Rockwell Automation 1760-xxxx Pico GFX-70 Controllers User Manual - Manual (Page 210)

Publication 1760-UM002B-EN-P - March 2005
4-100 Wiring with Pico GFX-70
The proportional component in the PID controller
The proportional component Y
P
is the product of the gain (K
p
) and the
control difference (e). The control difference is the difference between the
setpoint (X
s
) and the actual value (X
i
) at a specified scan time. The equation
used by the device for the proportional component is as follows:
Y
P
(t) = K
p
x [X
s
(t) - X
i
(t)]
K
p
= proportional gain
X
s
(t) = Setpoint with scan time t
X
i
(t) = Actual value with scan time t
The integral component in the PID controller
The integral component Y
I
is proportional to the sum of the control
difference over time. The equation used by the device for the integral
component is as follows:
Y
I
(t) = K
p
x T
c
/T
n
x [X
s
(t) - X
i
(t)] + Y
I
(t-1)
K
p
= proportional gain
T
c
= Scan time
T
n
= Integration time (also known as reset time)
X
s
(t) = Setpoint with scan time t
X
i
(t) = Actual value with scan time t
Y
I
(t-1) = Value of the integral component of the manipulated variable with scan time t-1
The differential component in the PID controller
The differential component Y
D
is proportional to the change in the control
difference. So as to avoid step changes or jumps in the manipulated variable
caused by the differential behavior when the setpoint is changed, the change of
the actual value (the process variable) is calculated and not the change in the
control difference. This is shown in the following equation:
Y
D
(t) = K
p
x T
v
/T
c
x (X
i
(t-1) - X
i
(t) )
K
p
= proportional gain
T
c
= Scan time
T
v
= Differential time of the control system (also called the rate time)
X
i
(t) = Actual value with scan time t
X
i
(t-1) = Actual value with scan time t - 1