Chapter 10 Built-in PID Functions
10 - 4
10.3.4 PI control
As shown in the following expression (10.3.10), PI (Proportional-Integral) control is calculated as the sum of
the proportional and integral terms. To reduce the offset, the shortcoming of the proportional term, PI control
uses the integrated error.
)10.3.10(
)9.3.10(
)8.3.10(
ip
i
p
i
pp
MVMVMV
dtE
T
K
MV
EKMV
+=
=
∫
If the error, though constant, is integrated until it is reduced to zero, the integral amount is accumulated over
time. Therefore the PI controller can be used to compensate for the offset characteristic of P control. It should
be noted that the integral time constant (Ti) is the denominator of the integral term, therefore, the smaller the
Ti value, the larger the integral effect. The following graph shows the result of PI control of the previously
described P controlled system.
As a result of adding the integral effect, the offset disappears and the system converges exactly to 50 . At ℃
the initial control, however, there occurs an overshoot in which the temperature rises to 61.2 and then falls. ℃
An excessive overshoot imposes a burden on the system or, in some cases, unstabilizes the system,
therefore, it should be reduced through proper coefficient tuning or can be improved through PID control using
the integral effect.
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
0
24 6810 12 14 16
Second
Temperature
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