On Thu, Jun 27, 2013 at 11:13 AM, Dave <[email protected]> wrote:

> Your PID loop is likely running a lot faster than what is required.


Agreed.


> The PID loop should run 10x to 50x the time constant of the control
> system.  Any faster and you will end up with very small changes in tuning
> values that make a huge difference in loop performance and the loop will be
> difficult to tune.
>

I respectfully disagree.  As long as the integral term is normalized to the
run rate, there is nearly no effect to running the loop faster than then
the time constant.  Analog PID works at a (near) infinite rate.  The exact
same gains there will work in a z-domain approximation as long as the
sample/loop rate is sufficiently higher.  The 10x you mentioned is only a
rule of thumb minimum so that integral and derivatives become fair analog
approximations.  The only practical maximum is the KI*error/sample rate
becoming too small to accurately represent and accumulate numerically.  Not
usually a problem w/ double precision floats.  In this case there is no
real benefit to running the loop significantly faster than the sample rate
but it can be well above the thermal time constant.

PID in the z-domain is just an approximation of the simple classic linear
time invariant analog controllers.  There are much better control methods
that digital control lends itself to (cough, state-space, cough) but some
are more complicated to understand and thus often not widely implemented.
For temperature control the "take back half" non-linear method has shown
rapid convergence, high stability, and single parameter tuning.

Stephen
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