WEG CFW-11 Series, Programming Manual, Page: 288 / 307

PID Regulator [46]
20-16
20
20.7 ACADEMIC PID
The controller implemented in the CFW-11 is of the academic type. The equations that characterize the Academic
PID, which is the base of this function algorithm, are presented next.
The transfer function in the Academic PID regulator frequency dominion is:
y(s) = Kp x e(s) x [ 1 +
1
+ sTd]
sTi
By replacing the integrator by a sum and the derivative by the incremental quotient, one gets an approximation for
the discrete transfer equation (recursive) presented next:
y(kTa) = y(k-1)Ta + Kp[(e(KTa) - e(k-1)Ta) + Kie(k-1)Ta + Kd(e(kTa) - 2e(k-1)Ta + e(k-2)Ta)]
Being:
Kp (Proportional gain): Kp = P0520 x 4096.
Ki (Integral gain): Ki = P0521 x 4096 = [Ta/Ti x 4096].
Kd (Differential gain): Kd = P0522 x 4096 = [Td/Ta x 4096].
Ta = 0.02sec (PID regulator sampling time).
SP*: reference, it has 13 bits (0 to 8191) maximum.
X: process variable (or controlled), read by means of one of the analog inputs (AIx), it has 13 bits maximum.
y(kTa): PID actual output, it has 13 bits maximum.
y(k-1)Ta: PID previous output.
e(kTa): actual error [SP*(k) – X(k)].
e(k-1)Ta: previous error [SP*(k-1) – X(k-1)].
e(k-2)Ta: error two samples before [SP*(k-2) – X(k-e2)].