Gain-bandwidth optimal design for the new formulation quantitative feedback theory

Recent work in Quantitative Feedback Theory (QFT) has extended the methodology to include a more mathematically tractable formulation which allows consideration of both parametric and non-parametric uncertainty. An issue that remains largely unsolved is that of constructive existence conditions for optimal QFT controllers. The methodology developed in Thompson and Nwokah (1994) was to build upon the classical Bode analysis approach to loop shaping by defining the structure and parameters of an acceptable initial QFT controller a priori; locally optimal controllers of this structure could then be computed via a constrained nonlinear programming algorithm. The primary purpose of this paper is to extend this methodology to the sensitivity-based, 'new formulation' QFT bounds. This technique is demonstrated for the nonminimum-phase problem of Nordgren et al. (1994).