Automationdirect.com D4-454 PLC User Manual page 418

Chapter 8: PID Loop Operation
The D4-454 also combines the integral sum and the initial output into a single term called
the bias (Mx). This results in the following set of equations:
The D4-454 by default will keep the normalized output M in the range of 0.0 to 1.0. This
is done by clamping M to the nearer of 0.0 or 1.0 whenever the calculated output falls
outside this range. The D4-454 also allows you to specify the minimum and maximum
output limit values (within the range 0 to 4095 in BCD if using 12 bit unipolar).
NOTE: The equations and algorithms, or parts of, in this chapter, are only for references. Analysis
of these equations can be found in most good text books about process control.
Reset Windup Protection
Reset windup can occur if reset action (integral term) is specified and the
computation of the bias term Mx is:
For example, assume the output is controlling a valve and the PV remains at some
value greater than the setpoint. The negative error (en) will cause the bias term (Mx)
to constantly decrease until the output M goes to 0 closing the valve. However, since
the error term is still negative, the bias will continue to decrease becoming ever more
negative. When the PV finally does come back down below the SP, the valve will stay
closed until the error is positive for long enough to cause the bias to become positive
again. This will cause the process variable to undershoot.
One way to solve the problem is to simply clamp the normalized bias between 0.0 and 1.0.
The D4-454 CPU does this. However, if this is the only thing that is done, then the output
will not move off 0.0 (thus opening the valve) until the PV has become less than the SP.
This will also cause the process variable to undershoot.
The D4-454 CPU is programmed to solve the overshoot problem by either freezing the
bias term, or by adjusting the bias term.
8-10
D4-454 PLC User Manual, 1st Edition, Rev. D
Mxo = Mo
Mx = Ki * en + Mxn-1
Mn = Kc * en - Kr(PVn-PVn-1) + Mxn
Mx = Ki * en + Mxn-1