## 2 Fixed Weighting Matrices

A weighting matrix (W), as shown in Fig. 14.1, is useful because it can be used to precondition the plant to simplify the QFT design processes and, in some cases, is required to complete a QFT design. Fixed weighting matrices can be used for such purposes as achieving a square plant matrix, achieving a m.p. determinant of the effective plant (Pe), and reducing cross coupling for the nominal plant. If the weighting matrix is variable and scheduled based on operating condition, then it can be used for such purposes as reducing crosscoupling for the full operating envelope, reducing the size of the templates, as well as other purposes discuss later in Sec. 14.3. Fixed weighting matrices can be constructed from constant elements or from dynamic elements. The variable weighting matrices can be generated from a set of table look-ups or be calculated based on the operating condition. An example of the latter form of variable weighting matrix is dynamic control allocation, which uses linear, or nonlinear, programming to compute control effector commands based on the operating condition and the inputs from the compensator. Chapter 7 contains a discussion of the techniques for designing W to remediate the problem of n.m.p. plants. This chapter discusses design of fixed and variable weighting matrices and how they can be used to achieve square Pe(s), how to reduce cross-coupling, how to achieve fixed compensator for the full operational envelope, and how to improve closed-loop system performance.