121
New Brunswick Scientific
User’s Guide
19.6
What Do the Constants Mean?
The control signal, S
N
, for a loop that is N seconds into a run is expressed
mathematically as:
S
N
= P(e
N
/k) +
Σ
(I/60)(e
n
/k) + D[(e
N
-e
N-1
)/k]
Where:
P
,
I
, and
D
are, respectively, the proportional, integral and derivative
constants
e
is the loop setpoint minus the current value, or error
k
is a normalizing constant for the loop
The controller reevaluates S
N
every second.
I
is divided by 60, so any value entered
by the user should be in reciprocal minutes.
The normalizing constant k can be set to any non-zero value, but is usually set to the
full-scale reading of the loop. For example, if the range of expected temperatures is
0 to 125, setting k to 125 results in a
P
term value of
P
when the error is at a
maximum, i.e.:
P(e
N
/k) = P(125/125) = P
Similarly, with a full-scale error, the
I
term (after 1 minute) and the
D
term will be
I
and
D
respectively.
