Siemens SIMATIC S7-1200 Manual page 170

PID is easy
PID algorithm
The PID (Proportional/Integral/Derivative) controller measures the time interval between two
calls and then evaluates the results for monitoring the sampling time. A mean value of the
sampling time is generated at each mode changeover and during initial startup. This value is
used as reference for the monitoring function and is used for calculation. Monitoring includes
the current measuring time between two calls and the mean value of the defined controller
sampling time.
The output value for the PID controller consists of three components:
● P (proportional): When calculated with the "P" component, the output value is proportional
to the difference between the setpoint and the process value (input value).
● I (integral): When calculated with the "I" component, the output value increases in
proportion to the duration of the difference between the setpoint and the process value
(input value) to finally correct the difference.
● D (derivative): When calculated with the "D" component, the output value increases as a
function of the increasing rate of change of the difference between the setpoint and the
process value (input value). The output value is corrected to the setpoint as quickly as
possible.
The PID controller uses the following formula to calculate the output value for the
PID_Compact instruction.
y
w
K
p
T
1
T
D
The PID controller uses the following formula to calculate the output value for the PID_3Step
instruction.
y
w
K
p
T
1
T
D
170
Output value
Setpoint value
Proportional gain
(P component)
Integral action time
(I component)
Derivative action time
(D component)
Output value
Setpoint value
Proportional gain
(P component)
Integral action time
(I component)
Derivative action time
(D component)
x Process value
s Laplace operator
a Derivative delay coefficient
(D component)
b Proportional action weighting
(P component)
c Derivative action weighting
(D component)
x Process value
s Laplace operator
a Derivative delay coefficient
(D component)
b Proportional action weighting
(P component)
c Derivative action weighting
(D component)
Manual, 03/2014, A5E02486774-AF
Easy Book