Automating Manufacturing Systems - Process Control and ...

plc pid - 25.13
Recall the cruise control system for a car. Figure 25.15 shows various equations
that could be used as the controller.
PID Controller
dv error
θ gas
K p
v error
K i ∫ v error
dt ⎛ K ⎞
= + + d
----------------
⎝ dt ⎠
PI Controller
θ gas
= K p
v error
+ K i
v error
dt
∫
PD Controller
dv
θ ⎛
gas
= K p
v error
+ K error ⎞
d
----------------
⎠ dt
P Controller
θ gas
=
K p
v error
⎝
Figure 25.15
Different Controllers
When implementing these equations in a computer program the equations can be
rewritten as shown in Figure 25.16. To do this calculation, previous error and control values
must be stored. The calculation also require the scan time T between updates.
u n
u n – 1
e n
K p
K i
T K ⎞ d
+ + ----- e ⎛
T n – 1
– K p
2 K d
K
–
⎛
----- ⎛ ⎞ d
= + e ⎞
+ +
T n – 2
-----
T
⎝
⎠
⎝
⎠
⎝
⎠
Figure 25.16
A PID Calculation
The PID calculation is available as a ladder logic function, as shown in Figure
25.17. This can be used in place of the SUB and MUL functions in Figure 25.12. In this
example the calculation uses the feedback variable stored in Proc Location (as read from
the analog input). The result is stored in N7:2 (to be an analog output). The control block
uses the parameters stored in PD12:0 to perform the calculations. Most PLC programming
software will provide dialogues to set these value.