Optimal Selection of Controlled Variables

Abstract

This paper considers the selection of controlled variables for the unconstrained degrees of freedom, such that near-optimal operation is achieved with constant setpoints ("self-optimizing control"). From a second-order Taylor approximation around the optimal point, we derive an exact local method. This may be used to find the optimal linear combination of measurements to use as controlled variables. We also derive the approximate singular value rule, which is very useful for quick screening and elimination of poor candidate variables.

Single-cycle mixed-fluid LNG process Part II: Optimal operation

“…A preliminary screening was performed by using the maximum scaled gain method (Halvorsen et al, 2003). Some variables where discarded based on these results (e.g.…”

Near-optimal operation by self-optimizing control: from process control to marathon running and business systems

“…A detailed derivation of the minimum singular value is given in Halvorsen, Skogestad, Morud, & Alstad ( 2003). It is shown that for small disturbances (local behavior) and with the scaling mentioned above, the expected worst-case loss is bounded by…”

“…It is possible to find the locally optimal linear measurement combination H as proposed by Halvorsen et al (2003). The local-behavior assumption makes it possible to use the maximum singular value of a matrix M to effectively evaluate the loss for all expected disturbances and implementations error.…”

“…However, if we also were to include the implementation error, then there would be a single optimal combination of the three measurements in terms of the overall expected loss (Halvorsen et al, 2003) (see Section 5).…”

“…As mentioned earlier, numerical approaches may be used, at least locally (Halvorsen et al, 2003), but these are quite complicated.…”