We discuss the design of cross-directional controllers which are guaranteed to be robustly stabilizing while incorporating a quadratic program for steady state performance. In particular we propose implementing cross-directional controllers in modal form with a constrained internal model control structure. Nominal optimal steady state performance is guaranteed via a non-linear element that incorporates a quadratic program. The quadratic program can be expressed as a continuous sector bounded nonlinearity together with two linear transformations. Thus the multivariable circle criterion can be used to guarantee closed-loop stability in the presence of disturbances and modeling uncertainties.
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