Increase of accuracy of measurement signals reading from analog measuring transducers

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ZESZYTY NAUKOWE 5th INTERNATIONAL CONFERENCE POLITECHNIKI ŚLĄSKIEJ 2005 tfgAŃŚPORT SYSTEMS TELEMATICS TST’05 TRANSPORT z. 59, nr kol. 1691

increase of accuracy, dynamie correction, measurement transducers Mirosław L U F T 1

Radosław C IO Ć 2

INCREASE OF ACCURACY OF MEASUREMENT SIGNALS READING FROM ANALOG MEASURING TRANSDUCERS

The article presents way o f increase o f measurement signals accuracy o f reading defining safe criteria from analog measuring transducers. The increase o f accuracy has been obtained by software correction o f measuring transducer dynamic errors based on the differential equation o f mathematical model describing the transducer dynamics. Results o f the measuring transducer work simulation obtained before and after correction have been shown.

ZWIĘKSZANIE DOKŁADNOŚCI ODCZYTU SYGNAŁÓW POMIAROWYCH Z ANALOGOW YCH PRZETW ORNIKÓW POMIAROWYCH

Artykuł przedstawia sposób zwiększenia dokładności odczytu sygnałów pomiarowych z analogowych przetworników pomiarowych, określających kryteria bezpieczeństwa. Zwiększenie dokładności osiągnięto przez program ową korekcję błędów dynamicznych przetwornika pomiarowego opartą na równaniu różniczkowym opisującym jego dynamikę. Przedstawiono wyniki symulacji pracy przetwornika pomiarowego przed i po korekcji.

1. PREFACE

Means o f transport are being tested in view o f safe criteria on the basis o f measuring transducers data analysis. Accuracy o f transducer measurement, especially coming from his inertia, is important part o f measuring chain [1],

Software estimate o f measurand can be a corrective element o f measuring transducers dynamic errors [4], Measuring chain with correction o f dynamic errors is shown in Fig.l [5].

Faculty o f Transport, Technical University o f Radom, Malczewskiego 29, 26-600 Radom, Poland

¡® luft@pr radom.pl, phone (48) 3617071

acuity o f Transport, Technical University o f Radom, M alczewskiego 29, 26-600 Radom, Poland CIOC@pr.radom.pl, phone (48) 3617763

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2 8 2 M ir o sła w L U F T . R a d o sła w r p y -

x(t) - input signal e(t) - input noise signal

y(th) - result o f a measurement quantity in time v(k) - random noise signal

x(k)~ estimate o fx(t)

Fig. 1. Measuring chain with correction o f dynamic errors

2. MEASURING SYSTEM

Simulation o f dynamic errors correction has been done on the basis o f real data got ffom accelerometers which have been mounted on the electrodynamic vibration exciter. Output data has been obtained ffom measuring accelerometer with sensitivity l,16m V /m s'2. Standard data has been obtained ffom standard accelerometer with sensitivity 10,61mV/ms‘2. Function signals fiom two accelerometers have been watched on a digital oscilloscope ffom which the signals were transmitted to computer by RS232 and next calculated by software estmation.

Measurement system is shown in Fig.2.

Fig.2. M easuring system

3. IDENTIFICATION OF DYNAMIC PARAMETERS OF MEASURING SYSTEM

Algorithm o f dynamic correction needs knowledge o f dynamic parameters in form of n order differential equation. It was assumed that the parameters will be determined by model ARX (AutoRegressive with eXogenious input). The identity signal is a displacement of exciter motion element got by passing a signal ffom standard accelerometer through integrating amplifier. The input signal is signal ffom standard accelerometer. Identification model, signals ffom accelerometers, characteristics o f verification and identification error are shown in Fig.3. As a result o f conversion o f the obtained model to continuous form was transfer function.

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o f a c c u ra c y o f m e a su r em e n t s ig n a ls r ea d in g from a n a lo g m e a su r in g tran sd u cers 2 8 3

G (s) =6,169 s 2 + 5,6278 • 105s + 1,698 • 109

i 2 + 1,108 - 105s + 1,698 - 109 ^{( 1 )}

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p of U A t* 3 ^ f?. $ >•. .0 3 □ A cti» Output (Red Line) vs. The Sinuated P-edicted Model output (Blue Line)

Outl

0ut2 displacement S ta nd ard s ig n a ls

M e asu rem e n t ac cele ration

0 3

0 2 i ' " ~ X

0 1 I / \

/

/ \ •

01 ' \ /

-0.1\ / ^\ ^/

4) ?

0015 0.0155 0.016 0.0165 0 017 0 0175 0 018 0 0185 0C19 00105 Tine (secs)

Error in Simulated Mode»

04 '

0015 0.0155 0.018 0.0165 0.017 0.0175 0018 0 0185 0.C19 0.0195 Tine (secs)

F #

A u toR egressive w ith e xte rn a l input

m o d el estim ator

Fig.3. Identification model o f measuring system

4 . A L G O R IT H M O F D Y N A M I C C O R R E C T IO N

Equation (1) can be written

y +1,108 • 105>- +1,698 • 109y = 6,769x + 5,627 • 105x +1,698 ■ 109x

or

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ÿ + a ,y + a0y = b2x + b,x + b0x (3)

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2 8 4 M ir o sła w L U F T . R a d o sła w Inserting to equation (3) variable

= y - b 2x

and noting them as a system o f equations

and as a matrix

where

w, = - a tu] +M, +(£>, - a tb2)x

« 2 = - a 0“ i + (bQ- a 0b1)x

ii = Fu + Gx

F =

- a,_i ¹ ¹ ¹ ^p ^O^'

, G =

_ -a 0 ⁰ ^-o ô ¹ â Ô ^«N

Solution o f an equation (6) between moments t(k> i t(k+i) is equation [2]

=efT' M« .) + y ^ G x ^ d r

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(5)

(6)

(7)

(8)

where Td = / (t+l) - t(k) - digitize time

Taking assumption that change o f input quantity proceeds by steps in discrete moments there is obtained discrete equation

where

*2<*)

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( 10)

<Pu <Pn

? i\ <Pn

OD

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o f a c cu ra c y o f m e a su r e m e n t s ig n a ls rea d in g from a n a lo g m e a su r in g tra n sd u cers 2 8 5

Matrixes Fd and Gd are constant for given digitize time Td and determined on the basis 0f the formula (7) as expressions

Fd = e n * (13)

Gd =

^{e F(T^ d x}

Algorithm o f dynamic correction for equation (3) is written as following [4]

*<*> _ u [^(*) “ '(*)]

u

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1(*+1) — + <P\2^2(k) + (^l *(*) (15)

“2(*+l) = #>2l“l (*) +<Pl2^2(k) + (^2*(*)

where

x(k) - estimate o f input quantity at moment k calculated on the basis o f measurement result Xfkj and estimation o f variable ui from the previous step

<pn■■ <P22, Wi~ H>2 - factors o f discrete state-space model transducer.

5. SIMULATION

Algorithm o f dynamic correction in form o f equation (15) has been written in MATLAB 7 environment. Simulation block diagram and its result as characteristics are shown in Fig.4. Standards signals and measuring displacement are real signals obtained by procedure written in point 2.

Standard acceleration and displacement signals are shown in Scope 1. Differences between standard acceleration and measuring acceleration are shown in Scope 2. Differences between input and output estimator signals are shown in Scope 3. Estimation final result compared to the standard displacement are shown in Scope 4.

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D ï a a "i ą ą f l s : i T D S "'.¿ a '

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Measurem ent estim ation

acceleration

Fig.4. Estimation o f measuring data

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rgpj-pase o f a c cu ra c y o f m e a su r em e n t s ig n a ls r ea d in g from a n a lo g m e a su r in g tra n sd u cers 2 8 7

Simulation block diagram and simulation final result o f displacement estimation with added random noise are shown in Fig.5. Input displacement and output acceleration for tr a n s d u c e r’s model written by equation ( 2 ) are shown in Scope 1. Result o f estimation c0inpared to input displacement are shown in Scope 2.

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D e i H ô k « D O D

Displacem ent

num (s)

der<s) m acceleration

□

s c o p e 1

s c o p e 2 estim ated m.acceleration, displacem ent>

Fig.5, Estimation o f measuring data with noise

6. CONCLUSIONS

Presented way o f increase o f accuracy o f measurement signals reading by algorithm o f dynamic correction for showed simulations was correct. Data output from software estimator compared to transducer’s input data was proper.

Simplicity o f algorithm o f dynamic correction depending on performance only multiplications and additions allows measuring signals correction on-line.

Used method o f determining parameters o f differential equation describing measuring transducer model, ARX (AutoRegressive with eXogenious input), allows universal tmplementation o f dynamic correction algorithm. The method can be used for single transducer as well as for measuring systems.

Destination o f the estimator, thanks to accurate and fast reproduce o f measuring system

“ Put data, should be increasing o f accuracy o f measuring systems reading especially rasponsible for safe criteria.

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288 M ir o sła w L U F T . R a d o sła w PJo a

BIBLIOGRAPHY

[1] CHWALEBA A., LUFT M., Właściwości i projektowanie wybranych przetworników mechano- elektrycznych, W ydawnictwa Politechniki Radomskiej, Radom 1998.

[2] FRANKLIN G. F., POWELL J.D., WORKMAN M., Digital control o f dynamic systems, Addison Wesley Publishing Company, M enlo Park, 1998

[3] HAGEL R., ZAKRZEW SKI I , Miernictwo dynamiczne, Wydawnictwa Naukowo-Techniczne, Warszawa 1984

[4] JAKUBIEC J., Bieżące programowe odtwarzanie wartości chwilowych dynamicznych przebiegów wejściowych nieliniowych przetworników pomiarowych, Politechnika Śląska, Zeszyty Naukowe nr 964 Gliwice, 1988

[5] LUFT M., CIOĆ R., ’On-line’ correction o f dynamic errors in an electro-mechanical transducer Automation and control technologies -2004, Kaunas University o f Technology, Kaunas, 2004

Reviewer: Ph. D. Jerzy Mikulski