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The Accuracy Of Measurement Systems
In The Steady State
Dr. Bashir NOURI
Department of Mechatronics Engineering
Faculty of Engineering
An-Najah National University
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Dr. Bashir M. Y. NOURI
FACULTY OF
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M Introduction:
E Accuracy is a property of a complete measurement system rather than a
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single element. It is quantified using measurement error (E).
H E = Measured Value – True Value = System Output – System Input
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Measurement Error of a System of Ideal Elements
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O =O
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O =I
O =I
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n Measured
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A system of n-ideal elements in series (The system is perfectly linear and not
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subjected to environmental inputs and the bias (a) is zero.
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a=0
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Oi = ki Ii
Input-output equation for ideal element with zero intercept.
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Dr. Bashir M. Y. NOURI
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i 1, ,n
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k i Linear Sensitivity or Slope
O2 k 2 I2 k 2 k1 I
O3 k 3 I3 k 3 k 2 k1 I
O On ( k 1 k 2 k 3 k i k n ) I
E O I ( k1 k 2 k 3 k i k n 1 ) I
if k 1 k 2 k 3 k i k n 1 E 0
The system is perfectly accurate.
Example: Thermocouple Temperature Measurement System.
Simple temperature measurement system
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Dr. Bashir M. Y. NOURI
FACULTY OF
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TM k 1 k 2 k 3 TT
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k 1 k 2 k 3 ( 40 10 6 ) ( 1000 ) ( 25 ) 1
TM TT E TM TT 0
The system is perfectly accurate.
The real system is in error because:
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1.
The input temperature changes the sensitivity of the thermocouple (k1)
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Changes in reference junction temperature (TC ≠ 0) cause the e.m.f to
change.
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The ambient temperature affects the output voltage of the amplifier
(ambient temperature is a modifying input that changes k2).
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The sensitivity of the indicator (k3) depends on the stiffness of the
restoring spring, that is affected by changes in environmental temperature
and wear.
Dr. Bashir M. Y. NOURI
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Conclusions:
The error of a measurement system depends on the non-ideal characteristics
e.g. nonlinearity, environmental and statistical effects of every element in the
system.
The general model of a single element must be used.
O(I) = k I + a + N(I) + kM IM I + kI II
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Dr. Bashir M. Y. NOURI
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Error Reduction Techniques
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Compensation methods for nonlinear and environmental effects.
1. A compensating nonlinear element into the system.
Example: Design a nonlinear deflection bridge to compensate for the nonlinearity
of thermistor.
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Dr. Bashir M. Y. NOURI
FACULTY OF
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2. Isolation: To isolate the transducer from environmental changes (I M = II = 0)
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3. Zero environmental sensitivity (kM = kI = 0): The element is completely
insensitive to environmental inputs.
Example: Use a metal alloy with zero temperature coefficient of expansion and
resistance as a strain gauge element.
4. Compensation methods for interfering environmental effects.
a) Opposing environmental inputs: Is a successful method of coping with
environmental inputs (Interfering Inputs).
The two effects tend to cancel out.
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Dr. Bashir M. Y. NOURI
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b) Differential system: The use of two matched strain gauges in adjacent arms
of a bridge (will be discussed later in the course) to provide compensation for
ambient temperature changes. One strain gauge is measuring a tensile strain
(+ e) and the other an equal compressive strain (- e). The deflection bridge
effectively subtracts the two resistances so that the strain effect is doubled and
the environmental effects cancel out.
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Dr. Bashir M. Y. NOURI
FACULTY OF
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5. High – gain negative feedback: An important method of compensating for
modifying inputs and nonlinearity.
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Example: Closed loop force transducer
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Dr. Bashir M. Y. NOURI
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Questions
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