static and dynamic characteristics

8/9/2019 Static and Dynamic Characteristics

1/10

Static and Dynamic Characteristics

The Performance of an instrument is evaluated based on its static ordynamic characteristics. Static characteristics refer to the case when the

different inputs to the system are either held constant or vary slowly withrespect to time. Whereas, dynamic characteristics refer to the performance of

the system when the inputs are varying rapidly with respect to time.

For example, the slow rise in temperature in the peak hour in the noon can be considered as a static characteristic as the temperature attained is some what

constant and is subected to a very slight change. Whereas, the pressure

conditions in an !." engine which changes rapidly is considered to be a

dynamic characteristic.

There are many phenomena which can be conveniently described by staticresponse while there are some which can only be represented by dynamic

response. The overall performance of a system, many a times, can be evaluated

by a semi#$ualitative superposition of static and dynamic characteristics. This

approach is in fact a convenient mathematical study with acceptable

approximation.

Static Calibration

% Static "alibration & refers to a situation in which all inputs 'desired, interfering,

modifying( except one are kept at some constant values. Then the one input

under study is varied over some range of constant values, which causes theoutput to vary over some range of constant values. The input output relation

developed in this way represents a static calibration valid under the stated

constant conditions of all the other inputs.

% This procedure is repeated for every other input of interest 'keeping rest of the

inputs constant(. Thus the overall instrument behavior to all kinds of inputs

applied together can be approximated by means of superposition of the effects

of the individual inputs.

The statement that one input is varied and others are held constant implies

that all the inputs are determined independently of the instrument beingcalibrated. For interfering or modifying inputs, the measurement of these inputs

usually need not be an extremely high accuracy level. For example, in a pressure

gauge temperature is an interfering input so that a temperature change of )** deg

causes a pressure error of .)**+. ow, if we have measured the )** deg

interfering input with a thermometer which itself had an error of -.*+ the

pressure error actually would have been *.)*-+. This error of *.)*-+ is


2/10

completely negligible in engineering conditions. ut while calibrating the

instruments utmost care is to be taken. !t is impossible to calibrate an instrument

to accuracy greater than that of the standard with which it is compared to.

% y means of calibration & The instrument is checked against a known standard thereby helping in

evaluation of errors and accuracy

& !t involves a comparison of the particular instrument with either

i. Primary standard

ii. / Secondary standard with a higher accuracy than the instrument to be

calibrated or

iii. /n instrument of known and higher accuracy

/ll working instruments in actual use must be calibrated against somereference instruments which have higher accuracy. These reference

instruments in turn must be calibrated against higher standards of

secondary or tertiary levels. These standards are also calibrated against primary standards

Primary standards are the 0state of the art1, most accurate way known to

measure the $uantity of interest. Such standards are developed, maintained

and improved by national laboratories such as !ST, 2S/ 'ational !nstitute

of Standards and Technology( or P3, ew 4elhi 'ational Physical

laboratory.

The following steps are necessary while calibrating an instrument5

). 6xamine the construction of the instrument, and identify 7 list all the

possible inputs

-. /scertain which of the inputs will be significant in the application forwhich instrument is calibrated

8. 9ave apparatus that will allow to vary all the significant inputs over the

ranges considered necessary

:. 9ave standards to measure inputs

;. y holding some inputs constant, vary other input's( and record the

output's(, develop the desired static input output relations.


3/10

Static Characteristics

% True Value: - !f the input value of calibration is known exactly then it can be called the true value.

% Accuracy: - /ccuracy of a measuring system is its ability to indicate a true

value exactly.

% Static error (e):- is defined as the difference between the true value appliedto a measuring system 'input( and the measured value of the system

'output(.

e < true value & measured value

From which + accuracy can be found by relation.

% y definition, accuracy can be determined only when true value is knownsuch as during a calibration.

% Precision :- of a measurement system refers to the ability of the system to

indicate a particular value upon repeated but independent applications of a

specific value of input . / precise system has both repeatability andreproducibility. 9owever precision of a system may or may not guarantee

accuracy of the system.

% Precision Error :- is a measure of random variation found during repeated

measurement

% Bias Error: - is the difference between average value and the true value.

oth Precision error and bias error affect the acceptability of the system.


4/10

% Linearity :

!f an instruments calibration curve for desired input is not straight,

the instrument may still be accurate. 9owever, in many applications, linear

behavior is desirable. The conversion from a scale reading to the

corresponding measured value of input $uantity is most convenient if we

merely have to multiply by a fixed constant rather than consult a non#linearcalibration curve. When the instrument is part of a larger data or control

system, linear behavior of the parts often simplifies design and analysis.

Thus, linearity is simply a measure of maximum deviation of any

calibration points from this straight line. This maybe expressed as a

percentage of the full scale reading or a combination of the two.

!f the relationship between the output and input can be expressed in

the following e$uation form

$o < a = k > $i

Where a and k are constants, the instrument is said to posses

linearity. !n practice linearity can never be achieved. 4eviations from ideal

linearity relations are termed as linearity tolerances.


5/10

3inearity can be specified as !ndependent linearity and the proportional

linearity. / 8+ independent linearity means that the output will remain

within values set by two parallel lines spaced =8+ of the full scale output

from the ideali?ed line 'fig a(. 8+ proportional linearity is illustrated in 'fig

b(. The ideal value is never more than =8+ away from recorded value

regardless of the magnitude of the input.

ote5#

% / non linear input output relation may also be approximated as linear over a

restricted range.

% /n instrument which does not posses linearity can still be highly accurate.

% !n some instruments which are inherently non linear in nature the

lineari?ation can be achieved mechanically or electrically over a limited

range.

• San ! "an#e :-

% !nstrument is operated from a minimum input value to a maximum input

value. This becomes the operating range of the measuring system. !f

xmin 7 xmax are the respective minimum 7 maximum input values

defining the input operating range extending from xmin 7 xmax. Theinput span is expressed as

ri < xmin # xmax

% Similarly, the output operating range is specified from ymax to ymin Theoutput span of the full scale operating range 'FS@( is expressed as.

ro < ymax & ymin

% !n the proper procedure of calibration the inputs are applied within the

operating range. !n practice during measurements it is important to

avoid extrapolation beyond the range of known calibration, since the behavior of the system is uncharted in these regions.


6/10

• Dri$t

% Dri$t is a #radual shi$tin# o$ calibration o$ instrument o%er a eriod

o$ time

% &ero Dri$t: !f the whole calibration 'output value against input value(

gradually shifts by a certain $uantity it is called a ?ero drift.

% San Dri$t: !f there is proportional change in the indication all alongthe upward scale, the drift is called the span drift.

% &onal Dri$t: !n case the drift occurs only in a ?one of the span, it is

called ?onal drift. There are many environmental factors which causedrift e.g. stray electric 7 magnetic fields, temperature, mechanical

vibrations, wear 7 tear etc.

e.g. consider a strain gauge, an interfering input to it is the

temperature. This causes the resistance of the gauge to vary and thus

would drift the output value even when the strain is ?ero. Temperature is

also a modifying input which changes sensitivity of strain gauge and

introduce a span drift as shown below.

% 4rift occurs in flow meters because of wear of orifices or venturies.

4rift may occur in thermocouples due to changes in their metals caused by contamination or chemical reaction etc.

% "eroducibility:-

!tAs the degree of closeness with which a given value of same measurand,may be repeatedly measured under changed conditions of measurement

such as different observer, different method of measurement, different

location etc. Perfect reproducibility means that the instrument has no drift.


7/10

% "eeatability

% !tAs the degree of closeness of value of the results of successive

measurements of same measurand carried out under same conditions of

measurement over a certain period of time.

% !f an instrument is used many times and at different time intervals, the

output may not be the same but shows a scatter.% When this deviation from the ideal static characteristics is expressed in

absolute units or as a fraction of the full scale, !t is called the repeatability

error.

% 'ysteresis

% The se$uential test is an effective diagnostic techni$ue to identify and

$uantify a hysteresis error in measurement system. 9ysteresis error refers to

differences in the values found between going upscale and downscale in ase$uential test. !t is often seen that the input#output graphs do not coincide

for continuously ascending and then descending values of the input. This

non#coincidence of input#output graphs for increasing and decreasinginputs arises due to the phenomenon of hysteresis.

% Some causes for hysteresis effect in an instrument are internal friction,

sliding or external friction, free play or looseness of mechanisms etc..

% The effect of hysteresis on calibration curve is shown in the figure above.

For a particular input value, the hysteresis error is found from the difference

in the upscale and downscale output value.eh


8/10

% Some hysteresis is normal for any system and affects the precision of the

system. 9ysteresis effects are best eliminated by taking readings

corresponding to ascending and descending values of the input and then

taking the arithmetic average.

% Threshold ! "esolution% Threshold is the smallest measurable input while the resolution is the

smallest measurable change.

% "onsider an instrument to which an input is applied gradually. !t is

observed that no output change is detected until certain minimum value of

input. This minimum value is taken as threshold input of the instrument.

% Similarly if there is a certain minimum change in input to an instrument

there would be corresponding detectable change in output. This incremental

change in input is referred as resolution.

% Threshold is measured when input is varied from ?ero while the resolution

is measured when the input is varied from any arbitrary non ?ero value.

% Static Sensiti%ity:

When an input output calibration has to be performed, static sensitivity

of the instrument can be defined as the slope of the calibration curve. !f the

curve is not normally a straight line, the sensitivity will vary with the input

value. To get a meaningful definition of sensitivity, the output $uantity must

be taken as the actual physical output $uantity.

% !f the input#output relation is linear, the sensitivity is constant for all values

of input.

% The sensitivity of an instrument having a non linear static characteristics

depends on the value of input $uantity and should be specified as


9/10

For 6xample, while measuring pressure we plot it against kPa. ut theactual physical output is an angular rotation of the pointer. The angular spacing

of the kilopascal marks on the pressure gauge. Suppose it is ; angular degB kPa

and the slope of the graph is ).*C. We get a static sensitivity of ';( > ').*C( <;.: angular degBkPa. !n this form, the sensitivity allows comparison of this

pressure gauge with the others as regards its ability to detect pressure changes.

While the instrumentAs sensitivity to its desired input is of primary concern,

its sensitivity to interfering or modifying inputs also may be of interest. For,

example, if we consider temperature as an input to the pressure gauge.Temperature can cause expansion and contraction that will result in change in

output reading even though the pressure has not changed. Temperature can also

alter the modulus of elasticity of the gauge spring. !n this sense itAs a modifying

input.

% Accuracy /ccuracy indicates the closeness of the measured value with the actual or

the true value, and is expressed in the form of maximum error as a + of the fullscale reading. Thus, if the accuracy f a temperature indicator, with a full scale

range of *#;** deg is specified as D*.;+, it indicates that the measured value

will be within -.;deg of the true value, measured through a standard instrument

during the process of calibration. Thus, if it indicates a reading of -;*deg, the

error will also be D-.; deg, i.e D)+ of reading.


10/10

% Precision

Precision indicates the repeatability or reproducibility of an instrument. !f

an instrument is used to measure the same input, but at different instants, spread

over the whole day, successive measurements may vary randomly. The random

fluctuations of readings, is often due to random variations of several other factors

which have been taken into account, while measuring the variable. / precisioninstrument indicates that the successive reading would be very close, or in other

words, the standard deviation Ee of the set of measurements would be very small.

static and dynamic characteristics

Documents