Design of a 3×3 multivariable feedback system with large plant uncertainty†

A recent paper presented a quantitative synthesis theory based on Schauder's fixed point theorem, for uncertain multiple input-output feedback systems. This paper is devoted to practical design execution, by means of a detailed 3×3 problem with large plant uncertainty, including open-loop instability and some non-minimum-phase plant elements. The outstanding features of the theory are : 1. The quantitative nature of the assigned tolerances on the nine closed-loop system response functions. In this problem four are specified basically non-interacting and the other five interacting. 2, The design problem is translated into separate quantitative single-loop problems, each with plant uncertainty, external disturbances and closed-loop tolerances derived from the original problem. The solutions for these single-loop problems are guaranteed to solve the original multivariable problem, whose system characteristic equation need never be examined. 3. There is developed a systematic means of (a) optimization of the ...