Proportional Term - Siemens SIMATIC S7-200 System Manual

SIMATIC Instructions
Since the digital computer must calculate the output value each time the error is
sampled beginning with the first sample, it is only necessary to store the previous
value of the error and the previous value of the integral term. As a result of the
repetitive nature of the digital computer solution, a simplification in the equation
that must be solved at any sample time can be made. The simplified equation is:
M
n
output
where:
M
n
K
C
e
n
e
n - 1
K
I
MX
K
D
The CPU uses a modified form of the above simplified equation when calculating
the loop output value. This modified equation is:
M
n
output
where:
M
n
MP
n
MI
n
MD
n

Proportional Term

The proportional term MP is the product of the gain (K
sensitivity of the output calculation, and the error (e), which is the difference
between the setpoint (SP) and the process variable (PV) at a given sample time.
The equation for the proportional term as solved by the CPU is:
MP K
n =
where:
MP
n
K
C
SP
n
PV
n
9-90
= K e +
C n
= proportional term +
is the calculated value of the loop output at sample time n
is the loop gain
is the value of the loop error at sample time n
is the previous value of the loop error (at sample time n - 1)
is the proportional constant of the integral term
is the previous value of the integral term (at sample time n - 1)
is the proportional constant of the differential term
= MP
n
= proportional term
is the calculated value of the loop output at sample time n
is the value of the proportional term of the loop output at sample
time n
is the value of the integral term of the loop output at sample time n
is the value of the differential term of the loop output at sample time n
* (SP - PV )
C n n
is the value of the proportional term of the loop output at sample
time n
is the loop gain
is the value of the setpoint at sample time n
is the value of the process variable at sample time n
K e MX
n
I
integral term
+ MI
n
+ integral term
), which controls the
C
S7-200 Programmable Controller System Manual
+
K (e –e )
n
D n–1
+ differential term
+ MD
n
+ differential term
A5E00066097-02