Instrumentation and Measurement Techniques

Performance of measurement

Objective

•Defining terms of performance of measurement systems

•Reliability of measurement system

•Discuss the requirement of measurement system

Function of Instruments & Measurement Systems

Indicating instruments :Meter display, digital display

Example: speedometer in car, pressure gauge

Recording function : Data Keeping

Example: Printer, magnetic disc

Controlling function :Temperature, position, speed, liquid level, flow control.

Performance assessment • An ideal measuring system is one where the output

signal has a linear relationship with the measurand.• Error is the difference between the indicated value

and the true value. • Measuring and control system performance can be

examined in two ways ,• Static performance –when steady or constant input

signals are applied• Dynamic performance – when changing input signals

are applied

Static Performance Indication • Static sensitivity is defined as the ratio of the

change in output to the corresponding change in input under static or steady state conditions,

• For a system having static sensitivities of K1 ,K2,K3 ……, the overall system sensitivity is given by

Static Performance Indication• Dynamic performance of both measuring and control

system is specified by response to certain standard test inputs

• Step input- abrupt change from one steady value to another ,will give the transient response

• Ramp input –which varies linearly with time, will give the ramp response

• Sine wave input – will give the frequency response

Terms of performance of measurement

•True value

•Measured value

•Nominal value

•Static error

•Relative static error

•Accuracy

•Precision

•Sensitivity

•Reliability

•Hysterisis

•Resolution

•Response time

•Life time

•Frequency response

•Switching time

•Bandwidth

True value

•The real numerical unit.

•It is almost impossible to obtain in practice.

For example:

Light speed = 299792458.63… m/s

Measured value

•Value indicated by an instrument.

•It should always follow by its uncertaintyin measurement

For example:

l = (3.5± 0.1) cm

R = (102.5 ± 0.2) Ω

Nominal value

•Value of the quantity specified by the manufacturer

•It follows by toleranceFor example:

l = 3.5cm ± 10%

R = 10k Ω ± 5%

(True value is between 9.9k Ω and 10.1k Ω)

Static error

•The different between the measured value and the true value of the quantity.

δA = Am - At

δA = static error

Am = measured value

At = true value

Relative Static error

•The ratio of static error to true value

εr= δA/ At

εr= (Am - At )/ At

εr = relative static error

Accuracy

•Closeness with which an instrument reading approaches the true value of the quantity measured

Example:

Reading from instrument A, l = 3.82cm

Reading from instrument B, l = 3.91 cm

True value, l = 3.90cm

Conclusion: Instrument B is more accurate.

Precision

•It is a measure of reproducibility of the measurement

•It composed of 2 characteristics:

a) Conformity

b) Number of significant figures

Instrument A, l= 3.82, 3.82, 3.81, 3.82…

Instrument B, l = 3.82, 3.84, 3.83, 3.80…

Conclusion: Instrument A is more precise.

Accuracy and Precision

True value, l = 1.50mm

Instrument A, l = 1.475mm

Instrument B, l = 1.49mm

Conclusion:

Instrument A is more precise

Instrument B is more accurate

Accuracy and Precision

Sensitivity

The ratio of the magnitude of the output signal or response to a change the magnitude of input signal.

ExampleA wheastone bridge requires a change of 7Ωin an unknown arm of the bridge to produced a change in deflection of the galvanometer.

Determine the sensitivity

magnitude of output responseMagnitude of input

Sensitivity =

= 3mm7Ω

= 0.429 mm/Ω

Hysterisis A phenomenon which depicts/shows the difference in output when loading and unloading

Cause: friction, backslash,elastic deformation, magnetic and thermal effects.

Resolution/ DiscriminationThe smallest increment in input which can be detected with certainty by an instrument

Example:

A mercury thermometer react every 0.5°Cof changes of ambient temperature.

This thermometer won’t have any reaction if the changes of temperature is 0.4°C

And it only move a step if the changes of temperature is 0.6°C

Response timeThe period of time which from it sensing till it reach to steady state condition.

Example:

A mercury thermometer react every 0.5°Cof changes of ambient temperature which require 1.5s to settle.

If the temperature change rapidly every 1s, then this thermometer will never could gives a proper value.

Frequency response

The minimum time that an instrument can sense an instantaneous changes.

Example:

our eyes cannot see light photon because the rapidly moving of photons is much more faster than our brain processing time.

Switching timeThe best on-off time for a switching device which is distortion free.

Example:

For a device which require 2s to charge up and 3s to discharge. Hence the switching time must be always larger than 5s.

BandwidthA range of frequency that can sense by an instrument.

Example:

The bandwidth of our ears is from 20Hz to 20kHz. Any sound that outside this range is undetectable.

Others

• Range – the limit within which the input can vary-resisted thermometer can be quoted to have range of -200 to + 800 degree celcius

• Dead band or dead space is used for range where there is no output

• Stability –ability of system to give the same output when used to measure a constant input over a period of time.

• Dynamic characteristics – are characteristics of measurement that are time dependent

Reliability

A period of an instrument that maintain its accuracy and precision.

Example:

After two years of using an instrument…

Accuracy of Instrument A drop 1%

Accuracy of Instrument B drop 5%

Conclusion: Instrument A is more reliable

Requirement • Fitness of purpose – measurement to predefined

accuracy • Calibration – comparing output with the standards -Company standard-National standards calibration records normally include: Reference

number, calibrations data, calibration result, frequency of calibration,, repair and modification information , limitation

National Standards• National standards are defined my international agreement maintain by

national establishment like national physics laboratory in great Britain, and national bureau of standards in the US.

Primary standards Mass:• Length• Time• Current• Temperature• Luminous intensity• Amount of substance

Supplementary standards:• Plane angle• Solid angleSafety system

Error Calculation• Accuracy can be stated in terms of errors

introduced

• Percentage error = Indicated value – True value . X . 100%Maximum scale value

%100xvalueTrue

valueTruevalueIndicated −

Precision is used to specify the closeness of output result when a measuring device is subjected to the same input on a number of occasions

EXAMPLEA measuring system consist of a transducer , an

amplifier and a recorder, with an individual sensitivities as follows :

• Transducer sensitivity 0.2 mV /0 C• Amplifier gain 2.0 V/mV• Recorder sensitivity 5.0 mm /V• Determine the overall system sensitivity• K= K1 x K2x K3• = 0.2 mV/0C x 2.0V/mVx 5.0 mm/V• =2.0 mm/0 C

EXAMPLEA 0 to 10 bar pressure gauge was found to have an error of ±

0.15 bar when calibrated by the manufacturer .Calculate (a) the percentage error of the gauge and (b) the possible error asa percentage of the indicated value when reading of 2.0 bars was obtained in a test .

Percentage error = 0.15/10. x 100 = ± 1.5%Possible error = ± 0.15%∴ error at 2.0 bars = 0.15/10. x 100 =± 7.5%

• The gauge is therefore more unreliable at the lower end of its range, and alternative gauge with a more suitable range should be used .

EXAMPLE• For a general measuring system where the errors in

the transducer, signal conditioner , and recorder are ±2 % , ± 3%,and ±4 % respectively, calculate the maximum possible system error and the probable or root- sum –square error.

• Maximum possible error = ± (2+3+4)% =±9%• Root –sum-square error = ± √(22+32+42)%• = √ 29% =± 5.4%• Thus the error is possibly as large as ± 9% but

probably not larger than ± 5.4%.