
0
0 102030405060708090100
0 102030405060708090100
f
1
(t), (cu ft per min)
h
2
(t), (ft)
20
40
60
80
f
1
(t) vs. t
h
2
(t) vs. t
0
10
20
30
40
t (min)
h
2
(50)
0
t
Area =
∫
f
1
(t)dt
1
A
2
h
2
(50) =
×Area
FIGURE E3.3
3.3 EULER INTEGRATION
The previous section presented a framework for finding a discr ete-time system approximation of a
continuous-time integrator. An approxi mation to the integral term in Equation 3.16 is needed. The
simplest approach assumes the integrator input u(t) is constant over the interval, that is, u(t) u(n),
nT t (n þ1)T where u(n) is short for u(nT) as shown in Figure 3.5.
The exact area under the function u(t), nT t (n þ1) T is being approximated by