Robust performance case study (Matlab) 5: mu-synthesis order reduction, PID tuning, loop simulations

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 16:15

*Enlace a Spanish version

Summary:

This video continues the case study started in the video [cerp1EN] and, in particular, it analyses the musyn command output which was introduced in the preceding video [cerp4muEN], The frist two and a half minutes here summarise the preceding videos.

The scaled small gain 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.

The initial part of the video discusses reducing the order of the mu-synthesis regulator (order 11) with balred and freqsep down to order 2. The result is very much like a PID, so in the second half of this video, musyn is used to directly optimize the parameters of a tunable PID, giving a very similar result.

Last, simulations in time and frequency domain of the PID and the musyn full-state-state (+ order reduction) regulator are shown; the simulations are satisfactory both in time and in frequency domains, with random plants within the family with additive uncertainty for which everything has been designed. This concludes the case study.

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