SVD decoupling and principal maneuvers in process control (1): theory outline

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 17:40

*Enlace a Spanish version

Summary:

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 $y=(US{V}^T)u$ 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).

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