Automating Manufacturing Systems - Process Control and ...

plc pid - 25.12
25.3.4 PID Control Systems
Proportional-Integral-Derivative (PID) controllers are the most common controller
choice. The basic controller equation is shown in Figure 25.13. The equation uses the system
error e, to calculate a control variable u. The equation uses three terms. The proportional
term, Kp, will push the system in the right direction. The derivative term, Kd will
respond quickly to changes. The integral term, Ki will respond to long-term errors. The
values of Kc, Ki and Kp can be selected, or tuned, to get a desired system response.
u = K c
e + K i
de
edt + K d
----- Kc
dt Ki
Kd
Relative weights of components
Figure 25.13
PID Equation
Figure 25.14 shows a (partial) block diagram for a system that includes a PID controller.
The desired setpoint for the system is a potentiometer set up as a voltage divider. A
summer block will subtract the input and feedback voltages. The error then passes through
terms for the proportional, integral and derivative terms; the results are summed together.
An amplifier increases the power of the control variable u, to drive a motor. The motor
then turns the shaft of another potentiometer, which will produce a feedback voltage proportional
to shaft position.
proportional
PID Controller
V
+
-
K p
( e)
integral
e
( e ∫ )
K i
derivative
d ⎛ K ⎞
d
----e
dt
⎝
⎠
+
+
+
u
+V
amp
-V
motor
V
Figure 25.14
A PID Control System