Multi‐variable quantitative feedback theory based controller using directional transfer ratio

Abstract

This article proposes a novel method, inspired from eigen decomposition technique, to design a quantitative feedback theory (QFT) based robust controller for a multiple input multiple output (MIMO) uncertain plant. The proposed method is a direct and sufficiently generalized one. Unlike existing practice, it does not require to transform a “n×n” MIMO‐QFT based design problem into “n” sequential multiple input single output QFT based design problems. Apart from the frequency dependency, the frequency response of a MIMO system also has the spatial dependency. This makes the frequency domain analysis and design for a MIMO system, more challenging than its SISO counterpart. Three new concepts namely directional transfer ratio (DTR), output directionality (OD), and principle of control along characteristic vectors (PCCV) are introduced to take care of the complexities of the frequency response of a MIMO feedback system. The DTR, OD, PCCV and existing techniques of QFT are combined together to develop the proposed design method. A case study is presented considering a “2×2” ill‐conditioned plant to illustrate the method. The proposed method is expected to open up new avenues in the area of MIMO‐QFT based design.