Optimalty of SVD controllers

Plant structure is utilized for the simpli cation of system analysis and controller synthesis. For plants where the directionality is independent of frequency, the singular value decomposition (SVD) is used to decouple the system into nominally independent subsystems of lower dimension. In H2and H1-optimal control, the controller synthesis can thereafter be performed for each of these subsystems independently, and the resulting overall SVD controller will be optimal (the same will hold for any norm which is invariant under unitary transformations). In H1-optimal control the resulting controller is also super-optimal, as a controller of dimension n n will minimize the norm in n directions. For robust control in terms of the structured singular value, , the SVD controller is optimal for a practically relevant class of block diagonal structures and uncertainty and performance weights. The results are applied to the ill-conditioned distillation case study of Skogestad et al. (1988), where it is shown that an SVD controller is -optimal for the case of unstructured input uncertainty.

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