Synthesis of cascaded multiple-loop feedback systems with large plant parameter ignorance |
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Authors: | Isaac Horowitz Marcel Sidi |
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Affiliation: | 3. Department of Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel;1. Department of Electrical Engineering University of Colorado, Boulder, Colorado USA;4. Israel Aircraft Industry, MBT, Yahud, Israel |
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Abstract: | 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 Li almost as if the remaining loops (Li+j, j>0) are perfect. Even in large plant ignorance problems, only the outer loop Li may be large over some frequency range. In general |Li|max < 1, i ≠ 1 and |Li+1|max < |Li|max. Each Li has only one distinct frequency range say at ωc, i requiring trade-off between Li and Li+1. Only in this range is significant design effort required. However, ωc, i+1 >ωc, 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. |
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