A simplified approach for the design of basically non‐interacting multiple‐input‐multiple‐output systems using qft

Abstract

AbstractQuantitative 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 = [Tij]. In many practical applications the specifications are of the basically non‐interacting (BNIA) type, i.e. aii(ω) < | Tii(jω) | < bii(ω), | Tij(jω) | < bij(ω), (i ≠ j) and bij(ω) < aii(ω) in a significant range of frequencies. In one QFT technique the design is based on expressing magnified image when the matrix of compensators G = diag(Gii(s)), Li = GiiQii, P−1 = [1/Qij], Dij 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(Fii(s)), the effect of the disturbance acting on the main diagonal terms (i.e. Dii) can be neglected. This observation saves some computational burden because satisfaction of specifications on the Tiis 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.