Controlled/manipulated variable selection: partial disturbance rejection, polyhedra quadprog (5)

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 13:46

*Enlace a Spanish version

Summary:

In this fifth video of the case study that began in the videos [sacerf1EN], [sacerf2EN], [sacerf3EN] and [sacerf4EN], the partial cancellation of steady state disturbances is addressed, with the geometry of polyhedra.

First, the “admissible residual error” vertices are generated from the problem specifications and, with them, for each of them, the feasibility of a quadratic programming problem is addressed, which we will test by executing quadprog. The most appropriate cost index to minimize is briefly discussed, although this discussion would only be relevant if the real-time controller on the process were to use quadprog (predictive control, usually) and the disturbances were measurable or observable. Since we are only looking for feasibility, really $H=I$, $f=0$ would work for us (and that is the only thing that would be required to my students in a ‘pen-and-paper’ exam).

In the second half of the video, optional additional considerations are discussed; in particular, the margin of increase of disturbances so that the problem remains feasible, and the graphical representation of the achievable polyhedra in the space of the outputs $y$ for a better understanding of the concepts (the code is not analyzed in detail, which is left to the reader).

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.