karakteristik sistem pengukuran
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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
Characteristics of
Instrumentation System
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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
Physics Department
Brawijaya University
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
Physics Department
Brawijaya University
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASIPhysics Department Brawijaya University
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASIPhysics Department Brawijaya University
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
Physics Department
Brawijaya University
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
Physics Department
Brawijaya University
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
First order instrument characteristic
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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASIPhysics Department Brawijaya University
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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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
Response characteristics of second order instruments
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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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Didik_RS [dieks@ub.ac.id]
Instrumentation & Measurement Lab.SISTEM INSTRUMENTASI
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
SELESAITERIMA KASIH ATAS PERHATIANNYA
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