Siemens SIMATIC S7-200 - Integral Term

SIMATIC Instructions
9-91
S7-200 Programmable Controller System Manual
A5E00066097-02
Integral Term
The integral term MI is proportional to the sum of the error over time. The equation
for the integral term as solved by the CPU is:
MI
n=
K
C
* T
S
/ T
I
* (SP
n
- PV
n
) + MX
where:
MI
n
is the value of the integral term of the loop output at sample time n
K
C
is the loop gain
T
S
is the loop sample time
T
I
is the integration period of the loop (also called the integral time or reset)
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
MX is the value of the integral term at sample time n - 1 (also called the
integral sum or the bias)
The integral sum or bias (MX) is the running sum of all previous values of the
integral term. After each calculation of MI
n
, the bias is updated with the value of
MI
n
which may be adjusted or clamped (see the section “Variables and Ranges” on
page 9-95 for details). The initial value of the bias is typically set to the output
value (M
initial
) just prior to the first loop output calculation. Several constants are
also part of the integral term, the gain (K
C
), the sample time (T
S
), which is the
cycle time at which the PID loop recalculates the output value, and the integral
time or reset (T
I
), which is a time used to control the influence of the integral term
in the output calculation.