A synthesis theory for a class of multiple-loop systems with plant uncertainty

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Abstract
There is given a single input-output linear, time-invariant plant with large parameter uncertainty consisting of two parallel branches, one of which has n internal sensing points. The objective is to satisfy specified frequency domain bounds on the system response to commands and disturbances over the parameter range, and to do so with sensibly minimum net effect at the plant input, of the n + 1 sensor noise sources. The basic problem is how to best divide the feedback burden among the n + 1 available feedback loops Li. The procedure developed has high transparency, giving early perspective on the loop bandwidths, permitting approximate loop trade-offs without a detailed design. While the development is more difficult than in the single cascaded plant system, the procedure and final results are very similar : each Lihas only one distinct frequency range say ωi, in which there is trade-off between Liand LI+1and ωi i+1 <ωiwith steadily increasing loop bandwidths going backwards from plant output to input. It is shown that for a class of problems the sensor noise can be tremendously reduced, when compared to an optimum single-loop design satisfying the same specifications.