When
the instrument is subjected to rapidly varying inputs, the relation between
input and output becomes totally different than that in case of static or
constant inputs. As the input varies from instant to instant, output also
varies from instant to instant. The behaviour of system under such conditions
is called dynamic response of the system.
The
dynamic behaviour of the measuring system is determined by applying some known
and predetermined variations of input to the sensing element. The standard
variations in the input, used practically to obtain the dynamic behaviour, are
as follows:
1. Step
input
This represents sudden,
instantaneous and finite change in the input. The step input of magnitude A is
denoted as Au (t) and can be indicated as shown in the fig.
Its
Laplace transform is given by,
F(s) =
……. Laplace of step input.
When
A=1 it is called unit step input.
 |
| Step |
2. Ramp
input
This represents linear change in input. The input, i.e. a variable to be
measured varies linearly with time. It changes at a constant rate with respect
to the time. The ramp input of magnitude A denoted as At u (t)
and can be shown in the fig.
The Laplace transform of rape is
given by,
F(s)
=A/S²………..Laplace of ramp input
When A=1, it is called unit ramp
input.
 |
| Ramp |
3. Parabolic
input
This represents an input signals which is proportional to the square of
the time and hence represents constant acceleration. The parabolic input of
magnitude A is denoted as
u(t) and can be shown in fig.
The Laplace transform of parabola is given by,
F(s) =
2A/s³……….Laplace of parabolic input
 |
| Parabolic |
4. Impulse
input
It exists only at t=o and has zero value at any other time.
f(t) =0 for t≠ 0
And area under it is its magnitude. If it
is unity, it is called delta function denoted as δ (t). It is shown in fig. it
shows the concept of impulse input and it shows its representation. It is
basically a pulse with its base Δt approaching to zero. The Laplace transform
of δ(t) is 1.
L
(δt) =1……………Laplace of unite impulse input
 |
| Impulse Input |
5. Sinusoidal
input This represents an input which changes in accordance with a Sinusoidal
function of constant amplitude. The frequency is the independent variable in
this case. For a linear system subjected to Sinusoidal input, the output is
also Sinusoidal in steady state, but it differs from input in amplitude and
phase. Analyzing the dynamic behaviour includes the study of variation in
output amplitude and phase as input is Sinusoidal in nature.
The Sinusoidal input is given by A sinɷt where Ais its amplitude
as shown in fig. its Laplace transform is given by,
F(s)= Aɷ/s²+ɷ²………Laplace of Sinusoidal input.
The various dynamic characteristics of an
instrument are speed of response, fidelity, lag and the dynamic error.
 |
| Sinusoidal Input |
Speed of Response
It is the rapidity with which the system responds to the
changes in the quantity to be measured. It gives the information about how fast
the system reacts to the changes in the input. It indicates activeness of the
system.
Fidelity
It indicates how much faithfully the system reproduces the
changes in the input. It is the ability of an instrument to produce a wave
shape of input with respect to time.
Lag
Every system takes some time, whatever small it may be, to
respond to the changes in the measured variable. This retardation or delay in
the response of a system is called lag.
The lags are of two types:-
1. Retardation
Lag: In this case, the response of the system begins immediately after a change
in the variable has occurred.
2. Time
Delay : In this case,response begins after some time called dead time, after
the application of input. Such a delay shifts the response along time axis and
hence causes the dynamic error.
Dynamic Error
 |
| Dynamic characteristics |
It is the difference between the true value of the variable
to be measured, changing with time and the value indicated by the measurement
system, assuming zero static error.
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