Frequency Domain Design for Robust Performance Under Parametric, Unstructured, or Mixed Uncertainties

This article looks at direct frequency domain design for satisfying robust performance objectives in uncertain, linear time invariant (LTI) plants embedded in a single feedback loop. The uncertain plants may be described by parametric, nonparametric (or unstructured), or mixed uncertain models. Quantitative Feedback Theory (QFT) is one frequency domain design methodology that is direct and is equally effective with any of these models. It can be separated from other frequency domain robust control methods such as H∞ optimal control, μ synthesis, and LQG/LTR for at least (i) its emphasis on cost of feedback measured in terms of controller bandwidth, (ii) its ability to deal nonconservatively with parametric, nonparametric and mixed uncertainty models, and (iii) its utilization of both amplitude and phase of the loop transfer function, pointwise in frequency, for the quantification of robust performance. An exposition of these attributes, unique to QFT, and the basic design methodology, coupled with a recently developed mathematical framework and some existence results for the standard single-loop QFT problem are the salient features of this paper.