A Simplified Multi-Input Multi-Output Formulation for the Quantitative Feedback Theory

A simplified multi input/output formulation is developed for the quantitative feedback theory (QFT) for the 2×2 (n=2) case. This formulation is consistent with basic QFT philosophy in that performance is specified for the individual closed-loop transfer functions and design insight is provided for minimization of control bandwidths. The simplified formulation turns the solution of a simultaneous robust stability and robust model matching problem into a two (n in general) step procedure of solving constrained quadratic equations (whose coefficients are linear functions of the plants and the performance constraints); the traditional procedure requires six (n+2n² in general) steps for a similar problem. This establishes the main contribution of this paper. A numerical example is utilized to illustrate the simplified formulation and to demonstrate the QFTs procedure of minimization of control bandwidths in MIMO problems.