For more information visit:
www.EatonElectrical.com
Programming wiring
MN05013005E
218
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
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
×
T
c
/T
n
×
[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
×
T
v
/T
c
×
(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)