Page 357 - Modern Control Systems

Section 5.7 Performance Indices 331

(a) r(t)

(b)

(c)

(d) e\t)

FIGURE 5.25 (e) je (t) dt
2
The calculation of
the integral squared
error.

Another readily instrumented performance criterion is the integral of the
absolute magnitude of the error, IAE, which is written as
T
IAE = f \e(t)\ dt. (5.38)
Jo
This index is particularly useful for computer simulation studies.
To reduce the contribution of the large initial error to the value of the perfor-
mance integral, as well as to emphasize errors occurring later in the response, the
following index has been proposed [6]:

ITAE = I t\e(t)\ dt. (5.39)

This performance index is designated the integral of time multiplied by absolute error,
ITAE. Another similar index is the integral of time multiplied by the squared error, or

ITSE = / te\t) dt. (5.40)