Wavelength Electronics LFI-3751, User Manual

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The sensor temperature eventually overshoots the setpoint temperature,
forcing the integrator to charge in the opposite direction, reversing the output
current. The thermal load’s lag causes an overshoot in this direction also and
the cycle simply repeats itself. A large enough integrator time constant can
be set to compensate for a thermal load’s lag time by charging slowly enough
to not over-drive the output current. Commonly, temperature controllers
will exhibit a damped oscillation when settling to temperature. This occurs
because the integrator is set large enough to compensate for the thermal
load’s lag time but small enough that the integrator must overshoot several
times to properly balance the charge on the integrator to deliver the correct
output current.
The calculated value of integrated time constant, I, depends on whether the
thermal load has been optimized using Setpoint Response or Disturbance
Rejection Tuning. Setpoint Response determines I from the thermal load’s
time constant, T. Disturbance Rejection uses the thermal load’s lag time, L,
to calculate I. Notice that T is always greater than L and so that Setpoint
Response Tuning always calculates a more conservative value of I. Too large
a value of I is detrimental when rejecting disturbances because a slower
charging integrator will take longer to settle the load’s temperature.
3. Differentiator Time Constant – “D” and Autotune
Optimization
The differentiator’s time constant, D , is also measured in seconds. The
differentiator uses the derivative of the Error Voltage versus time to compensate
for the proportional gain’s and the integrator’s tendency to cause the thermal
load’s temperature to overshoot the setpoint temperature. To understand the
differentiator, we must fi rst examine how the proportional gain responds as the
load’s temperature approaches the setpoint temperature.
As long as the Error Voltage is non-zero, the proportional gain will drive
the output to move the thermal load’s temperature towards the setpoint
temperature. The proportional gain stops driving the output current once the
Error Voltage drops to zero (when the load’s temperature equals the setpoint
temperature). At this point, the load’s thermal inertia forces it to overshoot
the setpoint temperature. It is not until the Error Voltage reverses polarity
that the proportional gain provides an output current that drives the actual
temperature back towards the setpoint temperature, which now results in
an undershoot condition.
The differentiator is dependent on the slope of Error Voltage versus time and
not its magnitude. The faster a load responds, the more the differentiator
forces the output current to reduce changes in the Error Voltage. Unlike the
proportional gain that moves the load temperature to the setpoint temperature,
the differentiator forces the output current to maintain a stable temperature
or zero slope whether the load’s temperature is at the setpoint temperature
or not. Therefore the differentiator produce’s a “braking” current that resists
changes to the thermal load temperature.
Chapter 2 - Front Panel Operation
Theory of Autotune PID