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30.3.1 PID Control Systems

• The basic equation for a PID controller is shown below. This function will try to compensate for error in a controlled system (the difference between desired and actual output values).

	de
u = Kce + Ki∫ edt + Kd	-----
	dt

• The figure below shows a basic PID controller in block diagram form.

	proportional				PID Controller
V		Kp( e)				V
					+V
	integral			+
+	e	Ki( ∫ e)			u
				+	amp	motor
-	derivative			+	-V
	K		d
		d	----e
			dt

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e.g.

θ

= K

v

+ K

v

dt + K

dverror

gas

c

error

i∫

error

----------------

d

dt

Rules 2 & 3

Rule 4

(general difference)

(Immediate error)

Rule 1

(Long term error)

Kc

Ki Relative weights of components

Kd

This is a PID Controller

Proportional

Integral

Derivative

For a PI Controller

θ gas = Kcverror + Ki∫ verrordt

For a P Controller

θ gas = Kc verror

For a PD Controller								dverror
θ		= K		v		+ K
	gas		c		error			----------------
							d	dt

• The PID controller is the most common controller on the market.

30.3.1.1 - PID Control With a PLC

•The PID calculation is effectively a calculation in the PLC. One basic method of PID control is

i)read voltage, ii) do PID calculation, iii) set output voltage. (Note: it is also common to get a self contained PID card for the PLC that deals with all inputs and outputs). The ladder logic below shows a PID control function.