EP 320Process Instrumentation and Instrumental Analysis

January April, 2015

1. Introduction Instrument characteristics.

Class Revision

Describe about deflection type and null typeinstruments with the help of an example (oneexample for each type)

[8 marks]

Teaching Plan: EP320(W1 to W4)

Introduction

The most obvious way to make observations is to use the human senses of seeing, feeling, and hearing.

In many cases, however, sensors are used that have been devised by man to enhance or replace our natural sensors.

The process of sensing is often called transduction that being made with transducers.

These man-made sensor assemblies, when coupled with the means to process the data into knowledge.

Introduction

When a fever thermometer is used to measure a persons body temperature.

we are looking to see if the personis at the normally expected value.

if it is not, to then look for changes over time as an indicator of his or her health.

Introduction

if the thermometer gives errors in its use, wrong conclusions could be drawn.

It could be in error due: to incorrect calibration of the thermometer or because no allowance for the dynamic response of the

body temperature.

Therefore, adequate/correct information can beobtained if we understand the static and dynamiccharacteristics of both the measurand and theinstrumentation.

A patients temperature chart shows changes taking place over time.

Fig. Temperature profile

Measurand (Process) Characteristic

Dynamic

Static (Steady-State)

Instrument Characteristic

Indication of the capabilities and limitation of theinstrument for particular application.

It is important as it enables us to have quantitativeestimate of pros/cons of instrument

Instrument performance Characteristic1. Static Characteristic

2. Dynamic Characteristic

NOTE: Measurement outcomes are rarely static over time.

Instrument Characteristic

A mercury-in-glass fever thermometer is placed in a patientsmouth.

The indication slowly rises along the glass tube to reach the finalvalue, the body temperature of the person.

The slow rise seen in the indication is due to the time it takes forthe mercury to heat up and expand up the tube.

The static Sensitivity will be expressed as so many scale divisionsper degree and is all that is of interest in this application.

The dynamic characteristic will be a time varying function thatsettles to unity after the transient effects have settled.

This is merely an annoyance in this application but has to beallowed by waiting long enough before taking a reading. The wrongvalue will be viewed if taken before the transient has settled.

Tem

per

atu

re, o

C

Time, s

Instrument Characteristic

Dynamic Characteristic

Instrument rarely respond instantaneously to changes in the measured variables

It exhibit a characteristic slowness/sluggishness due to mass, thermal capacitance, fluid capacitance or electric capacitance.

Pure delay in time is often encountered where the instrument are wait for some reaction to take place.

The dynamic behavior of an instrument is determined by subjecting its primary element to some known and predetermined variation in measured quantity.

Static characteristics

When the desired input (process response) to the instrument constant/varying slowly with time, the dynamic characteristic is not important.

The various quantitative description of the static performance instrument parameters like:

1. Accuracy2. Precision3. Resolution4. Sensitivity

5. Linearity6. Hysteresis7. Drift8. Over load

9. Capacity10. impedance

loading

Static Characteristic1. Error and uncertainties

2. Static performance parameters

Error and uncertainties

The degree of perfection of a measurement can only be determined if the goal of the measurement can be defined without error.

Practically, Measuring instrumentation cannot give ideal sensing

performance

Select the allowable error based on a given situation.

ERROR & UNCERTAINTIES

The static performance parameters of the instrument are obtained by performing certain specified tests depending the type of instrument, nature of application etc.

Some salient static performance parameters are tested periodically by means of a static calibration.

No measurement can be made with perfect accuracy and precision. Therefore, it is instructive to know the various types of errors and uncertainties that are in general, associated with measurement system.

Types of error

Error the difference between the measured and the true value (as per standard)

Diff. types of error:

Error

Systematic/ Cumulative

Accidental / Randomly

Miscellaneous

Errors that tend to have the same magnitude and sign for a given set of condition

These errors are caused due to random variations in the parameters/systems measurement

Errors that can not be strictly classified as either systematic/random

Known as instrument bias Can be eliminated/alternatively instrument

calibration

Instrument errors Inherent in the instruments systems Caused by poor design / construction of the instrument Example:

Divisions of graduated scales Inequality of the balance arm irregular spring tension

Can be avoided if select the suitable instrument, apply suitable correction and calibrate the instrument

Systematic /Cumulative Errors

Environment errors Caused due to variation of conditions external to the measuring

device, including the condition in the area surrounding the instrument

Commonly occurring change on environment conditions Effect the instrument characteristics T, barometric P, humidity,

wind forces, magnetic & electrostatic field Example:

Change in ambient T causes errors due to expansion of the measuring tape

Buoyant effect of the wind causes errors on weight of the chemical balance

Loading errors Caused by the act of measurement on the physical system being

test Example

Introduction of additional resistance in the circuit by measuring milliammeter which may alter the circuit current by significant amount

Obstruction type flow meter may partially block/disturb the flow conditions, consequently flowrate shown by the meter may not be same as before the meter installation

Accidental / Random error

Caused due to random variations in the parameter or system of measurement

Vary in magnitude & may be either +/- on the basis chance alone

tend to compensate one another- also known as change/compensate error

Detected by a lack of consistency in measured value when the same input is imposed repeatedly

Main contributing factors: Inconsistencies associated with accurate measurement of

small quantities Presence of certain system defects Effect of unrestrained and randomly varying parameters

Miscellaneous

Mainly cause by:

A. Human error Due to limitations in the human senses

Necessary to exercise extreme care with mature & considered judgement in recording the observations

B. Error due to faulty component/adjustments Misalignment of moving parts, electrical leakage, poor optics

etc. in measurement systems

C. Improper application of the instrument caused due to the use of the instrument in conditions which

do not conform to the desired design/operating conditions

STATIC PERFORMANCE PARAMETERS

Accuracy Precision Resolution Threshold

Static sensitivity

LinearityRange &

SpanHysteresis

Dead band

Backlash Drift

Accuracy

The closeness of the instrument output to the true value of the measured quantity (as per standard)

It is specified as the % deviation or inaccuracy of the measurement from true value

Depends on inherent limitations of the instrument & on the various systematic error involved in measurement

The accuracy of the instrument can be specified:

% =

100

% =

100

# accuracy specification of the instrument as % of fsd less accurate than % of TV

%

Accuracy (inaccuracy) appear in several forms:

1. Measured variable; the accuracy is 20C in some T measurement. Thus, there would be an uncertainty of 20C in any value of T measured

2. Percentage of the instrument full-scale (FS) reading. Thus an accuracy of 0.5 % FS in a 5-V full scale range meter would mean the inaccuracy/uncertainty in any measurement is 0.025 V

Accuracy (inaccuracy) appear in several forms:

3. Percentage of instrument span (% of the range of instrument measurement capability). For device measuring 3% of span for a 20 to 50 psi range of P, the accuracy is (0.03) (50-20) = 0.9 psi

4. Percentage of the actual reading. Thus, for a 2 % of reading voltmeter, an inaccuracy of 0.04 V for a reading of 2 V

Precision

The ability of the instrument to reproduce a certain set of readings within a given accuracy

Dependent on repeatability (ability of the instrument to reproduce a groups of measurements of the same measured quantity)

High precision with poor accuracy

Poor precision with average accuracy

High precision with high accuracy

Poor precision with poor accuracy

The smallest increment in the measured value that can be detected with certainly by the instrument

It is the degree if fineness with which a measurement can be made

The least count of any instrument is taken as the resolution of the instrument. A high resolution is one can detect smallest possible variation in the input

Example: A ruler with a least count of 1 mm may be used to measure

to nearest 0.5 mm by interpolation. Its resolution is considered 0.5 mm

Resolution / Discrimination

Threshold

The minimum/maximum value of the input below which no output can be detected

It is particular case of resolution.

Both threshold & resolution can either be specified as absolute quantities in term of input units/ as % of full scale deflection.

Statistic Sensitivity

The ratio of the magnitude of response (output signal) to the magnitude of the quantity being measured (input signal)

Also termed as scale factor /gain of the instrument

Determined from result of static calibration

Sensitivity is represented by the slope of the input output curve if the ordinate are represented in actual units

Static Sensitivity, K =

= 0

Linearity

A linear indicating scale is one of most desirable features of any instrument

Linearity is never completely achieved and the deviations from the ideal are termed as Linearity error

In commercial instruments, the max departure from linearity is specified by this following way: Independent of the input

Proportional to input

combined

Independent of the input

If the deviations of the output of the instrument from the best fitting straight line (drawn through the calibration points) does not vary with the input

then non-linearity is specified in the terms of higher value of the maximum deviation that occurs on the positive and negative sides of the best fitting or idealised straight line.

This value is usually expressed as percentage of scale deflection.

Proportional to input

If the deviation of the output of the instrument from idealized straight line vary with the input, then non-linearity is specified as function of the input

The max deviation point on the + and sides of idealized straight line are join with the origin and their slope are determined

The higher value of % change slope with respect to the idealized line is expressed as % non linearity with respect to the magnitude of input values

This value is usually expressed as percentage with respect to input values

Range and Span

The range of the instrument is specified by the lower & upper limits

The algebraic difference between lower & upper range values is termed as span of the instrument

The range of the instrument can either be unidirectional (0-100 0c) or bidirectional (-10 to 100 0C)

Hysteresis

The magnitude of the error caused in the output for a given value of the input, when this value is approached from opposite directions

This is caused by backlash, elastic deformations, magnetic characteristics, but mainly caused due to frictional effects.

Dead bandThe largest change of measurand to which the instrument does not respond

Backlash The max distance / angle through which any part of

the mechanical system may be moved in one direction w/o causing motion of the next part

Can be minimized if the component are made to very close tolerances

Driftthe variation of the output for a given input caused due to change in the sensitivity

Example: A load cell calibrated at a T of 200C has the following output/input

characteristic

When it is used in an environment of 400C, its characteristic change to the following:

Determine: (i) zero drift (ii) sensitivity drift (iii) sensitivity drift per 0C change in ambient T

If 0.5 mm of scale division can be read with a fair degree of certainty, determine the resolution od the instrument in both case

Load in KN 0 0.4 0.8 0.12 0.16 0.20

Deflection of meter in mm

3 14 25 36 47 58

Solution

y = 25x

y = 27.5x + 3

0

5

10

15

20

25

30

35

40

45

50

55

60

65

0 0.5 1 1.5 2 2.5

o/p 20C

o/p 40C

Linear (o/p 20C)

Linear (o/p 40C)

Solution

a-i) load cell at 400C. The zero drift which represents no load deflection & considered the instrument bias/systematic error is found to be 3 mm. A systematic error of 0.109 kN at 400C output-input characteristic

ii) at 200C

Static Sensitivity, K =10

0.4= 25 mm/kN

at 400C

Static Sensitivity, K =11

0.4= 27.5 mm/kN

iii) Sensitivity drift /0C = 2.5/20 = 0.125 (mm/kN)/ 0C

Sensitivity drift of the instrument = 27.5 25 = 2.5 mm/kN

b) inverse sensitivity 1/K or deflection factor at 200C = 1/25 = 0.04 kN/mm

Resolution of load cell corresponding to 0.5mm meter scale reading = 0.5mm x 0.04 kN/mm

= 0.02 kN = 20 N

inverse sensitivity 1/K or deflection factor at 400C = 1/27.5 = 0.036 kN/mm

Resolution of load cell corresponding to 0.5mm meter scale reading = 0.5mm x 0.036 kN/mm

= 0.018kN = 18 N