Application of MIMO Phase and Gain Margins to the Evaluation of a Flight Control System

Robustness criteria of multi-input multi-output feedback control systems using matrix singular value properties and their relation to the classical gain and phase margins have been the subject of earlier research. The phase and gain margins which have received the most attention in the literature are obtained directly from the return difference matrix or the inverse return difference matrix. However, the gain margin derived from the return difference matrix cannot exceed -6 dB while the gain margin derived from the inverse return difference matrix cannot exceed +6 dB. Such characteristics make the correlation of these stability margins with the more widely utilized SISO margins difficult. A related problem is the inability to obtain acceptance of the MIMO margins by the classical flight control designers who expect gain margins of at least /spl plusmn/6 dB. Here, the problem is illustrated by considering a commercial transport aircraft modelled by an LTI system with two inputs and four outputs and a fighter aircraft modelled by two inputs and five outputs. The MIMO stability margins are computed by using both the return difference matrix and the inverse return difference matrix.