User Manual

Wiring with easy800
188
08/04 AWB2528-1423GB
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 timet
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 timet
X
i
(t) = Actual value with scan time t
Y
I
(t–1) = Value of the integral component of the manipulated
variable with scan timet –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
behaviour 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