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 first 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 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.