Siemens SIMATIC S7-200 - Proportional Term

SIMATIC Instructions
9-90
S7-200 Programmable Controller System Manual
A5E00066097-02
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:
ÁÁÁÁ
ÁÁÁÁ
M
n
ÁÁÁ
ÁÁÁ
=
ÁÁÁÁÁÁ
ÁÁÁÁÁÁ
K
C
 e
n
ÁÁ
ÁÁ
+
ÁÁÁÁÁÁÁÁ
ÁÁÁÁÁÁÁÁ
K
I
 e
n
 MX
ÁÁ
ÁÁ
+
ÁÁÁÁÁÁ
ÁÁÁÁÁÁ
K
D
 (e
n
–e
n–1
)
ÁÁÁÁ
ÁÁÁÁ
output
ÁÁÁ
ÁÁÁ
=
ÁÁÁÁÁÁ
ÁÁÁÁÁÁ
proportional term
ÁÁ
ÁÁ
+
ÁÁÁÁÁÁÁÁ
ÁÁÁÁÁÁÁÁ
integral term
ÁÁ
ÁÁ
+
ÁÁÁÁÁÁ
ÁÁÁÁÁÁ
differential term
where:
M
n
is the calculated value of the loop output at sample time n
K
C
is the loop gain
e
n
is the value of the loop error at sample time n
e
n - 1
is the previous value of the loop error (at sample time n - 1)
K
I
is the proportional constant of the integral term
MX is the previous value of the integral term (at sample time n - 1)
K
D
is the proportional constant of the differential term
The CPU uses a modified form of the above simplified equation when calculating
the loop output value. This modified equation is:
ÁÁÁÁ
ÁÁÁÁ
M
n
ÁÁ
ÁÁ
=
ÁÁÁÁÁÁÁ
ÁÁÁÁÁÁÁ
MP
n
ÁÁÁ
ÁÁÁ
+
ÁÁÁÁÁÁÁ
ÁÁÁÁÁÁÁ
MI
n
ÁÁ
ÁÁ
+
ÁÁÁÁÁÁ
ÁÁÁÁÁÁ
MD
n
ÁÁÁÁ
ÁÁÁÁ
output
ÁÁ
ÁÁ
=
ÁÁÁÁÁÁÁ
ÁÁÁÁÁÁÁ
proportional term
ÁÁÁ
ÁÁÁ
+
ÁÁÁÁÁÁÁ
ÁÁÁÁÁÁÁ
integral term
ÁÁ
ÁÁ
+
ÁÁÁÁÁÁ
ÁÁÁÁÁÁ
differential term
where:
M
n
is the calculated value of the loop output at sample time n
MP
n
is the value of the proportional term of the loop output at sample
time n
MI
n
is the value of the integral term of the loop output at sample time n
MD
n
is the value of the differential term of the loop output at sample time n
Proportional Term
The proportional term MP is the product of the gain (K
C
), which controls the
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
n=
K
C
* (SP
n
- PV
n
)
where:
MP
n
is the value of the proportional term of the loop output at sample
time n
K
C
is the loop gain
SP
n
is the value of the setpoint at sample time n
PV
n
is the value of the process variable at sample time n