A nonparametric method for mixed-sensitivity Frobenius norm H∞ controller design

This paper presents a nonparametric approach to the design of feedback for stable invertible MIMO plants using Frobenius norm H_∞, Hadamard weighted feedback control for mixed-sensitivity criterea. It is shown that the corresponding mixed sensitivity performance function may be reduced to one of quasi-circular type, appropriate for using Nehari-solution algorithms to achieve good solution-convergence by disk iteration. A non-parametric interpolation scheme is developed to retain the quasi-circular function and to guarantee internal stability. The disk-iteration method of Helton-Merino for analytic function optimisation may then be applied to optimise the mixed sensitivity criterion subject to the required internal stability constraints. The complete design process is thus based entirely on the plant frequency response. A simulation study of a 2 × 2 MIMO automotive IC engine torque and fuelling controller is given which compares the Frobenius norm H_∞ method with a maximum singular norm H_∞ controller . It is shown that the Frobenius norm method gives direct control over disturbance decoupling but otherwise enjoys similar robustness and performance to the maximum singular norm controller. The approach thus presents a nonparametric alternative to the state-space Frobenius norm methods of Van Diggelen and Glover.