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INSTRUMENT TYPES AND PERFORMANCE
CHARACTERISTICSMeasurement and Instrumentations
TYPE OF INSTRUMENT
Active and passive instruments
Null-type and Deflection-type
Analog and Digital
Indicating and Signal Output Instrument
Smart and Non-smart
ACTIVE AND PASSIVE INSTRUMENTS
Passive Active
NULL‐TYPE AND DEFLECTION‐TYPE
Null TypeDefection Type
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ANALOG AND DIGITAL INDICATING AND SIGNAL OUTPUT
SMART AND NON‐SMART
IEEE 1451
STATIC CHARACTERISTIC OF INSTRUMENTS
Accuracy
Precision
Tolerance
Range or Span
Linearity
Sensitivity
Threshold
Resolution
Sensitivity to Disturbance
Hysteresis
Dead Space
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ACCURACY AND PRECISION
The accuracy of an instrument is a measure of how close the output reading of the instrument is to the correct value.
The precision of a measurement system, related to reproducibility and repeatability, is the degree to which repeated measurements under unchanged conditions show the same results.
ACCURACY AND PRECISION
TOLERANCE
The permissible range of variation of a
characteristic from its nominal value.
RANGE OR SPAN
The range or span of an instrument defines the minimum and maximum values of a quantity that the instrument is designed to measure.
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LINEARITY SENSITIVITY
THRESHOLD
The minimum value of input signal that is required to make a change or start from zero
RESOLUTION
The resolution of a measurement system is the smallest yet to distinguish different in values.
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SENSITIVITY TO DISTURBANCE: DRIFT HYSTERESIS
DEAD SPACE DYNAMICS CHARACTERISTIC
Order of Instrument
1 2
1 2 1 01 2
m m
m mm m
d y d y d y dya a a a a y bf tdt dt dt dt
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ZERO ORDER SYSTEM
Output = K (input)
FIRST ORDER SYSTEM
1 0dya a y f tdt
SOLUTIONS STEP INPUT
*1 0
dya a y udt
0 00
u tu t
u t
h py y y
1
0
a dy y u ta dt
dy y u tdt
HOMOGENEOUS SOLUTION
sthy Ae
0st stAse Ae
stdy Asedt
1 0sts Ae
0
1
1asa
t
hy Ae
0hh
dy ydt
Let
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PARTICULAR INTEGRAL
pp
dyy u
dt
py u
PARTICULAR SOLUTIONS
t
y Ae u
00y u A u
0
t
y u u e u
h py y y
Initial Condition
0 1t t
y u e u e
0A u u
SPECIAL CASE
0 0u
0 0
0t
u tu t
1t
y u e
TIME CONSTANT OF STEP RESPONSE
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SECOND ORDER SYSTEM
)(2
2
tFkydtdyc
dtydm
RLC‐CIRCUIT
LCVi
LCdtdi
LR
dtid
1
2
2
SOLUTION FOR FREE & UNDAMPED
ubyadtdya
dtyda 0012
2
2
Seek Solution
tAy nsintA
dtdy
nn cos
ytAdt
ydnnn222
2
2
sin
01 aUn-damp, Free Response
0u002
2
2 yadt
yda
1
0
aa
n
SOLUTION FOR SECOND ORDER
ubydtdy
dtyd
nnn2
02
2
2
2
02 22
2
wdtdw
dtwd
nn
ubdtd
dtd
nnn2
02
2
2
2
wy
Homogeneous Solution
Particular Integral
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HOMOGENEOUS SOLUTION
02 22
2
wdtdw
dtwd
nn stAew
02 22 stn
stn
st AesAeAes
02 22 stnn Aess
02 22 nnss 0stAe
12 nns
GENERAL SOLUTION
over damp > 1
critical damp = 1
under damp < 1
OVER DAMP
21 1 nns
22 1 nns
tsts eAeAw 2121
CRITICAL DAMP
nss 21
tneBtAw )(
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UNDER DAMP
12 nn is21 nd
dn is 1
dn is 2
titi dndn eAeAw )(2
)(1
tBtBew ddtn sincos 21
SECOND ORDER STEP RESPONSE
0021 )sincos( ubtBtBey nntn
UNDERDAMP STEP RESPONSE UNDERDAMP STEP RESPONSE
Rise time Peak timeOvershootOscillation decay หรือ decrement Settling time Period
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EX:
Second order system with natural frequency 2.0 Hz มี damped frequency 1.8 Hz. Determine
(a) damping ratio ของระบบ
(b) 100% rise time
(c) over shoot
(d) 2% settling time
(e) จํานวนรอบการแกว่งก่อนที่สู่การ set ตัว
