A Graphical Interpretation of SISO H-infinity Controller Approximation
Goddard P. J. and Glover K.
Presented at the 1995 ACC, 1995Abstract
Given a stabilising controller which satisfies a $hinf$ performance bound on the closed loop transfer function, sufficient conditions for any other controller to be stabilising and satisfy the same $hinf$ performance bound are presented in [Goddard and Glover 1993,1994]. Such controllers are said to be $pga$, where $P$ is the model of the plant under consideration and $gamma$ is the required level of prespecified $hinf$ performance. The conditions are expressed as norm bounds on particular frequency weighted errors where the weights are selected to make a specific transfer function a contraction. Subject to this constraint, approximation is made easier if the weights are as large as possible. Here we show that for scalar controllers the sufficient conditions of[Goddard and Glover 1993,1994]. have a natural frequency by frequency interpretation as either the inside or outside of a circle in the complex plane. We show that given a multivariable $pga$ controller maximising the product of the determinants of the weights always leads to a {em direction} where the weights are the best possible. Further, we show that for scalar weights maximising the product of the traces of the weights always leads to a direction where the weights are the best possible.
BibTex Entry
- @InProceedings{,
- author = {Goddard P. J. and Glover K.},
- title = {A Graphical Interpretation of SISO H-infinity Controller Approximation},
- booktitle = {Presented at the 1995 ACC},
- year = {1995}
- }
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