karakteristik sistem pengukuran

7/24/2019 Karakteristik Sistem Pengukuran

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Didik_RS [[email protected]]

Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI

Characteristics of

Instrumentation System


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Elemen Dasar Pengukuran

Input

True value of

variable

INSTRUMEN

(Standar Ukur)

Output

Measured value

of variable

MEASURAND

(Besaran fisis

yang diukur) OBSERVER

Measurand, yakni parameter fisis yang akan diukur.

Instrumenatau alat ukur, yang akan digunakan dalam proses

penetuan nilai atau kuantitas measurand.Observer, yakni orang yang melakukan kegiatan

pengukuran.


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Kualitas Hasil Pengukuran, ditentukan oleh:

1. Instrumenatau alat ukur yang akan digunakan

Kualitas kinerja sistem instrumentasi

Mengakibatkan kesalahan sistematis

2. Observer atau orang yang melakukan pengukuran

Kemampuan observer dalam melakukan pengukuran

Mengakibatkan kesalahan umum (gross)

3. Kondisi Lingkungan saat pengukuran dilakukan

Kondisi lingkungan yang tidak stabil (berubah-ubah)

mempengaruhi hasil pengukuran

Jika masih dapat diidentifikasi mengakibatkan kesalahan

sistematis

Jika tidak dapat diidentifikasi mengakibatkan kesalahan random

(acak)


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CHARACTERISTICS

OF MEASUREMENT SYSTEM

1. STATICS CHARACTERISTICSThe static characteristics of instruments are related with

steady state response, it means the relationship between

the output and the input when the input does not change,or the input is changing with a slow rate.

2. DYNAMICS CHARACTERISTICSThe dynamic characteristics of a measuring instrument

describe its behavior between the time a measured

quantity changes value and the time when the instrument

output attains a steady value in response.


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Static Characteristics

Static or Steady-State Characteristics (of elements) ofmeasurement system: these are the relationships which mayoccur between output (O) and input (I) of element when I iseither at a constant value or changing slowly.

General static characteristics of MS:

Accuracy (measurement uncertainty) Precision/repeatability/reproducibility

Sensitivity

Resolution

Linearity

Hysteresis

Threshold

Range or Span


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A measure how close the output reading of the MS is tothe correct value.

Accuracy (measurement uncertainty)

In practice, it is more usual to quote the inaccuracyfigure ratherthan the accuracyfigure for a MS. Inaccuracy is the extent to

which a reading might be wrong, and is often quoted as percentageof the full-scale (fs.) reading of a MS.

Example: A pressure gauge of range 0-10 bar has a quoted inaccuracy of 1.0%fs., then the maximum error to be expected in any reading is 0.1 bar. This

means that when the instrument is reading 1.0 bar, the possible error is10% of this value. For this reason, it is an important system design rulethat instruments are chosen such that their range is appropriate to thespread of values being measured.

Sodont used an instrument with a range of 0-10 bar if you will measurepressures with expected values between 0 and 1 bar


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Is a term that describes an MSs (Instruments) degree offreedom from random error.

If a large number of reading are taken of the same quantity by ahigh precision instrument, then the spread of readings will verysmall.

Repeatability the closeness of output readings when the sameinput is applied repetitively over short period of time, with thesame measurement conditions, same instrument and observerand same location.

Reproducibility the closeness of output readings when the sameinput where there are changes in the method of measurement,observer, measuring instrument, location, conditions of use andtime of measurement.

Precision/repeatability/reproducibility


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Precision is often, though incorrectly, confused with accuracyHere it is.

Highprecision

Low

accuracy

Low precision

Low accuracy

Low

precision

High

accuracy

High

precision

High

accuracy


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Instrumentation & Measurement Lab.SISTEM INSTRUMENTASIPhysics Department Brawijaya University

Is a measure of the change in instrument output that occurs whenthe quantity being measured changes by given amount.

Thus, sensitivity is the ratio of

scale deflection / value of measurand producing deflection.

Sensitivity

Sensitivity is Graphics Gradient


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Physics Department

Brawijaya University

for example, a pressure of 2 bar produces a

deflection of 10 degrees in a pressuretransducer, the sensitivity of the instrument is

5 degrees/bar.

The sensitivity of measurement


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Physics Department


Example

The following resistance values of a platinum resistance thermometer were

measured at a range of temperatures. Determine the measurement sensitivity

of the instrument in ohms/C.

Solution

If these values are plotted on a graph, the straight-line relationship between

resistance change and temperature change is obvious. For a change in

temperature of 30C, the change in resistance is 7. Hence the measurement

sensitivity: 7/30 = 0.233 /C.

y = 0.2333x + 260.33

300

305

310

315

320

325

330

150 200 250 300 350

Resista

nce

Temperature


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Physics Department


When an instrument is showing a particular output reading,

there is a lower limit on the magnitude of the change in the

input measured quantity that produces an observable change

in the instrument output.

resolution is how finely its output scale is divided intosubdivisions. Sometimes specified as an absolute value and

sometimes as a percentage of f.s. deflection.

Resolution


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Range the input of MS is specified by the minimum andmaximum values of I, i.e. IMINto IMAX. The output range isspecified by the minimum and maximum values of O, i.e. OMINtoOMAX.

Span maximum variation in input and output, i.e. input span isto IMAX IMIN, and output span is OMAX OMIN.

Examples ???

Range or Span


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An MS is said to be linear if corresponding of I and O lie on astraight line.

The ideal straight line connect the minimum point A(IMIN,OMin)tomaximum point B(IMax,Omax)and therefore has linear equation.

Graphics ???Equations ???

Linearity

Ph i D t t


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Physics Department


If the input measured quantity to the instrument is steadily increased from a

negative value, the output reading varies in the manner shown in curve (a). If the

input variable is then steadily decreased, the output varies in the manner shown

in curve (b). The non-coincidence between these loading and unloading curves is

known as hysteresis.

Ph i D t t


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Physics Department


Hysteresis is most commonly found in instruments that

contain springs. Devices like the mechanical flyball (a device for measuring

rotational velocity) suffer hysteresis from both of the above

sources because they have friction in moving parts and also

contain a spring. Hysteresis can also occur in instruments that contain

electrical windings formed round an iron core, due to

magnetic hysteresis in the iron. This occurs in devices like the

variable inductance displacement transducer, the LVDT and

the rotary differential transformer.


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DYNAMICS CHARACTERISTICS

The dynamic characteristics of a measuring instrument

describe its behavior between the time a measured quantity

changes value and the time when the instrument

output attains a steady value in response.

1. Zero order measurement system

2. First order measurement system

3. Second order measurement system


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In any linear time-invariant measuring system, thefollowing general relation can be written between inputand output for time (t)>0:

Mathematical Model

: Measured quantity

: Output reading

+1

1

1 ++ 1

+ 0

=

+1

1

1 ++ 1

+ 0

: Constants


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If we limit consideration to that of step changes in the measuredquantity only, then the equation reduces to:

+ 1

1

1 ++ 1

+ 0 =0

Further simplification can be made by taking certain special casesof that equation, which collectively apply to nearly allmeasurement systems.

Zero order instrument

First order instrument

Second order instrument


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Is all coefficient a1 an other than a0are assumed zero, then

Zero order instrument

io qbqa 00 or iio Kqqa

bq

0

0

K is a constant known as the instrument sensitivity

K= b0/a0

Where Kis a constant known as the instrument sensitivity

Any instrument that behaves according to the equation is

known as a zero order instrument.

Following a step change in the measured quantity at time t,

the instrument output moves immediately to a new value at

the same time instant t


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Zero order instrument characteristic

A potentiometer, whichmeasures motion, is a

good example of such an

instrument, where the

output voltage changes

instantaneously as the

slider is displaced alongthe potentiometer track.


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Is all coefficient a2 an other than a0and a1are assumed zero,then

First order instrument

ioo qbqa

dt

dqa 001

]1[])/(1[

)/(

01

00

D

Kq

Daa

qabq iio

If Ddt

d

then

Where time constant of the system01/ aa

ioo qbqaDqa 001


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If equation is solved analytically, the output quantity q0 in

response to a step change in qiat time t varies with time

The time constant of the step response is the time taken for

the output quantity q0to reach 63% of its final value.

Any instrument that behaves according to the equation is

known as a first order instrument.


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First order instrument characteristic


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Example

A balloon is equipped with temperature and altitude measuring instrumentsand has radio equipment that can transmit the output readings of these

instruments back to ground. The balloon is initially anchored to the ground

with the instrument output readings in steady state. The altitude-measuring

instrument is approximately zero order and the temperature transducer first

order with a time constant of 15 seconds. The temperature on the ground, T0,

is 10C and the temperature Txat an altitude of x metres is given by the

relation: Tx= T0 - 0.01x

a) If the balloon is released at time zero, and thereafter rises upwards at a

velocity of 5 metres/second, draw a table showing the temperature and

altitude measurements reported at intervals of 10 seconds over the first50 seconds of travel. Show also in the table the error in each

temperature reading.

b) What temperature does the balloon report at an altitude of 5000

metres?


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Solution

Let the temperature reported by the balloon at some general time t be Tr.

Then Tx is related to Trby the relation:

= 15 s T0 = 10C x = 5tGiven:

(a)


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This result might have been inferred from the table above where it can be

seen that the error is converging towards a value of 0.75.

For large values of t, the transducer reading lags the true temperature

value by a period of time equal to the time constant of 15 seconds. In this

time, the balloon travels a distance of 75 metres and the temperature fallsby 0.75.

Thus for large values of t, the output reading is always 0.75 less than it

should be.


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Is all coefficient a2 an other than a0, a1and a2are assumedzero, then

Second order instrument

iooo qbqa

dt

dqa

dt

qda 0012

2

2

][ 2210

0

DaDaa

qb

q

i

o

Then applying D operator again:iooo qbqaDqaqDa 001

2

2


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It is convenient to re-express the variables a0, a1, a2and b0 interms of tree parameters:

K : static sensitivity: un-damped natural frequency: damping ratio

00/ abK where

20/ aa 201 2/ aaa

We get:

io q

DD

Kq

122

2

This is the standard equation for second

order system and any instrument whose

response can be described by it is known

as second order instrument.


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Response characteristics of second order instruments


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Reference Book


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Reference Book

1. Principes of Measurement System: John P. Bentley, Prentice

Hall, 1995

2. Measurement and Instrumentation Principles: Alan S.

Morris, Elsevier, 2003

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