Siemens SIMATIC S7-200 System Manual page 161

The S7-200 uses a modified form of the above simplified equation when calculating the loop
output value. This modified equation is:
M = MP
n n
output = proportional term
where: Mn is the calculated value of the loop output at sample time n
MP is the value of the proportional term of the loop output at sample time n
n
MI is the value of the integral term of the loop output at sample time n
n
MDn is the value of the differential term of the loop output at sample time n
Understanding the Proportional Term of the PID Equation
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 S7-200 is:
MP = K
n C
where: MPn is the value of the proportional term of the loop output at sample time n
K is the loop gain
C
SP is the value of the setpoint at sample time n
n
PV is the value of the process variable at sample time n
n
Understanding the Integral Term of the PID Equation
The integral term MI is proportional to the sum of the error over time. The equation for the integral
term as solved by the S7-200 is:
MI = K
n C
where: MI is the value of the integral term of the loop output at sample time n
n
K is the loop gain
C
T is the loop sample time
S
T is the integration period of the loop (also called the integral time or reset)
I
SP is the value of the setpoint at sample time n
n
PV is the value of the process variable at sample time n
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 , the bias is updated with the value of MI
n
clamped (see the section "Variables and Ranges" for details). The initial value of the bias is
typically set to the output value (M
constants are also part of the integral term, the gain (K
time at which the PID loop recalculates the output value, and the integral time or reset (T
is a time used to control the influence of the integral term in the output calculation.
+ MI
n
+ integral term
(SP - - PV )
*
n n
T / T
*
S I
) just prior to the first loop output calculation. Several
initial
S7-200 Instruction Set
+ MD
n
+ differential term
), which controls the sensitivity of the
C
* (SP - - PV ) +
n n
which might be adjusted or
n
), the sample time (T ), which is the cycle
C S
Chapter 6
MX
), which
I
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