CHAPTER 6
INTRODUCTION TO SYSTEM IDENTIFICATION
Broadly speaking, system identification is the art and science of using measurements obtained
from a system to characterize the system. The characterization of the system is usually in some
mathematical form. The limited cases considered here will use differential equations, in
particular, first and second order differential equations. When the form of the differential
equation
is
known
the
system
identification
problem
is
reduced
to
that
of
parameter
identification.
Present industrial practice presents several situations where system identification is used. An
important application is in industrial controls. Before a controller can be designed some things
must be known about the system which is to be controlled. Many systems do not lend themselves
to modeling and the most effective way to find out about the system is to make measurements
and apply the methods of system identification. The use of the methods covered in this course
and even more sophisticated methods such as finite element methods for modeling real
engineering systems, even simple ones, yield only approximate results and the models must be
adjusted using data obtained from the system. For most mechanical systems there are no
analytical methods for predicting system damping so that engineering judgment or system
identification methods must be used.
The measurements which are used for system identification can arise in one of several ways.
For large systems such as a building, ambient data is used. That is, natural excitations such as
wind, are used to excite the system. Even for uncontrolled random excitations such as this,
spectra that show the average distribution of response signal power as a function of frequency
can be used to identify system characteristics. These methods will not be discussed further here.
We will use several controlled inputs to give system responses which are easier to analyze. These
would include a step input (such as a sudden change in temperature of a thermo system), a snap
back (such as deflecting a springmass system and then suddenly releasing it), an impulse (such
as striking a springmass system with a sharp blow), or sinusoidal input. The selection of which
input to use is a function of your ability to generate the input and record and analyze the
response.
These notes will only cover 1st and 2nd order systems. Real engineering systems are rarely 1st
or 2nd order systems so the practical utility of these simple systems is questionable. Fortunately,
from an analysis point of view, even complex mechanical systems can be represented by several
connected first and second order systems. Consider as an example the measurement system
shown in Figure 1. The first component is an accelerometer which is a second order system, it is
connected to an amplifier which is a first order system, and a recording device which can be
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modeled as a second order system. The total measurement system is thus fifth order but can be
modeled as three simpler systems connected in series.
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 Spring '08
 Staff
 Math, Impulse response, Sine wave, frequency response function

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