Siemens Simatic S7-200 System Manual page 246

Instruction Set
Differential Term
The differential term MD is proportional to the change in the error. The equation for the
differential term:
MD K
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
results in the calculation of the change in the process variable instead of the change in the
error as shown:
MD K
n =
or just:
MD K
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
equal to PV .
n
Selection of Loop Control
In many control systems it may be necessary to employ only one or two methods of loop
control. For example only proportional control or proportional and integral control may 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 should
be specified for the integral time (reset). Even with no integral action, the value of the integral
term may 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.
10-58
* T / T * ((SP - PV ) - (SP
C D S n n
* T / T * (SP - PV - SP
C D S n n
* T / T * (PV - PV
C D S n - 1 n
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
- PV ))
n - 1 n - 1
n
+ PV )
n n - 1
)
is initialized to be
n - 1
S7-200 Programmable Controller System Manual
C79000-G7076-C230-02
= SP ). This
n - 1