For those that are keen to understand the math behind the PID loops the following discussion explains the The output value of a PID Loop is calculated according to the following formulas:
OUTPUT = Op + Oi + Od + Ob
Op = Proportional Output = A * 100 / Pb * ( I - S )
Oi = Integral Output = A * R * t/60 * ( I - S ) + Oi
Od = Derivative Output = A * D*(( I - S ) - ( It-1 - St-1 )) / t
Ob = Bias
A = Action (+1 for direct acting, -1 for reverse acting)
Pb = Proportional Band
I = Input
S = Setpoint
R = Reset Constant = Repeats per hour Definition: One repeat per hour will cause an output change of one over one hour for an error of one.
D = Rate Constant = Minutes Definition: One minute will cause an output of one for an error changing by one per minute.
T = Time in Minutes since last scan.
It-1 = Input on last scan.
St-1 = Setpoint on last scan.
Note: The PID loop math is executed once per second.
Output Limiting Procedure:
1. The sum of Op + Od + Ob is clipped at 100%, it cannot go to any number larger than that to avoid windup.
2. Oi is added to the previous sum.
3. The output is again limited to 0-100.
4. Oi is adjusted by the amount that the output was limited in step 3.
Note: Oi is reset to zero when the I term is set to 0.
