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TECHNICAL PAPERS

On Multiloop Interaction and Relative and Bristol Gains

[+] Author and Article Information
Eduard Eitelberg

NOY Business and University of KwaZulu-Natal, P. Bag X54001, Durban 4000, South AfricaEitelberg@ukzn.ac.za

J. Dyn. Sys., Meas., Control 128(4), 929-937 (Mar 23, 2006) (9 pages) doi:10.1115/1.2363412 History: Received December 20, 2004; Revised March 23, 2006

The relationship between multiloop design and Bristol gains of a multivariable plant is shown. The Bristol and relative gains are distinguished. The Bristol gains B characterize the plant and the relative gains Λ characterize the designed feedback system. It is Λ, not B, that determines the interaction in loop designs. Λ is equal to B in a loop only at frequencies where all other loop gains are much above 0dB, usually significantly below the respective loop gain crossover frequencies. Λ=1 in a loop at frequencies where all other loop gains are much below 0dB, usually significantly above the respective loop gain crossover frequencies. The transition of Λ in a loop from B to 1 in the important medium frequency range is one of the most interesting and under-researched aspects of loop design interaction.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Multiloop regulation: multivariable regulation with diagonal controller G. The plant P is square.

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Figure 2

2DOF feedback structure for the “benchmark.”

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Figure 3

General loop design perspective with LP1=LP2. Here, ωPgc<1rad∕min.

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Figure 4

Loop design: Solid lines, “worst case,” dotted lines, a selection of L1&2

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Figure 5

General loop design perspective with LP1=LP2. Here, ωPgc<0.5.

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Figure 6

Loop design: Dashed-dotted line, both of the other loops open; dashed line, one of the other loops is closed; solid line; both of the other loops are closed

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Figure 7

Loop design: Dashed-dotted line: both of the other loops open; dashed line, one of the other loops is closed; solid line, both of the other loops are closed

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Figure 8

Sequential loop design: Dashed-dotted line, loops j and k are open; dashed line, loop i is closed and loop k is open; solid lines, both of the other loops are closed

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Figure 9

Loop design of Hovd and Skogestad

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