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Chapter 3
Converting Models
Forward Rectangular Method
The Forward Rectangular method considers ƒ(τ) constant and equal to
ƒ(t + T) along the integration range. This consideration results in the
following equation:
y ( t + T ) = y ( t ) + f ( t + T )T
This method considers the incremental area term between sampling times t
and t + T as a rectangle of width T and height equal to ƒ(t + T ), as shown
in Figure 3-2.
Forward
f(t + T)
f(t)
t
t+T
Figure 3-2. Forward Rectangular Method
Figure 3-2 shows that, for this example, the Forward Rectangular method
overestimates the area under the curve. To minimize this overestimation,
use a small sampling interval. Depending on the direction and size of the
curve you are measuring, this overestimation might not occur.
Backward Rectangular Method
The Backward Rectangular method considers ƒ(τ) constant and equal to
ƒ(t) along the integration range. This consideration results in the following
equation:
y ( t + T ) = y ( t ) + f ( t )T
Control Design User Manual
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