SVD decoupling and principal maneuvers in multivariable process control: theory outline [1/7]

This video provides a brief theoretical review of the SVD decoupling technique in multivariable control.

The video reviews the concept of "principal maneuvers", input and output directions, and null space.
Then, we propose a change of variable so that y^{SVD}=U^T·y, u^{SVD}=V^T·u.
With that change of variable y^{SVD}=S·u^{SVD}, when y=(USV^T)·u is the SVD decomposition of the static gain matrix.
In this way, the apparent behavior between "virtual" SVD variables is diagonal S, and regulators (slow ones, since the decoupling is at zero frequency) can be designed exploiting that idea, resulting in u=VK(s)U^T·e, with a diagonal K(s) separately controlling each principal maneuver.

If some principal maneuvers are not controlled (because of low gain or/and poor numerical conditioning), to avoid frequent saturation and sensitivity to modeling errors, then u=VK(s)U^T·e would be constructed with only a subset of columns of U and V (a sort of so-called `economy size' SVD).

This is the beginning of a 6-video case study in the playlist:
   • SVD decoupling in multivariable process co...  
If you wish to just watch the next one in the queue, this is it:
   • SVD decoupling case study (2): one control...  

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PDF/code/notes at: https://personales.upv.es/asala/YT/V/...
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Antonio Sala, UPV
University lectures
Full collection of videos at: https://personales.upv.es/asala/YT/in...