Controlled/manipulated variable selection: setpoint tracking, SVD, Matlab example (1)

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 14:43

*Enlace a Spanish version

Summary:

This video, the first of a case study with a total of 7 videos, poses the problem of determining if a process $y=Gu$ has properly chosen controlled variables $y$ and manipulated variables $u$, in order to increase $y$ a minimum amount required for a given application (setpoint tracking). Only the steady state case (static gain matrix) is discussed.

In this first video, the problem is presented, and its resolution is addressed using SVD methodology (geometry of ellipses, or spheres of radius 1 once scaled). The scaling process is reviewed and, subsequently, the scaled transfer matrix and the minimum gain (smallest singular value) are calculated, checking that minimum gain is greater than 1 and that the conditioning of 2.9 is also satisfactory, so the problem is considered as feasible.

This brief reasoning is what is required in the pen-and-paper exams in my M.Sc. courses. Additional discussion and graphical representation of the ellipses underlying this methodology is discussed in the video [sacerf2EN], a continuation of this one.

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