Controlled/manipulated variable selection: partial disturbance rejection, SVD (6)

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 16:51

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Summary:

This is the sixth video of the case study that started in video [sacerf1EN]. Here we discuss partial cancellation of steady state disturbances with SVD techniques; the ‘exact’ geometry of polyhedra (quadprog) was discussed in the video [sacerf5EN].

Basically, keeping the scalings of manipulated variables and disturbances from previous problems, a new output scaling based on the maximum tolerable error threshold is now discussed. With this new scaling, the problem is that of calculating an optimal $u$ such that $\parallel e_{esc}{\parallel }^2+\parallel u_{esc}{\parallel }^2\le 1$ when $\parallel d|\le$1. Thus, each of the two terms being added will obviously be less than 1.

Since this is a least-squares problem, it is solved with pseudoinverse, and the SVD of the resulting matrix is checked.

The case study concludes in the video [sacerf7EN], which analyzes the transient case.

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