LSIS XGK-CPUU - PID Control Operation

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(
dip
dpd
i
p
i
pp
MVMVMVMV
dt
dE
TKMV
dtE
T
K
MV
EKMV
PVSVE
++=
=
=
=
−=
∫
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.