Lecture 3Lecture 3

Performance characteristics for Performance characteristics for measurement and measurement and

instrumentation systeminstrumentation system

3 classifications to define the performance of measurement system: operational, static, dynamic

Operational characteristic• Range• Span• Sensitivity• Resolution• Dead band/threshold

RangeRange--will give the minimum and maximum rangewill give the minimum and maximum range

SpanSpan-the difference between the maximum and minimum -the difference between the maximum and minimum

rangerange

Eg: A specification of a thermometer reads as Eg: A specification of a thermometer reads as follows: follows:

Range and subdivision Range and subdivision ooC - C - -0.5 to +40.5 -0.5 to +40.5 0.10.1 Min is –0.5Min is –0.500C and max is 40.5C and max is 40.500CC Span = 41Span = 4100CC

SensitivitySensitivity

-ratio of a change in output to the change in -ratio of a change in output to the change in input which causes it at steady-states input which causes it at steady-states conditioncondition

-Eg. A galvanometer has a sensitivity of -Eg. A galvanometer has a sensitivity of 17mm/17mm/AA

-for a 1-for a 1A input display, a light spot moving A input display, a light spot moving across the scale shows a movement of an across the scale shows a movement of an index of 17 mmindex of 17 mm

ResolutionResolution

The least incremental value of input or output that The least incremental value of input or output that can be detectedcan be detected

Dead band / ThresholdDead band / Threshold

The largest range of values of a measured variable The largest range of values of a measured variable to which the instrument does not respondto which the instrument does not respond

RULERSRULERS

Normal - straight Folding ruler

VERNIER CALIPERSVERNIER CALIPERS

Digital vernier caliper

HOW TO READ A VERNIERHOW TO READ A VERNIER

Scale reading = 3.70cm

Vernier reading = (0.1/10) x 4 = 0.04

Caliper reading = 3.74cm

SCREW GAUGESCREW GAUGE

Static characteristic:ErrorAccuracyPrecisionRepeatabilityLinearityHysteresiscalibration

ErrorError

-Error is the difference between the true value -Error is the difference between the true value YYnn and and

instrument reading instrument reading XXnn

e = e = YYnn – – XXnn

-Types of errors: systematic error (bias error) and-Types of errors: systematic error (bias error) and random error (precision error)random error (precision error)

-Bias (systemic) error-consistent and repeatable error-Bias (systemic) error-consistent and repeatable error

Bias error = average readings – true valueBias error = average readings – true value

--Random error-the lack of repeatability in the output Random error-the lack of repeatability in the output of the measuring systemof the measuring system

Random error = reading – average readingRandom error = reading – average reading

Accuracy

-Ability of the system to respond to a true value

-Limit of error of a measuring device under certain operating conditions and can appear is several forms:

1. Measured variable: the accuracy is 0.2 of the measurement

-If the temperature reading = 30.10C, the actual temperature lies between 29.90C and 30.30C

2. Percentage of full scale (FS), accuracy 1% f.s

-If the full scale is 10 A, accuracy = 0.1 A

3. P3. Percentage of instrument span, accuracy ercentage of instrument span, accuracy 3% span3% span

-If the span for pressure measurement is 20-50 psi,-If the span for pressure measurement is 20-50 psi,

accuracy = accuracy = 0.03 (50-20) = 0.03 (50-20) = 0.9 psi0.9 psi

4. Given as percentage of actual reading, e.g. for a 4. Given as percentage of actual reading, e.g. for a 2% 2%

--If the true value of the voltmeter is 2 V, accuracy = (2If the true value of the voltmeter is 2 V, accuracy = (2 0.02) = 0.02) = 0.04 V0.04 V

Example 1.1Example 1.1 A temperature sensor has a span of 20A temperature sensor has a span of 2000C –C –

25025000C. A measurement results in a value of C. A measurement results in a value of 555500C for temperature. Specify the error if the C for temperature. Specify the error if the accuracy is:accuracy is:

a) a) 0.5%FS0.5%FS b) b) 0.75% of span0.75% of span c) c) 0.8% of reading0.8% of reading What is the possible temperature in each caseWhat is the possible temperature in each case

Example 1.2Example 1.2

A temperature sensor has a transfer function A temperature sensor has a transfer function of 5 mV/of 5 mV/00C with an accuracy of C with an accuracy of 1%. Find 1%. Find the possible range of the transfer function?the possible range of the transfer function?

Example 1.3Example 1.3

Suppose a reading of 27.5 mV results from Suppose a reading of 27.5 mV results from the sensor used in previous example. Find the sensor used in previous example. Find the temperature that could provide this the temperature that could provide this reading.reading.

System accuracySystem accuracy Overall accuracy of many elements in a Overall accuracy of many elements in a

process-control loop to represent a process process-control loop to represent a process variablevariable

VV VV = ( = (KK KK) () (GG GG))CC VV = output voltage = output voltage VV = uncertainty in output voltage = uncertainty in output voltage KK,,GG = nominal transfer functions = nominal transfer functions KK, , GG = uncertainty in transfer functions = uncertainty in transfer functions CC = dynamic variable = dynamic variable

The overall system accuracy as the root-The overall system accuracy as the root-mean-square (rms):mean-square (rms):

KK KK GG GG VV VVCC

22

G

G

K

K

V

V

rms

Example 1.4Example 1.4

Find the system accuracy of a flow process Find the system accuracy of a flow process if the transducer transfer function is 10 if the transducer transfer function is 10 mV/(mmV/(m33/s) /s) ±1.5% and the signal-±1.5% and the signal-conditioning system-transfer function is conditioning system-transfer function is 1mA/mV ±0.05% 1mA/mV ±0.05%

Precision

-The degree of exactness of which an instrument is designed or intended to performed

-Significant figures convey actual information regarding the magnitude and the measurement precision of a quantity

-The more the significant the figure, the greater the precision of measurement

Repeatability-The ability of the system to display the same

output for a series of applications of the same input signal, under the same operating conditions

Linearity-The output reading of the measurement is

linearly proportional to the quantity being measured

Hysteresis

-different reading may be obtained if the variable was increasing prior to taking the reading if the variable was decreasing

-causes: friction, mechanical flexure of internal part, electrical capacitance

CalibrationCalibration

-process of checking a measuring system -process of checking a measuring system against a standard readingagainst a standard reading

-purposes:-purposes:

1.1. To ensure readings from an instrument are To ensure readings from an instrument are consistent with other measurementsconsistent with other measurements

2.2. To determine the accuracy of the To determine the accuracy of the instrument readingsinstrument readings

3.3. To establish the reliability of the To establish the reliability of the instrument i.e. that it can be trusted instrument i.e. that it can be trusted