Rockwell Automation 1771-PD PID MODULE (+DU) - Manual (Page 235)

Appendix
E
EĆ1
Comparing ISA 1771ĆPD Algorithms
The ISA standard algorithm and the Allen-Bradley 1771-PD algorithm are
different although they achieve the same closed loop control. By
understanding the differences, you can convert proportional gain, reset
and rate values from ISA standard to equivalent 1771-PD gain values.
ISA Standard Algorithm
The equation for PID closed loop control is:
V
O
= K
C
(E)+ K
C
/T
I
/(E)dt +K
C
(T
D
)d(E)/dt
Where K
C
= controller gain
1/T
I
= reset term in repeats per minute
T
D
= rate term in minutes
1771-PD Algorithm
The equation for PID closed loop control is:
V
O
= K
P
(E) + K
I
/(E)dt + (K
D
)d(E)/dt + Bias
Where K
P
= proportional gain
K
I
= integral gain in inverse seconds
K
D
= derivative gain in seconds
Comparison
The ISA standard algorithm contains dependent variables. When you
change your controller gain (KC), you also change your integral and
derivative values.
The 1771-PD algorithm contains independent variables. You adjust the
proportional, integral, and derivative terms independently.