The Benchmark Problem Solution by Quantitative Feedback Theory

In this paper we employ quantitative feedback theory (QFT) to synthesize compensators, satisfying various design specifications stipulated in the benchmark problem (Wie and Bernstein [1990]). Minimizing, the cost of feedback or the amount of controller bandwidth is the main objective in QFT. It emphasizes the fact that feedback is only necessary because of uncertainty and that the amount of feedback should therefore be directly related to the extent of plant uncertainty and external disturbances. QFT, quantitatively formulates these two factors in the form of (a) sets TR = {TR} of acceptable command or tracking input-output relations and TD = {TD} of acceptable disturbance input-output relations, and (b) a set P = { P } of possible plants. The control objective is to guarantee that the closed loop transfer function TR = Y/R is a member of TR and TD = Y/D is a member of TD, for all P in P.