Robust performance case study (Matlab) 4: mu-synthesis (building uncertain generalised plants)

Antonio Sala, UPV

Difficulty: ***** ,       Relevance: ,      Duration: 11:27

*Enlace a Spanish version

Summary:

This video continues the case study of the videos [cerp1EN], [cerp2EN] and [cerp3EN]. In these videos, the problem of robust performance was stated, a generalized plant was formed with uncertainty, and multipliers (scalars) were searched for manually, by trial and error.

Although of interest for didactic purposes in order to better understand the scaling small gain theorem, you rarely have to do things as said in these videos, because all that detail is taken care of by the internals of musyn mu-synthesis command. This video compares the generalized plant that musyn transparently builds when it is executed (we can do it explicitly with the command lftdata) with the plant that we built manually in the video [cerp2EN], verifying that they match.

Then, the multiplier lookup is done on one line with musyn; the multiplier for uncertainty LTI can be dynamic because if $\mathrm{\Delta }(s)$ is SISO then $\mathrm{\Delta }(j\omega )\cdot D(j\omega )=D(j\omega )\cdot \mathrm{\Delta }(jomega)$ and can be used in scaled small gain theorem. The musyn command with default options uses a scaling $D(s)$ of order 8 here, and produces a regulator of order 11.

For brevity, order reduction, closed-loop simulation, and comparison to musyn-PID results will be discussed in the video [cerp5muEN], a continuation of this one.

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