4 structures of sensor systems - tu chemnitz

4 Structures of Sensor Systems

4.1 Chain Structure

4.3 Closed Loop Structure

4.2 Parallel Structure

4.2.1 Sum Principle4.2.2 Difference Principle

4.2.4 Reference Principle4.2.3 Differential Principle

P. 4-1Prof. Dr.-Ing. O. KanounChair for Measurement and Sensor Technology

Structure of Measurement Systems

MeasurementSignal

Energy Supply

Indicator,Recorder,Counter

Measuring Amplifier,Electronical Computer

Measuring Transducer

MeasuredVariable

MeasurementSignal

Output Unit

InterfaceElementarSensor

Data

VDI/VDE 2600

4.0 Introduction


Sensor signaly

Zero Pointy(x=0) = e0

Measurement quantitiy

Transmission factor k

0exky

Item: Linear Sensor4.0 Introduction

Sensitivity xyE

x


0

k1 k2 k3x0

x1=k1 x0 x2= k2 x1 x3 =k3 x2

Thermo Couple AmplifierT Uth IA

Display

Y

x3=k3 k2 k1 x0

x3= (k3 + k3) (k2+k2) (k1+ k1 ) x0

Multiplicative Deviations: Deviations of transmissions factors

Error Propagation!!!

4.1 Chain Structure


k1 k2 k3x0

x1=k1 x0+e1

e1 e2 e3

x2=k2 (k1 x0+e1)+e2

x3= [k2 (k1 x0+e1) +e2] k3+e3

=k3k2k1 x0 + k3k2 e1 + k3e2 + e3

x1 x2 x3

Additive deviations are multiplied by the transmission factorsand involve an additional zero-displacement

4.1 Chain Structure

Linear dependence of transmission factors of T non-linear dependence of the whole transmission factors of T

x3 = k3(T) k2(T) k1(T) x0 + k3(T) k2(T) e1 + k3(T)e2 + e3

Temperature Effect


0 -1000°C

0-40mV 0-100mA 0°-180°Thermo Couple

(Typ K) AmplifierT Uth = kth T IA = kA Uth

Display

y = kdisp IA

e1

0 200 400 600 800 1000 12000.00

0.05

0.10

0.15

0.20

UthIADisplay

T in °C

Uth

in V

, IA

in A

, Dis

p/ 1

000

in °

2 mV additive deviation at the thermo couple

9 °C

5 mA

2 mV

T in °C

0 200 400 600 800 1000 12000.00

0.05

0.10

0.15

0.20

0.25

0.30

UthIADisplay

Uth

in V

, IA

in A

, Dis

p/ 1

000

in °

10%

21%

33%

10% deviation of the transmission factors

The chain structure amplifies both multiplicativeand additive errors.

4.1 Chain Structure



k1xe1

k2xe2

+/- xa

e1

e2

4.2.1 Sum Principle

4.2.2 Difference Principle

Calculate the output Signal in the case of the difference principle. What is the advantage thereby?

Sensor1 and Sensor2 are identical.

Calculate the output Signal in the case of the sum principle. What is the advantage thereby?

Both Sensors are exposed to different input signals Xe1 and Xe2

Both Sensors are exposed to the same input signals Xe1 and Xe2



k1xe1

k2xe2

+/-

xa1= k1 xe1+ e1

xa2=k2 xe2 + e2

xa = k1 xe1+ e1 ± (k2 xe2 + e2)

e1

e2

4.2.1 Sum Principle

Averaging process


kxe1

kxe2

-

xa1=k xe1+e

xa2=k xe2+e

xa = k (xe1-xe2)

Elimination of the zero point

e

e

4.2.2 Difference Principle

But also generally:

Common-mode rejection


Compensation of Influence EffectsStrain gauge with the basic resistance R0

kx1

ey1 = k (R0 + RT + R) + e

y = k R-e

kx2

y2 = k (R0 + RT) + e

- Temperature T- Extensions

Compensation of temperature effect

4.2.2 Difference principle

Torque Measurement with strain gauge

thermal coupling

Strain gauge 2


Example: Capacitive Measurement of Water Volume in Oil

Sensor Structure

Compensation of Influence Effects4.2.2 Difference principle


Example: NDIR CO2-Sensor LIM032, InfraTec GmbH

[O. Zhelondz 2006]

IR Source Vessel

Filters Detectors

IURef

UMes

I0

LIM032

CO2

IR Source Vessel

Filters Detectors

IURef

UMes

I0

LIM032

CO2

4.2.2 Difference principle


Effects on Measurement and Reference Signal

Additive effects

Temperature drift of filter

Temperature drift of the pyrodetector

Multiplicative effectsChanges in radiation intensity

(Ageing, Pollution)

Temperature dependence of radiation intensity

Temperature and pressure dependence of absorption processes

CO2

URef

UMes

URef

UMesUmess

Uref

CO2

URef

UMes

URef

UMesUmess

UrefURef

UMes

URef

UMesUmess

Uref

Umess

Uref

X X + +

Example: NDIR CO2-Sensor4.2.2 Difference principle


CO2

URef

UMes

URef

UMesUmess

Uref

CO2

URef

UMes

URef

UMesUmess

UrefURef

UMes

URef

UMesUmess

Uref

Umess

Uref

aeIkU VCO LxMeas 2

aIkUref

Elimination of Undesired Effects (1)

12 VCO LxrefMeas eIkUU

Ika

Ikae

UU

VCO Lx

ref

Meas

1

2

Declination of multiplicative effects

Elimination of additive effects



CO2

URef

UMes

URef

UMesUmess

Uref

CO2

URef

UMes

URef

UMesUmess

UrefURef

UMes

URef

UMesUmess

Uref

Umess

Uref

122

VCOVCO

LxLx

ref

refMeas eIk

IkeIkaU

UU

aeIkU VCO LxMeas 2

aIkUref

VCO

VCOrefMeas

Lx

IkLxIkUU

2

2 )log()log(loglog

0aif• Declination of

multiplicative effects

• Linearization

• Elimination of multiplicative effects


Elimination of Undesired Effects (2)


)(

21 xRRR

)(

22 xRRR

)(2)(2

)(2

xRkexRRkexRRkyo

KR1

KR2

-

Advantages: • Common-mode rejection• Increase of sensibility

RRx

0

e

e

4.2.3 Differential Principle

Inverse dependence!


Example: Differential Capacitive Measurement

220

0021

2xdxbl

xdbl

xdblCC

r

rr

220

0021

2xddbl

xdbl

xdblCC

r

rr

d ddx

CCCC

21

21

d+x d-x

C1C2

b

l

Advantages: • Common mode rejection• Independent on geometry

21

21

CCCCdx

x: Displacement



Advantages: • common-mode rejection!• linearization

)(2020101 fxxaxxaay

)(2020102 fxxaxxaay

xxaayyytotal 02112 22

Linearization with parallel structure and differential principle

Sensor1

Sensor2



k

xkxx aa 12

rraa

aa

xx

xkxk

xxxx

13

12

raa xkxx 13

01 ex 01 exa

xxe 2 02 exkxa

re xx 3 03 exkx ra

Zero point

Measured variable

Reference value

13

12

aa

aar xx

xxxx

Advantages: • common-mode rejection• elimination of multiplicative errors

e0

4.2.4 Reference Principle


P. 4-20

Example: capacitive level measurement after the reference principle

x

h

C

C0

Cfull

C

C0

C

Cvoll

0

x

h

suppression of:• Additive errors e• Multiplicative errors k

Possibility for self-testsw: width of capacitor platesa

0

0

CCCChx

full

hawx

awCCC rliquidair 00 )1(

k e

k

e

r

r=1

4.2.4 Reference Principle

hawC 00

hawC rfull 0


Why are small weight differences detectable?

also called null mode or compensation method

Also for Gold and Diamond !


k1xe xa

kgxg

-

agegea xkxkxxkx 11

1

1

1

1 11

11

kforxk

xk

k

xkk

kx eg

e

g

eg

a

Advantages:

• Stability consideration necessary!• Dynamic is dependent on the inverse feedback

Disadvantages:


• Precision more dependent on kg• Suitable for small changes of sensor signal • Measurement without influence on the measured quantity


Example: Acceleration Sensor


1: Seismic Mass2: Bulk3: Capacitive Sensor4: Coil

[LETI, Grenoble]


P 4-23Prof. Dr.-Ing. O. KanounChair for Measurement and Sensor Technology

4.1-4.3 Chain-, Parallel and Closed Loop Structure

• Often used

• Additive and multiplicative errors are Amplified

Chain Structure

K1 K2x0

e1e2

x1 x2

• High Stability• Suitable for small

changes of sensor signal

• High precision• Possibility of Self-Tests• Sensor dynamic

Closed Loop Structure

K1xe xa

Kgxg

-

Parallel Structure

Common Mode RejectionDifferential measurement

Reference measurement

Kxi1

Kxi2

-xO

e

e

• higher sensitivity

• Elimination of multiplicative errors

• Possibility of Self-Tests


4 structures of sensor systems - tu chemnitz

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