PID Controller Tuning

The web site de-emphasizes tuning of control functions, given that the underlying issues are subordinate and more widely recognized than those covered. Nevertheless an unfamiliar reader should not take tuning for granted or assume that the default tunings provided by some of the demos would be provided automatically in real practice. Until recently, controllers did not tune themselves, even though the manual tuning has been well understood (at least by practitioners) for a half century. Even now, when automatic tuning is well accepted commercially, the issues underlying tuning are not generally understood. There is an important distinction between academic computing of control parameters and the kind of manual tuning used by the authors and other practitioners.

Generally manual tuning can give better results than formal computation of parameters, in an iterative process which is easy to carry out but hard to theorize about. Tuning is better partly because real processes can only be approximated. Theory is hard because accurate approximation is typically much more difficult theoretically than exact solution. There is a large literature on both academic and practical ways of arriving at tunings. The Documentation Tool emphasizes PID control although this is not the only control function requiring tuning. The Simple Idiom Loop Demo allows experimental tuning of the P and I parameters of PI and PID controllers.

For a deeper discussion of this tuning look at E.H. Bristol, "Understanding the PID and Its Tuning", IFAC PID01 Workshop, Terrassa, Spain, April 2000. This paper is really a prayer for some bright thinker, deep theory capable and practice sympathetic, to seriously attack the problem as seen by the practitioner and, once and for all, provide that complete, general, teachable treatment of the subject [Unrequited Love #2]. The goal should be an end to the endless "Yet Another Tuning Strategy" papers, an end which would explain or disprove anything in the prior ART. At least for the linear aspects of the PID.

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As an afterthought, commercial PID controllers include a lot of mechanisms to accommodate nonlinear effects (e.g. valve limiting), outside of the linear theory. A best general reference on these mechanisms is: Karl J. Aström and Tore Hägglund, Advanced PID Control. Generally these mechanisms can be accommodated by tuning only in the linear controller regimes.

The "Understanding the PID and Its Tuning" workshop reference gives a proof that Derivative cannot be used on pure delay (dead time) processes. The problem was suggested by this same Karl Astrom in a discussion prior to the workshop. My own thinking was that some nonlinear Derivative variant could overcome the difficulty. This may still be true, but the proof is too elegant to undercut that way, even if in frequency domain, rather than in root locus like the main discussion! One wonders if there are other similar provable limits to PID use, to be found. They would be no substitute for a general treatment, but certainly contributory to it.