In steady state operation, a PID controller regulates the value of the
output so as to drive the error(e) to zero. A measure of the error is given by
the difference between the setpoint (SP) (the desired operating point) and the
process variable (PV) (the actual operating point). The principle of PID
control is based upon the following equation that expresses the output, M(t),
as a function of a proportional term, an integral term, and a differential
term:
Output
= Proportional term + Integral term + Differential term
t
M(t) = KC * e + Kc ∫ e dt + M +KC
* de/dt
0 initial
where: M(t)
is
the loop output as a function of time
KC is the loop
gain
e is the loop error (the difference
between setpoint and process variable)
Minitial
is
the initial value of the loop output
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For implement this control function in a
digital computer, the continuous function must be quantized into periodic
samples of the error value with subsequent calculation of the output. The corresponding
equation that is the basis for the digital computer solution is:
For S7-200 ,this equation is:
Role of Proportional Term in PID -
""Proportional
term MP is the product of the gain (KC), 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"
Equation is,
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:
Equation is,
Differential
Term of the PID Equation:
The differential term MD is
proportional to the change in the error. The S7-200 uses the following equation
for the differential term:
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