Differential Term; Selection Of Loop Control - Siemens SIMATIC S7-200 System Manual

SIMATIC Instructions

Differential Term

The differential term MD is proportional to the change in the error. The equation for
the differential term is shown below:
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
SP ). This results in the calculation of the change in the process variable instead
n - 1
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 is initialized to be equal to PV
n - 1

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.
9-92
* T / T * ((SP - PV
C D S n n
* T / T * (SP - PV
C D S n n
* T / T * (PV - PV
C D S n - 1
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
) - (SP - PV ))
n - 1 n - 1
- SP + PV )
n n - 1
)
n
.
n
S7-200 Programmable Controller System Manual
=
n
A5E00066097-02