Survey of quantitative feedback theory (QFT)

QFT is an engineering design theory devoted to the practical design of feed back control systems. The foundation of QFT is that feedback is needed in c ontrol only when plant (P), parameter and/or disturbance (D) uncertainties (sets P = {P}, D = {D}) exceed the acceptable (A) system performance uncert ainty (set a = {A}). The principal properties of QFT are as follows. (1) Th e amount of feedback needed is tuned to the (P, D, A) sets. If A 'exceeds' (P, D), feedback is not needed at all. (2) The simplest modelling is used: (a) command, disturbance and sensor noise inputs, and (b) the available sen sing points and the defined outputs. No special controllability test is nee ded in either linear or non-linear plants. It is inherent in the design pro cedure. There is no observability problem because uncertainty is included. The number of independent sensors determines the number of independent loop transmissions (L-i), the functions which provide the benefits of feedback. (3) The simplest mathematical tools have been found most useful-primarily frequency response. The uncertainties are expressed as sets in the complex plane. The need for the larger P, D sets to be squeezed into the smaller A set results in bounds on the L-i (j omega) in the complex plane. In the mor e complex systems a key problem is the division of the 'feedback burden' am ong the available L-i (j omega). Point-by-point frequency synthesis tremend ously simplifies this problem. This is also true for highly uncertain non-l inear and time-varying plants which are converted into rigorously equivalen t linear time invariant plant sets and/or disturbance sets with respect to the acceptable output set A. Fixed point theory justifies the equivalence. (4) Design trade-offs are highly transparent in the frequency domain: betwe en design complexity and cost of feedback (primarily bandwidth), sensor noi se levels, plant saturation levels, number of sensors needed, relative size s of P, A and cost of feedback. The designer sees the trade-offs between th ese factors as he proceeds and can decide according to their relative impor tance in his particular situation. QFT design techniques with these properties have been developed step by ste p for: (i) highly uncertain linear time invariant (LTI) SISO single- and mu ltiple-loop systems, MIMO single-loop matrix and multiple-loop matrix syste ms; and (ii) non-linear and time-varying SISO and MIMO plants, and to a mor e limited extent for plants with distributed control inputs and sensors. QF T has also been developed for single- and multiple-loop dithered non-linear (adaptive) systems with LTI plants, and for a special class (FORE) of non- linear compensation. New techniques have been found for handling non-minimu m-phase (NMP) MIMO plants, plants with both zeros and poles in the right ha lf-plane and LTI plants with incidental hard non-linearities such as satura tion.