing 210061 China

Correspondence should be addressed to Xuan Zhang sherryzhangxuangmailcom

Received 10 July 2013 Accepted 25 July 2013

Academic Editor Aiguo Song

Copyright copy 2013 Jianxin Liu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Force and tactile sensors are basic elements for robot perception and control which call for large range and high-accuracy amplifierIn this paper a novel 119860119863 conversion circuit for array tactile sensor is proposed by using nonlinear tent map phenomenon whichis characterized by sensitivity to small signal and nonlinear amplifying function The tent map based 119860119863 conversion circuits cansimultaneously realize amplifying and 119860119863 converting functions The proposed circuit is not only simple but also easy to integrateand produce It is very suited for multipath signal parallel sampling and 119860119863 converting of large array tactile sensor

1 Introduction

In recent decades with the rapidly development of robottechnology robot sensors have received much attention asa sensing element for robot Multiaxis force sensors andarray tactile sensors usually called haptic sensors especiallyhave become the major research content in the robot sensorresearch areas [1 2] People hope that robot haptic sensorcan be like human perception organs which have high mea-surement accuracy with similar hand force and tactile organof integration miniaturization and flexibility characteristicsFor instance Song developed a small four-degree-of-freedomwrist force sensor with high precision which consists ofsmall cross-elastic beam compliant beams and the base ofthe elastic body It is a kind of self-decoupling force sensorin mechanical structure [3] Beyeler et al designed a six-axis MEMS force sensor with a movable body suspended byflexures which allow deflections and rotations along the 119909-119910- and 119911-axes And the orientation of this movable bodyis sensed by seven capacitors based on transverse sensingresulting in a high sensitivity [4] Ma et al proposed a novelnonlinear static decoupling algorithm based on the establish-ment of a coupling error model for 3-axis force sensor inorder to avoid overfitting and minimize the negative effectof random noises in calibration data which can obtain

high precise measurement results of 3-axis force for robotforce control [5] Although robot array tactile sensor canbe regarded as a multipoint integrated force sensor due toflexible and miniaturization requirements of tactile sensorwhich are high the measurement principle is more complexthan the multiaxis force sensor [6 7] Song et al proposed anovel design of a haptic texture sensor by using PVDF filmto fabricate a high-accuracy high-speed-response texturesensor [8] Lee and Won developed a novel tactile imagingsensor by using a multilayer polydimethylsiloxane opticalwaveguide as the sensing probe which is capable of mea-suring the elasticity of the touched object with high preci-sion [9] Based on semiconductor technique piezoresistivecapacitive piezoelectric and other types of robot array tactilesensors are developing rapidly Array tactile sensors havea corresponding increase in array size and resolution [1011] Nonetheless because of measurement mechanism limitoutput signal of sensing element of most high-resolutiontactile sensors is relatively weak In addition as the expansionof tactile array it hopes that tactile image signal has a fast119860119863conversion rate Sharing the same 119860119863 conversion in smallscale tactile sensor cannot meet the real-time requirementsof signal acquisition for the large scale array tactile sensor

In recent years some of the unique properties of nonlin-ear systems have much in measurement area for their unique

2 Journal of Sensors

Read circuit

sensitive array

element Line scan circuitTiming

control circuit

Computer signal

processing etc

Interface circuitm times n

Figure 1 Tactile sensor array signal acquisition circuit

character such as the chaotic system sensitivity to small signal[12] nonlinear mapping [13] nonlinear information storage[14] and resonance stochastic [15] In this paper a tent mapis sensitive to small signal circuit and nonlinear transform ofunique properties A novel 119860119863 conversion circuit for robottactile sensor array is proposed to achieve parallel samplingof multichannel tactile signals and119860119863 conversion with highcost performance which has a conditioning amplificationand119860119863 conversion function integration advantages in com-bination simple circuit and easy integration to realize

2 Signal Acquisition System forRobot Tactile Sensor

Typical signal acquisition circuit for robot tactile sensor isshown in Figure 1 including timing control circuit line scancircuit read circuit and interface circuit The whole signalacquisition process was controlled and coordinated by timingcontrol circuit According to the arrangements of the timingcontrol circuit line scan circuit is ordered in 119898 clock cyclesto send the periodic excitation signal to119898-line array sensitiveelement while the read circuit is ordered in119898 clock cycles toread the output signal of 119899 column in parallel Then throughinterface circuit which consists of signal conditioning and119860119863 conversion tactile signals were transferred to the com-puter for processing and target recognition

Conventional robot array tactile sensor because of thesmall array size (about 8 times 8) often uses an 119860119863 conversionin order to complete the analog-digital conversion of outputsignal of119898 times 119899 sensitive elements

3 Small Signal Nonlinear Amplifier and119860119863 Conversion Based on Tent Map

Tent map was a typical one-dimensional chaotic system [16]which was described as

119909119899+1= 119879 (119909

119899) =

2119909119899 0 lt 119909

119899le 05

2 (1 minus 119909119899) 05 lt 119909

119899lt 1

(1)

where 119909119899isin [0 1] 119899 = 0 1 2

This map consisted of two steps the first step was touniformly elongate the interval [0 1] to its doubled rangethe second step was to fold the elongated interval into theoriginal interval [0 1]These iterative operations would causethe separation of adjacent points index eventually to achievethe state of chaos

Tent map on the initial value (the system input signal)amplification was different from the linear amplification

method Linear amplification multiples were a constant andalso limited by system operating range Tent map system inchaotic state amplified the signal doubly and folded the dou-bled range symmetrically in each iteration so that the initialsmall signal could eventually be greatly amplified withoutbeyond range of system operating after several iterations

The initial value 1199090 whichwas corresponding to the input

signal of tent map system 119881in could be described as a binaryfraction

1199090= 0119905011990511199052sdot sdot sdot =

infin

sum

119895=0

119905119895

2119895+1 (2)

In order to obtain the relationship of the iterative outputand the initial signal of discrete tent map here this paperwould introduce the nonlinear relationship of Bernoulli shiftits kinetic equation was

1199091015840

119899+1= 119861 (119909

1015840

119899) =

21199091015840

119899 0 lt 119909

1015840

119899le 05

21199091015840

119899minus 1 05 lt 119909

1015840

119899lt 1

(3)

In each iteration Bernoulli shift left shifted the binaryfraction 119905

1 1199052 one place

1199091015840

1= 119861 (119909

1015840

0) = 0119905

111990521199053sdot sdot sdot

1199091015840

2= 119861 (119909

1015840

1) = 0119905


(4)

For Bernoulli shift 119887119899= sgn(1199091015840

119899minus 05) was defined as the

119899th iteration output there 119887119899= 119905119899 and 119887

119894 119894 = 0 1 2 was a

binary sequence For tentmap if we define 119892119899= sgn(119909

119899minus05)

then the corresponding relationship between 119892119894 119894 = 0 1 2

and 119887119894 119894 = 0 1 2 was as follows

(1) when 0 lt 119909119896lt 025 that is 119887

119896= 0 then 119861(119909

119896) lt

05 119887119896+1= 0 119879(119909

119896) lt 05 and 119892

119896+1= 0

(2) when 025 lt 119909119896lt 05 that is 119887

119896= 0 then 119861(119909

119896) gt

05 119887119896+1= 1 119879(119909

119896) gt 05 and 119892

119896+1= 1

(3) when 05 lt 119909119896lt 075 that is 119887

119896= 1 then 119861(119909

119896) lt

05 119887119896+1= 0 119879(119909

119896) gt 05 and 119892

119896+1= 1

(4) when 075 lt 119909119896lt 1 that is 119887

119896= 1 then 119861(119909

119896) gt

05 119887119896+1= 1 119879(119909

119896) lt 05 and 119892

119896+1= 0

Therefore 119892119894 119894 = 0 1 2 was a Gray-code sequence of 119887

119894

119894 = 0 1 2

119892119896+1= 119887119896oplus 119887119896+1 119896 = 0 1 2 (5)

According to the above formula and initial time1199090= 1199091015840

0=

119881in we could obtain

119887119896+1= 119887119896oplus 119892119896+1 119896 = 0 1 2

1198870= 1198920

(6)

So we designed a tent map iteration output Gray-codesequence119892

119894 119894 = 0 1 2 into a binary sequence of Bernoulli

Journal of Sensors 3

Table 1 Results of the AD conversion

Sensitive element (8 1) (8 2) (8 3) (8 4) (8 5) (8 6) (8 7) (8 8)Output value (mV) 0 0 0 0 25 80 188 246Gray code11989201198921119892211989231198924119892511989261198927

00000000 00000000 00000000 00000000 00000101 00011111 00101000 00100001

Binary code11988701198871119887211988731198874119887511988761198877

00000000 00000000 00000000 00000000 00000110 00010101 00110000 00111110

Calculated value(mV) 00 00 00 00 234 820 1875 2422


01101000 00100111 00111110 00011001 00001100 00000000 00000000 00000000

Binary code11988701198871119887211988731198874119887511988761198877

01001111 00111010 00101011 00010001 00001000 00000000 00000000 00000000


Φ1

Φ1

Φ2

Φ2

VI

VO

C2

C1

T1 T2

minus

+

Figure 2 Switched capacitor integral circuit

map 119887119894 119894 = 0 1 2 and then calculated the initial value

through binary fraction sequence as follows

1199090=

119873

sum

119895=0

119887119895

2119895+1 (7)

where 119892119894 119894 = 0 1 2 was the needed digital value Here

tentmap completed signal amplification and119860119863 conversionfunction

4 Implementation on the Circuit ofTent Map for 119860119863 Conversion

119860119863 circuit basic element was switched capacitor integralcircuit shown in Figure 2 where 119879

1and 119879

2were analog

switches and 1198621and 119862

2were capacitors The clocks Φ

1 Φ2

were in reverse phase with same period 119879 During the formerhalf period of119879 the119879

1was on and119879

2was off thus the119862

1was

charged by input voltage 119881119868 During the latter half period of

119879 1198791was off and 119879

2was on so that the 119862

2was charged by

1198621119881119868 The output voltage of this circuit in a period was

119881119900(119899119905) = 119881

119900((119899 minus 1) 119905) minus

1198621

1198622

119881119868((119899 minus 1) 119905) (8)

The tent map circuit consisted of the above circuit asshown in Figure 3 Parts I and III implemented the functionof 119910 = 2119909 and parts II and III implemented the function of119910 = 2(1 minus 119909) Part IV was a circuit for holding and delay

Figure 4 shows the control logic for 119860119863 conversionFirst start signal got high and switch 119869

0connected the input

signal with the part I and part II After delay of 1199051 119863 trigger

produces a switch instruction if 0 le 119881119894le 05 then 119869

1was

switched on if 05 lt 119881119894lt 1 then 119869

2was switched on At

time 1199051+ 1199052 the control signal 119890 switches were high so that

the charge of 1198621or 1198622was transferred to 119862

3 due to 119862

3=

(12)1198621= (12)119862

2 so that the input voltage was amplified

doubly In the meantime 1198624was also charged At the next

time 0 the 119900 switches were switched off and e switches wereswitched on so that the charge of119862

4was transferred to119862

5and

results in 1198811198625

= 1198811198624

At the same time 1198690was disconnected

with input signal 1198810 so that an iterative feedback loop exists

in the 119860119863 conversion and 1198621 1198622were charged by the same

feedback voltage to realize 119910 = 2119909 and 119910 = 2(1 minus 119909) Thiscircle continuously iterated119873 times

Hence the119873 binary bits output of119863 trigger was the Gray-code sequence of 119860119863 conversion

119892119896= 119876119896(119896 = 1 2 3 )

1198870= 1198760

(9)

The above 119892119896sequence the initial condition 119887

0= 1198760into

(6) and Bernoulli binary sequence 119887119896(119896 = 0 1 2 ) could

be obtained

5 Array Tactile Sensor Signal AcquisitionSystem Based on Tent Map of 119860119863 Circuit

The schematic diagram of signal amplification of array tactilesensor analog and119860119863 conversion based on tent map circuitis shown in Figure 5 According to the arrangements of thetiming control circuit line scan circuit sent the periodicexcitation signal to 119898-line array sensitive element while theread circuit read the output signal of 119899 column in parallelThe119899-column signal was generated by simultaneously signalingnonlinear amplification and analog-digital conversion of 119899of 119860119863 converters based on tent map The resulting Gray-code sequence was sent directly to the computer which will


D

trigger

e

o

o

o

o

o

o

o

e

e

e

e

e

e

CP+ +

+

[I]

[II]

[III] [IV]

VO

VO

Vi

C2

C3

C4

C5

C1

minus minusminus

J0

J1

J2

Q

Q

1 V

05 V

Figure 3 The circuit of tent map for 119860119863 conversion

o

e

cp

Start

tetot1 t2

Figure 4 Circuit logic for the 119860119863 conversion

Columnread

circuitsensitive element

Line scan circuit Timing control circuit

Computer signal

processing etc

ADC 1

ADC 2

ADC n

m times n array

middot middot middot

Figure 5 The schematic diagram of array tactile sensor signalacquisition system based on tent map of 119860119863 circuit

complete the conversion of Gray code to binary code Thenunder the control of timing logic the read 119899-column signalon the next line and the completed amplification and 119860119863conversion after obtaining an 119898 times 119899 tactile image signal bythe computer we could process tactile signals

We could carry out the amplification and119860119863 conversionexperiments sensitive element signal of 16 times 16 microarraytactile sensor based on the above circuit The results ofthe 119860119863 conversion for eight sensitive elements in the8th line were shown in Table 1 which indicates that 119860119863circuits based on the tent map could effectively achieve theamplification and 119860119863 conversion of a small signal

Figure 6 is the output of a 16 times 16 micro array tactilesensor manufactured by us based on the tent map circuitwhen a very light hexagon aluminum flake was put on itThemeasurement range of each tactile sensing unit was from001N to 10N which shows that the proposed tent map

Figure 6 The output of a 16 times 16 array tactile sensor based on thetent map circuit when a very light hexagon aluminum flake was puton it

based 119860119863 conversion circuits had the advantages of largeamplification range and high resolution By comparison withthe conventional high precision array tactile sensor [17] ourmethod is more cost effective and easier to realize

6 Conclusion

This paper presents a novel 119860119863 conversion circuit for robotarray tactile sensor of unique properties The circuit makesuse of unique advantage for tent map sensitive to small signalcircuit and nonlinear transform and has conditioning ampli-fication and 119860119863 conversion function integration advan-tages simple circuit and easy integration to realize Thismethod can achieve the parallel sampling of multichanneltactile signal and 119860119863 converter which can meet the real-time requirements of signal acquisition for the large scalearray tactile sensor This experiment gives the effectivenessof this method

Acknowledgments

This work was supported by the Science and Technology Pro-ject of National Energy Administration (no NY20110702-1)


and the Technology Project of State Grid Corporation ofChina in 2013-2014 (project name is Study of Testing andDetection Technology for Electric Vehicle Charging andBattery Swap Infrastructure)

References

[1] H Yousef M Boukallel and K Althoefer ldquoTactile sensing fordexterous in-handmanipulation in roboticsmdasha reviewrdquo Sensorsand Actuators A vol 167 no 2 pp 171ndash187 2011

[2] J Ma and A Song ldquoFast estimation of strains for cross-beamssix-axis forcetorque sensors bymechanical modelingrdquo Sensorsvol 13 no 5 pp 6669ndash6686 2013

[3] A Song J Wu G Qin and W Huang ldquoA novel self-decoupledfour degree-of-freedom wrist forcetorque sensorrdquo Measure-men vol 40 no 9-10 pp 883ndash891 2007

[4] F Beyeler S Muntwyler and B J Nelson ldquoA six-axis MEMSforce-torque sensor with micro-Newton and nano-Newton-meter resolutionrdquo Journal of Microelectromechanical Systemsvol 18 no 2 pp 433ndash441 2009

[5] JMaA Song and J Xiao ldquoA robust static decoupling algorithmfor 3-axis force sensors based on coupling error model and 120576-SVRrdquo Sensors vol 12 no 11 pp 14537ndash14555 2012

[6] J-H Kim J-I Lee H-J Lee Y-K Park M-S Kim andD-I Kang ldquoDesign of flexible tactile sensor based on three-component force and itsrdquo in Proceedings of the IEEE Interna-tional Conference on Robotics and Automation pp 2578ndash2581April 2005

[7] M H Lee and H R Nicholls ldquoTactile sensing for mecha-tronicsmdasha state of the art surveyrdquoMechatronics vol 9 no 1 pp1ndash31 1999

[8] A Song Y Han H Hu L Tian and J Wu ldquoActive perception-based haptic texture sensorrdquo Sensors and Materials vol 25 no1 pp 1ndash15 2013

[9] J-H Lee and C-HWon ldquoHigh-resolution tactile imaging sen-sor using total internal reflection and nonrigid pattern match-ing algorithmrdquo IEEE Sensors Journal vol 11 no 9 pp 2084ndash2093 2011

[10] J Dargahi and S Najarian ldquoAdvances in tactile sensors designmanufacturing and its impact on robotics applicationsmdashareviewrdquo Industrial Robot vol 32 no 3 pp 268ndash281 2005

[11] S Saga H Kajimoto and S Tachi ldquoHigh-resolution tactile sen-sor using the deformation of a reflection imagerdquo Sensor Reviewvol 27 no 1 pp 35ndash42 2007

[12] N Singh and A Sinha ldquoChaos-based secure communicationsystemusing logisticmaprdquoOptics and Lasers in Engineering vol48 no 3 pp 398ndash404 2010

[13] L Zhang A Song and J He ldquoStochastic resonance of a subdif-fusive bistable system driven by Levy noise based on the sub-ordination processrdquo Journal of Physics A vol 42 no 47 ArticleID 475003 2009

[14] A Song J Duan JWu andH Li ldquoDesign 2D nonlinear systemfor information storagerdquoChaos Solitons and Fractals vol 41 no1 pp 157ndash163 2009

[15] D Rousseau J R Varela and F Chapeau-Blondeau ldquoStochas-tic resonance for nonlinear sensors with saturationrdquo PhysicalReview E vol 67 no 2 Article ID 021102 6 pages 2003

[16] X Yi ldquoHash function based on chaotic tent mapsrdquo IEEE Tran-sactions on Circuits and Systems II vol 52 no 6 pp 354ndash3572005

[17] H-K Kim S Lee and K-S Yun ldquoCapacitive tactile sensorarray for touch screen applicationrdquo Sensors andActuators A vol165 no 1 pp 2ndash7 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Read circuit

sensitive array

element Line scan circuitTiming

control circuit

Computer signal

processing etc

Interface circuitm times n

Figure 1 Tactile sensor array signal acquisition circuit

character such as the chaotic system sensitivity to small signal[12] nonlinear mapping [13] nonlinear information storage[14] and resonance stochastic [15] In this paper a tent mapis sensitive to small signal circuit and nonlinear transform ofunique properties A novel 119860119863 conversion circuit for robottactile sensor array is proposed to achieve parallel samplingof multichannel tactile signals and119860119863 conversion with highcost performance which has a conditioning amplificationand119860119863 conversion function integration advantages in com-bination simple circuit and easy integration to realize

2 Signal Acquisition System forRobot Tactile Sensor

Typical signal acquisition circuit for robot tactile sensor isshown in Figure 1 including timing control circuit line scancircuit read circuit and interface circuit The whole signalacquisition process was controlled and coordinated by timingcontrol circuit According to the arrangements of the timingcontrol circuit line scan circuit is ordered in 119898 clock cyclesto send the periodic excitation signal to119898-line array sensitiveelement while the read circuit is ordered in119898 clock cycles toread the output signal of 119899 column in parallel Then throughinterface circuit which consists of signal conditioning and119860119863 conversion tactile signals were transferred to the com-puter for processing and target recognition

Conventional robot array tactile sensor because of thesmall array size (about 8 times 8) often uses an 119860119863 conversionin order to complete the analog-digital conversion of outputsignal of119898 times 119899 sensitive elements

3 Small Signal Nonlinear Amplifier and119860119863 Conversion Based on Tent Map

Tent map was a typical one-dimensional chaotic system [16]which was described as

119909119899+1= 119879 (119909

119899) =

2119909119899 0 lt 119909

119899le 05

2 (1 minus 119909119899) 05 lt 119909

119899lt 1

(1)

where 119909119899isin [0 1] 119899 = 0 1 2

This map consisted of two steps the first step was touniformly elongate the interval [0 1] to its doubled rangethe second step was to fold the elongated interval into theoriginal interval [0 1]These iterative operations would causethe separation of adjacent points index eventually to achievethe state of chaos

Tent map on the initial value (the system input signal)amplification was different from the linear amplification

method Linear amplification multiples were a constant andalso limited by system operating range Tent map system inchaotic state amplified the signal doubly and folded the dou-bled range symmetrically in each iteration so that the initialsmall signal could eventually be greatly amplified withoutbeyond range of system operating after several iterations

The initial value 1199090 whichwas corresponding to the input

signal of tent map system 119881in could be described as a binaryfraction

1199090= 0119905011990511199052sdot sdot sdot =

infin

sum

119895=0

119905119895

2119895+1 (2)

In order to obtain the relationship of the iterative outputand the initial signal of discrete tent map here this paperwould introduce the nonlinear relationship of Bernoulli shiftits kinetic equation was

1199091015840

119899+1= 119861 (119909

1015840

119899) =

21199091015840

119899 0 lt 119909

1015840

119899le 05

21199091015840

119899minus 1 05 lt 119909

1015840

119899lt 1

(3)

In each iteration Bernoulli shift left shifted the binaryfraction 119905

1 1199052 one place

1199091015840

1= 119861 (119909

1015840

0) = 0119905


1199091015840

2= 119861 (119909

1015840

1) = 0119905


(4)

For Bernoulli shift 119887119899= sgn(1199091015840

119899minus 05) was defined as the

119899th iteration output there 119887119899= 119905119899 and 119887

119894 119894 = 0 1 2 was a

binary sequence For tentmap if we define 119892119899= sgn(119909

119899minus05)

then the corresponding relationship between 119892119894 119894 = 0 1 2

and 119887119894 119894 = 0 1 2 was as follows

(1) when 0 lt 119909119896lt 025 that is 119887

119896= 0 then 119861(119909

119896) lt

05 119887119896+1= 0 119879(119909

119896) lt 05 and 119892

119896+1= 0

(2) when 025 lt 119909119896lt 05 that is 119887

119896= 0 then 119861(119909

119896) gt

05 119887119896+1= 1 119879(119909

119896) gt 05 and 119892

119896+1= 1

(3) when 05 lt 119909119896lt 075 that is 119887

119896= 1 then 119861(119909

119896) lt

05 119887119896+1= 0 119879(119909

119896) gt 05 and 119892

119896+1= 1

(4) when 075 lt 119909119896lt 1 that is 119887

119896= 1 then 119861(119909

119896) gt

05 119887119896+1= 1 119879(119909

119896) lt 05 and 119892

119896+1= 0

Therefore 119892119894 119894 = 0 1 2 was a Gray-code sequence of 119887

119894

119894 = 0 1 2

119892119896+1= 119887119896oplus 119887119896+1 119896 = 0 1 2 (5)

According to the above formula and initial time1199090= 1199091015840

0=

119881in we could obtain

119887119896+1= 119887119896oplus 119892119896+1 119896 = 0 1 2

1198870= 1198920

(6)

So we designed a tent map iteration output Gray-codesequence119892

119894 119894 = 0 1 2 into a binary sequence of Bernoulli




00000000 00000000 00000000 00000000 00000101 00011111 00101000 00100001

Binary code11988701198871119887211988731198874119887511988761198877

00000000 00000000 00000000 00000000 00000110 00010101 00110000 00111110



01101000 00100111 00111110 00011001 00001100 00000000 00000000 00000000

Binary code11988701198871119887211988731198874119887511988761198877

01001111 00111010 00101011 00010001 00001000 00000000 00000000 00000000


Φ1

Φ1

Φ2

Φ2

VI

VO

C2

C1

T1 T2

minus

+




1199090=

119873

sum

119895=0

119887119895

2119895+1 (7)





1and 119879

2were analog



1 Φ2


1was on and119879


1was


119879 1198791was off and 119879


2was charged by


119881119900(119899119905) = 119881

119900((119899 minus 1) 119905) minus

1198621

1198622

119881119868((119899 minus 1) 119905) (8)






1was


2was switched on At



3 due to 119862

3=

(12)1198621= (12)119862





5and

results in 1198811198625

= 1198811198624






119892119896= 119876119896(119896 = 1 2 3 )

1198870= 1198760

(9)


0= 1198760into


be obtained




D

trigger

e

o

o

o

o

o

o

o

e

e

e

e

e

e

CP+ +

+

[I]

[II]

[III] [IV]

VO

VO

Vi

C2

C3

C4

C5

C1

minus minusminus

J0

J1

J2

Q

Q

1 V

05 V


o

e

cp

Start

tetot1 t2


Columnread



Computer signal

processing etc

ADC 1

ADC 2

ADC n

m times n array








6 Conclusion


Acknowledgments




References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












00000000 00000000 00000000 00000000 00000101 00011111 00101000 00100001

Binary code11988701198871119887211988731198874119887511988761198877

00000000 00000000 00000000 00000000 00000110 00010101 00110000 00111110



01101000 00100111 00111110 00011001 00001100 00000000 00000000 00000000

Binary code11988701198871119887211988731198874119887511988761198877

01001111 00111010 00101011 00010001 00001000 00000000 00000000 00000000


Φ1

Φ1

Φ2

Φ2

VI

VO

C2

C1

T1 T2

minus

+




1199090=

119873

sum

119895=0

119887119895

2119895+1 (7)





1and 119879

2were analog



1 Φ2


1was on and119879


1was


119879 1198791was off and 119879


2was charged by


119881119900(119899119905) = 119881

119900((119899 minus 1) 119905) minus

1198621

1198622

119881119868((119899 minus 1) 119905) (8)






1was


2was switched on At



3 due to 119862

3=

(12)1198621= (12)119862





5and

results in 1198811198625

= 1198811198624






119892119896= 119876119896(119896 = 1 2 3 )

1198870= 1198760

(9)


0= 1198760into


be obtained




D

trigger

e

o

o

o

o

o

o

o

e

e

e

e

e

e

CP+ +

+

[I]

[II]

[III] [IV]

VO

VO

Vi

C2

C3

C4

C5

C1

minus minusminus

J0

J1

J2

Q

Q

1 V

05 V


o

e

cp

Start

tetot1 t2


Columnread



Computer signal

processing etc

ADC 1

ADC 2

ADC n

m times n array








6 Conclusion


Acknowledgments




References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










D

trigger

e

o

o

o

o

o

o

o

e

e

e

e

e

e

CP+ +

+

[I]

[II]

[III] [IV]

VO

VO

Vi

C2

C3

C4

C5

C1

minus minusminus

J0

J1

J2

Q

Q

1 V

05 V


o

e

cp

Start

tetot1 t2


Columnread



Computer signal

processing etc

ADC 1

ADC 2

ADC n

m times n array








6 Conclusion


Acknowledgments




References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article a tent map based conversion circuit for ...tent map on the initial value (the...

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