Mixed H2/H Infinity Optimization with Multiple H Infinity Constraints.

摘要

A general mixed H2/H infinity optimal control design with multiple H infinity constraints is developed and applied to two systems, one SISO and the other MIMO. The SISO design model is normal acceleration command following for the F-16. This design constitutes the validation for the numerical method, for which boundaries between the H2 design and the Hoo constraints are shown. The MIMO design consists of a longitudinal aircraft plant (short period and phugoid modes) with stable weights on the H2 and H infinity transfer functions, and is linear-time-invariant. The controller order is reduced to that of the plant augmented with the H2 weights only. The technique allows singular, proper (not necessarily strictly proper) H infinity constraints. The analytical nature of the solution and a numerical approach for finding suboptimal controllers which are as close as desired to optimal is developed. The numerical method is based on the Davidon-Fletcher-Powell algorithm and uses analytical derivatives and central differences for the first order necessary conditions. The method is applied to a MIMO aircraft longitudinal control design to simultaneously achieve Nominal Performance at the output and Robust Stability at both the input and output of the plant.