The Proportional-Integral-Derivative Response is a feedback loop that can be used to maintain a controlled amount of, in this case, liquid helium in a reservoir. This page is dedicated to providing an understanding of the mathematics behind the mechanism and hopefully help in the ability to change the PID gains in the Response VI controlling the level of LHe (for more information on the VI, please click this link to the LabVIEW Virtual Instrument Manual).
The PID control system is a common algorithm that begins with an error function with respect to time, e(t), where...
ex: the actual level subtracted from the target level of a system
This error, which can be easily calculated in LabVIEW by simply using the value of the level for that iteration, is what will variable that will help the PID controller determine what action, and how much of one, needs to be taken.
The PID control utilizes three coefficients - the proportional (P), integral (I) and derivative (D) terms. Each term is multiplied with the error function, and the products are then summed to create the new controller output, z.
where z would be the valve position, and the expressions are (in order) the Proportional, Integral and Differential
Since these three expressions are summed together, it stands to reason that if a coefficient is larger than the others, then that term would have more weight than the others. Likewise, if that coefficient is less than the others, it will matter less in the overall calculation of the controller output.