ABB CL Series, Applications Manual

Page: 212 / 428

Function blocks
209
1SVC 440 795 M1100
PID controller equation:
Y( t ) = Y
P
( t ) + Y
I
( t ) + Y
D
( t )
Y(t) = Calculated manipulated variable with scan time t
Y
P
(t)= Value of the proportional component of the manipulated
variable with scan time t
Y
I
(t)= Value of the integral component of the manipulated variable
with scan time t
Y
D
(t)= Value of the differential component of the manipulated
variable with scan time t
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