A SIMPLIFIED APPROACH FOR THE DESIGN OF BASICALLY NONINTERACTING MULTIPLE-INPUT-MULTIPLE-OUTPUT SYSTEMS USING QFT

Quantitative feedback theory (QFT) has presented techniques for the design of multiple-input-multiple-output (MIMO) linear time invariant (LTI) systems with structured parameter uncertainty in the plant P for the satisfaction of specifications on the closed loop transfer function matrix T= [T(ij)]. In many practical applications the specifications are of the basically non-interacting (BNIA) type, i.e. a(ii)(omega) < \T(ii)(jomega)\ < b(ii)(omega), \T(ij)(jomega)\ < b(ij)(omega), (i not-equal j) and b(ij)(omega) much less than a(ii)(omega) in a significant range of frequencies. In one QFT technique the design is based on expressing T(ij) = F(ij)L(i) + D(ij)Q(ii)/1 + L(i) when the matrix of compensators G = diag(G(ii)(s)), L(i) = G(ii)Q(ii), P-1 = [1/Q(ij)], D(ij) a disturbance due to Plant interaction between the different system channels. It is shown in this paper that when the specifications are BNIA and F = diag(F(ii)(s)), the effect of the disturbance acting on the main diagonal terms (i.e. D(ii)) can be neglected. This observation saves some computational burden because satisfaction of specifications on the T(ii)s becomes a single-input-single-output (SISO) design problem instead of the more elaborated multiple-input-single-output (MISO) design problem which had to be designed originally. A detailed 2-input-2-output design example is presented illustrating the simpler approach, stressing the importance of considering the correlation between specifications in the design procedure.