Siemens Simatic S7-200 System Manual page 160

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
change in the process variable instead of the change in the error as shown:
MD
n
or just:
MD
n
where:
6
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
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 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.
148
= K T /
*
C D
= K * T /
C D
= K T /
*
C D
MD is the value of the differential term of the loop output at sample time n
n
K is the loop gain
C
T is the loop sample time
S
T is the differentiation period of the loop (also called the derivative time or rate)
D
SP is the value of the setpoint at sample time n
n
SP is the value of the setpoint at sample time n–1
n–1
PV is the value of the process variable at sample time n
n
PV is the value of the process variable at sample time n–1
n–1
T ((SP – PV ) – (SP
*
S n n
= SP ). This results in the calculation of the
n n – 1
T * (SP – PV – SP
S n n n
T (PV – PV )
*
S n – 1 n
is initialized to be equal to PV
n – 1
– PV ))
n – 1 n – 1
+ PV )
n – 1
.
n