Chapter 10 Built-in PID Functions
10 - 2
10.3 PID Control Operation
10.3.1 Terms
Below are the terms used to describe the PID control operation.
SV
: The target state the control object should reach
T_s (Ts)
: Sampling time (Control cycle)
K_p (Kp)
: Proportional coefficient
T_i (Ti)
: Integral time constant
T_d (Td)
: Differntial time constant
PV
: Current state of the control object, which is detected by the sensor
ERR
: Current error of the control object, which is represented by (SV – PV)
MV
: Control input or controller output
MV_p (MVp) : Proportaional componentof MV
MV_i (MVi) : Integral component of MV
MV_d (MVd) : Derivative component of MV
10.3.2 PID expressions
PID expressions are as follows.
)
5
.
3
.
10
(
)
4
.
3
.
10
(
)
3
.
3
.
10
(
)
2
.
3
.
10
(
)
1
.
3
.
10
(
d
i
p
d
p
d
i
p
i
p
p
MV
MV
MV
MV
dt
dE
T
K
MV
dt
E
T
K
MV
E
K
MV
PV
SV
E
+
+
=
=
=
=
−
=
∫
An error is a mathematical expression that tells about how far the current system is from the state desired by
the user.
Here is an example; a user wants the water in a electric pot to be kept at 50
℃
and the current water
temperature is 35
℃
. Then, SV is 50
℃
, PV is 35
℃
. The error (E) is 15
℃
, the difference between SV and PV.
Upon detection of the error, the controller performs PID operation.
Note that, as shown in (10.3.5), MV is the sum of the P, I and D compoents (MV_p, MV_i, and MV_d).
Therefore, if the D component is excluded from the PID control expression, then the PI control results and, if
the I and D components are excluded, then P control results.
