Synthesis of cascaded multiple-loop feedback systems with large plant parameter ignorance

In a cascaded plant with n sensing points, n independent feedback loops are available to achieve quantitative sensitivity specifications. The optimum design is defined as that which achieves this with minimum net effect, of the n sensor noise sources, at the plant input. A design procedure is presented wherein one works backwards step by step from the system output, designing each loop function L_i almost as if the remaining loops (L_i+j, j>0) are perfect. Even in large plant ignorance problems, only the outer loop L_i may be large over some frequency range. In general |L_i|_max < 1, i ≠ 1 and |L_i+1|_max < |L_i|_max. Each L_i has only one distinct frequency range say at ω_{c, i} requiring trade-off between L_i and L_i+1. Only in this range is significant design effort required. However, ω_{c, i+1} >ω_{c, i} so the primary price paid is in the steadily increasing “bandwidth” of each loop. The design procedure is highly transparent with strong universalistic features, permitting the use of universal design curves.