LumaSense Technologies PI 6000 - Handbuch (Seite 36)

Programmable controller PI 6000
36
Help with finding optimal control parameters for the PI 6000
The PID parameters
In principle, different control parameters will be found for different temperatures in a thermal process.
Xp "proportional element"
Xp is a dimension-less number that represents the reciprocal of the gain of the controller.
With Xp = 100% the controller has a gain of 1
With Xp = 0.1% the gain is 1000, with Xp = 1000% the gain is only one tenth.
This gain simply sets the control output (controlled variable) higher, the further apart the desired and
temperatures are, without any delay. If you select Xp too small (= gain too high), the controller may
have a tendency to oscillate. If Xp is too large (= gain too low) it may occur that the control output
amplitude is never high enough.
With only proportional control, the actual value for the temperature always remains below the desired
temperature (if oscillation does not occur), as with a control error of 0 the control output would also
be set to 0 and no more heat energy supplied. There is therefore a residual control error.
Ki "integral element"
Ki is given in units of time (e.g. in seconds). It represents a type of smoothing or delay and inte-
grates control errors to form a correction for the control output such that there is no residual control
error.
Basic rule:
Ki must be at least as large as the (thermal) time constant of the heating circuit.
Therefore, e.g., for a ceramic blackbody Ki must typically be in the range of minutes,
while fractions of a second are adequate for a filament.
Increasing the time Ki makes the control process slower, but also more stable.
Reducing Ki can result in overshoot or even continuous oscillation.
Kd "differential element"
Kd is also given in units of time. It represents the predictive component of the controller. If, e.g., the
desired temperature is almost the same as the actual temperature, but is still climbing steeply, Kd
"brakes" the rapid rise and prevents overshooting.
Rule of thumb:
Start with Kd = 0, then set Kd = Ki/4 and see whether the settling process improves.