QUANTITATIVE SYNTHESIS OF MULTIPLE-LOOP FEEDBACK-SYSTEMS WITH LARGE UNCERTAINTY

This work extends single input-output linear time invariant minimum-phase ‘ quantitative feedback synthesis ’ to two new complex plant structures with internal sensing points. One is the triangular structure. The second consists of parallel branches, each with cascaded sections. Due to uncertainty, the plant parameters are elements of given sets. The system response must satisfy specified time or frequency domain tolerances. The basic problem is how to divide the feedback burden among the available loops so as to minimize the net rms effect at the plant input, of the various sensor noise sources. Frequency-response formulations are presented which provide a clear understanding of the trade-off among the feedback loops. One vital feature is ‘ free uncertainty ’, wherein a loop optimized to cope with uncertainty U1may in fact for some frequency ranges, handle uncertainty U≫U1. A second is ‘ bandwidth propagation ’ wherein the loops take turns in dominating the design over the frequency range. Together, they locate the frequency regions in which the respective loops dominate, and the key trade-off parameters among them. ‘ Design perspective ’ then enables the designer to very rapidly find a close approximation to the precise design based on any choice of these parameters. Numerous design examples with very large uncertainty, illustrate the design procedures and the advantages of multiple-loop design. © 1979 Taylor & Francis Group, LLC.