Siemens SIMATIC S7-200 System Manual page 162

S7-200 Programmable Controller System Manual
Understanding the Differential Term of the PID Equation
The differential term MD is proportional to the change in the error. The S7-200 uses the following
equation for the differential term:
MD =
n
To avoid step changes or bumps in the output due to derivative action on setpoint changes, this
equation is modified to assume that the setpoint is a constant (SP
calculation of the change in the process variable instead of the change in the error as shown:
MD =
n
or just:
MD =
n
where: MD
n
K
C
T
S
T
D
SP
n
SP
n- -1
PV
n
PV
n- -1
The process variable rather than the error must be saved for use in the next calculation of the
differential term. At the time of the first sample, the value of PV
PV .
n
Selecting the Type of Loop Control
In many control systems, it might be necessary to employ only one or two methods of loop control.
For example, only proportional control or proportional and integral control might be required. The
selection of the type of loop control desired is made by setting the value of the constant
parameters.
If you do not want integral action (no "I" in the PID calculation), then a value of infinity "INF", should
be specified for the integral time (reset). Even with no integral action, the value of the integral term
might not be zero, due to the initial value of the integral sum MX.
If you do not want derivative action (no "D" in the PID calculation), then a value of 0.0 should be
specified for the derivative time (rate).
If you do not want proportional action (no "P" in the PID calculation) and you want I or ID control,
then a value of 0.0 should be specified for the gain. Since the loop gain is a factor in the equations
for calculating the integral and differential terms, setting a value of 0.0 for the loop gain will result
in a value of 1.0 being used for the loop gain in the calculation of the integral and differential
terms.
Converting and Normalizing the Loop Inputs
A loop has two input variables, the setpoint and the process variable. The setpoint is generally a
fixed value such as the speed setting on the cruise control in your automobile. The process
variable is a value that is related to loop output and therefore measures the effect that the loop
output has on the controlled system. In the example of the cruise control, the process variable
would be a tachometer input that measures the rotational speed of the tires.
148
K T /
*
C D
K T /
*
C D
K T /
*
C D
is the value of the differential term of the loop output at sample time n
is the loop gain
is the loop sample time
is the differentiation period of the loop (also called the derivative time or rate)
is the value of the setpoint at sample time n
is the value of the setpoint at sample time n- -1
is the value of the process variable at sample time n
is the value of the process variable at sample time n- -1
*
T ((SP - - PV ) - - (SP
S n n
*
T (SP - - PV - - SP
S n n
*
T (PV - - PV
S n - - 1
n - - 1
- - PV ))
n - - 1 n - - 1
= SP ). This results in the
n n - - 1
+ PV )
n n - - 1
)
n
is initialized to be equal to