Siemens Simatic S7-200 System Manual page 245

Proportional Term
The proportional term MP is the product of the gain (K
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 = C
where:
MP
n
K
C
SP
n
PV
n
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 K
n = C
where:
MI
n
K
C
T
S
T
I
SP
n
PV
n
MX
The integral sum or bias (MX) is the running sum of all previous values of the integral term.
After each calculation of MI
adjusted or clamped (see the section "Variables and Ranges" for details). The initial value of
the bias is typically set to the output value (M
calculation. Several constants are also part of the integral term, the gain (K
time (T ), which is the cycle time at which the PID loop recalculates the output value, and the
S
integral time or reset (T
the output calculation.
S7-200 Programmable Controller System Manual
C79000-G7076-C230-02
* (SP - PV )
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
* T / T * (SP - PV ) + MX
S I n n
is the value of the integral term of the loop output at sample time n
is the loop gain
is the loop sample time
is the integration period of the loop (also called the integral time or reset)
is the value of the setpoint at sample time n
is the value of the process variable at sample time n
is the value of the integral term at sample time n - 1 (also called the integral
sum or the bias)
, the bias is updated with the value of MI
n
), which is a time used to control the influence of the integral term in
I
), which controls the sensitivity of the
C
which may be
n
) just prior to the first loop output
initial
Instruction Set
), the sample
C
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