SVD decoupling case study (4): feasible (realizable) reference instead of user-provided setpoint

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 09:28

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Summary:

This video is a continuation of the video [dsvdintu3EN], reviewed in the first three minutes. Here we will add actuator operating points to work in non-incremental variables, and we will delve into the concept of ‘feasible reference’ (the value that would make $e^{SVD}=r^{SVD}-y^{SVD}$ zero if, for example, the PID of the referred video had integral action. This reference will actually be given by the expression: $r^{\ast }=U{r}^{SVD}=U{U}^{T}r$, which is an orthogonal projection onto the $U$ subspace. It is advisable to show such a realizable reference to the user, so that such user knows that the reference he has given is not really attainable (we do not have enough manipulated variables), and which is the actual reference to which the process will tend instead.

Since only one variable can be controlled with a single manipulated variable, we could also have thought about choosing a single thermocouple (the one with the most gain, for example) and putting a monovariable PID for it. This was indeed discussed in the preceding video in the case study.

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