Quantitative design for systems with uncertainty and control failures [flight control systems]

The paper is devoted to the application of quantitative feedback theory (QFT) to flight control systems in which the uncertainty consists of: (a) varying flight conditions (Mach and altitude) and (b) possible failures of effectors. There are more (m) control effectors than outputs (n), m>n, so ideally a maximum of (m-n) effector failures may be tolerable. In the n×n [n command inputs (d=0), n outputs] system there are n²t_ij(s)=y_i(s)/r_j(s), relating output i to command j. There are given n² separate performance tolerances 𝒬_ij, one for each of the n² t_ij [but of course for less input level before limiting], over any combination of up to f=(m-n) simultaneous effector failures. This is usually impractical. Practicality is invoked by fixing the minimum sampling frequency ω_s in a digital design, or maximum loop bandwidths in an analog design. Then for some failure combinations one may have to use less stringent 𝒬_ij tolerances or failure detection and identification (FDI). For simultaneous failures f>m-n, at most only (m-f)² t_ij can be controlled. The design procedure can do this, up to f=m-1