Weighting Matrix Selection for QFT (Quantitative Feedback Technique) Designs.

摘要

Use of the Quantitative Feedback Technique (QFT) in determining designs that satisfy performance criteria for a set of plants having structured parameter uncertainties rests heavily on the invertibility of the plant matrix. While other design constraints are appropriate, it is the requirement for plant invertability that forces the designer to either square-down or square-up a non square plant matrix. This thesis investigates the use of a frequency sensitive weighting matrix in squaring-down a non square plant having more inputs that outputs. It investigates selection of the frequency sensitive weighting matrix needed to convert a non square l x m plant matrix into a square plant matrix that satisfies QFT multiple-input, multiple-output design constraints. The method of pre-specifying a desirable plant matrix is used in determining the necessary weighting matrix. The study assumes that the non square plant matrix has more inputs than outputs and the option to square-up is not available (i.e., that inaccessible states cannot be reconstructed due to design limitations). Topics include energy and power spectral densities, singular value decompositions of matrices of transfer functions, QFT design constraints, QFT designs accomplished on non square plants by breaking up the non square plant into a sum of square plants, and both H-2 and H-infinity norm minimization. Keywords: Matrices mathematics; H-2 norm minimization; H-infinity norm minimization; Flight control; Theses. (EDC)