Wavelength Electronics LFI-3751, User Manual

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Obviously the differentiator should not be set so high that it counteracts the
proportional gain and integrator’s attempts to move the load’s temperature
to the setpoint temperature.
The differentiator time constant is dependent on the thermal load’s lag
time,
L , since this parameter contributes to the integrator overshooting the
setpoint temperature. A larger lag time results in a larger calculated D . The
differentiator value also depends on the magnitude of proportional gain. A
larger proportional gain results in a larger differentiator time constant to
compensate for the proportional gain’s tendency to cause overshoot.
The Setpoint Response Autotune results in smaller values for D than the
Disturbance Rejection. Disturbance Rejection Autotune takes advantage of
the differentiator’s resistance to temperature variations at the thermal load to
suppress the effects of thermal transients.
If your thermal load operates in an electrically noisy environment , it might
be to your advantage to turn the differentiator off since the differentiator will
interpret the resulting fast variations in the Error Voltage incorrectly as thermal
load temperature variations. The differentiator can actually cause poorer
temperature stability in this instance.
Understanding the Differentiator - A real life analogy
If you still do not understand the differentiator function, fortunately, the
LFI-3751 Autotune PID eliminates the need to completely comprehend this
control parameter. None the less, this following real life example may give
you some insight into the differentiator. Consider the everyday situation of
braking a car for a STOP sign. Imagine that the location of the STOP sign is
our setpoint temperature and the location of our car is the load temperature.
When we are far away from the STOP sign we step on the accelerator to
quickly get to the STOP sign. This is exactly what the proportional gain portion
of our brain tells us to do since we are far from our destination and want to
get there as quickly as possible. The gears in our car are like the current limit
function of the LFI-3751, a lower gear limits our acceleration rate towards the
STOP sign and a lower current limit setting decreases how much “gas” we
can apply and determines how fast we can approach the stop sign. If we did
not have a differentiator function in our brain we would not apply the brakes
until after we went through the stop sign. For most of us, we stop accelerating
our car and begin applying our brakes some distance before we reach the
STOP sign. This is exactly how the proportional gain and differentiator work in
the PID control loop. Now imagine that the road you are driving on is covered
with ice; this corresponds to thermal loads with long thermal lag times. In
the case of the icy road we would stop accelerating sooner and apply the
brakes for a longer period of time. Remember that a longer thermal lag time
results in a smaller proportional time constant and a larger differentiator
time constant.
Chapter 2 - Front Panel Operation
Theory of Autotune PID