ABSTRACT
Figure 22.18 represents an m×m MIMO closed-loop system in which F,G, and P are each m×m matrices, and P = {P} is a set of J matrices due to plant parameter uncertainty. There are m2 closedloop system transfer functions (transmissions) tij contained within its system transmission matrix (i.e., T = {tij}) relating the outputs yi to the inputs rj (e.g., yi = tijrj). These relationships hold for both the s-and w-domain analysis of a MIMO system. In a quantitative problem statement there are tolerance bounds on each tij, giving a set of m2 acceptable regions τij that are to be specified in the design; thus, tijτij and ) = {τij}. From Figure 22.18 the system control ratio relating r to y is:
T = [I + PG]−1PGF (22.32)
The tij expressions derived from this expression are very complex andnot suitable for analysis. TheQFT design procedure systematizes and simplifies the manner of achieving a satisfactory system design for the entire range of plant uncertainty. In order to readily apply the QFT technique, another mathematical system description is presented in the next section. The material presented in this chapter pertains to both the s-and w-domain analysis of MIMO systems [2,12,16,17].
