Instrumentation system
design
Instrumentation system
design
Sources of error
• Insufficient knowledge of process
parameters & design conditions
• Poor design
• Change in process parameters,
irregularities, upsets etc.
• Poor maintenance
• Error caused by person operating the
instrument or equipment
• Certain design limitations
Dynamic characteristics
these are determined by subjecting its primary element to unknown
and predetermined variations in the measured quantity
• Common variation
– Step change: primary element is
subjected to an instantaneous & finite
change in measured variable
– Linear change: primary element is
following a measured variable, changing
linearly with time.
– Sinusoidal change: primary element
follows a measured, magnitude of which
changes in accordance with a sinusoidal
function of constant variable.
Dynamic characteristics
• Speed of response : rapidity with which an
instrument responds to changes.
• Fidelity : degree to which an instrument
indicates the changes in measured value
w/o dynamic error.
• Lag : retardation in the response of
instrument to change
• Dynamic error: difference b/w true value of
quan. Changing with time and the value
indicated by the instrument (no static error
is assumed)
Dynamic response
• Zero order instruments
• 1
st
order instruments
• 2
nd
order instruments
• Link:
http://www.jgsee.kmutt.ac.th/exell/Prac
Math/Instruments.html
General Instrument
Response
The traditional way to investigate the dynamic
response of an instrument is to consider the
differential equation that describes the output. We
assume that the instrument response can be
modeled using a linear ordinary differential equation
with constant coefficients
where y is the instrument output, x is the input,
and n is the order of the instrument.
Zero Order Linear
Instrument
First Order Instruments
• A first order linear instrument has an output which is given
by a non-homogeneous first order linear differential equation
where τ (= a1/a0) is the time constant and K (= b/a0) is the
static gain.
• In these instruments there is a time delay in their response to
changes of input. The time constant tau is a measure of the
time delay.
• Thermometers for measuring temperature are first-order
instruments. The time constant of a measurement of
temperature is determined by the thermal capacity of the
thermometer and the thermal contact between the
thermometer and the body whose temperature is being
measured.
Response of a first-order instrument to a step change input
versus nondimensional time.
Second Order Instruments
• A second order linear instrument has an output which is given
by a non-homogeneous second order linear differential equation
K(= b/a0) is again the static gain, ζ(= a
1
/2√a
0
a
2
) is the damping
factor, and ωn(= √ a
0
/a
2
) is the natural frequency. Under a static
input a second order linear instrument tends to oscillate about its
position of equilibrium. The natural frequency of the instrument is
the frequency of these oscillations.
• Friction in the instrument opposes these oscillations with a
strength proportional to the rate of change of the output. The
damping factor is a measure of this opposition to the oscillations
Response of a second-order instrument to a step
change input for various damping factors.
Statistical analysis
• Arithmetic mean
• Deviation from the mean
• Average deviation
• Standard deviation
• Limiting errors