Dynamic System Response
Author: John M. Cimbala, Penn State University
Latest revision: 02 November 2007 – minor correction 31 March 2008
Introduction
•
In an
ideal
world, sensors respond instantly to changes in the parameter being measured.
•
In the
real
world, however, sensors require some time to adjust to changes, and in many cases exhibit
oscillations that take some time to die out.
•
In this learning module, we discuss the dynamic system response of sensors and their associated electronic
circuits.
[Much of this material is also covered in M E 370 – Vibration of Mechanical Systems.]
Dynamic systems
Measuring
system
Input
Output
y
•
Consider some generic measuring system with an input and an
output, as sketched to the right.
•
The
input
is the physical quantity or property being measured, s
etc. The input is given the symbol
x
, and is formally called the
measurand
.
The
measurin
uch as pressure, temperature, velocity, strain,
•
g system
converts the measurand into something different, so that we can read, record, and/or
•
changes as the measurand changes. The output is
•
) can be either
static
(steady within the time of measurement) or
dynamic
(unsteady).
analyze it. The measuring system can be a
sensor
like a strain gage (converts strain directly into a change in
resistance) or thermocouple (converts temperature directly into a voltage), or a
transducer
like a pressure
transducer (converts pressure into a voltage or current).
The
output
may be mechanical or electrical, and its value
given the symbol
y
.
The input (measurand
•
If the measurand is static, the output is generally some factor
K
times the input,
yK
x
=
, where
K
is called
the
static sensitivity
of the measuring system.
For time-dependent (unsteady or dynamic) measure
•
ments, the behavior is described by a differential
onse
.
•
rder of a dynamic system
re measurand
x
is not constant (static), but is changing with time (dynamic),
x
=
x
(
t
).
equation. Such systems are called
dynamic systems
, and their behavior is called
dynamic system resp
In this learning module, only
linear
measuring systems are considered. In other words, for static signals,
y
has a
linear
relationship with
x
, namely,
y
=
Kx
, rather than some nonlinear relationship like
y
=
K
1
x
+
K
2
x
2
.
O
•
Consider the case whe
•
In an
ideal
measuring system, output
y
would respond
instantaneously
to changes in
x
,
( ) ( )
yt
K
xt
=
.
•
We define
n
as the
order of the dynamic system
.
•
The order of an ideal dynamic system is zero, i.e.,
n
= 0
. An ideal measuring system is thus also called a
•
al, but a simple resistor circuit comes close. Consider
•
ll times:
zero-order dynamic system
.
No real system is perfectly ide
the resistor as the system, with voltage drop as the input, and current through the
resistor as the output, as sketched to the right.