On Multiloop Interaction and Relative and Bristol Gains

Abstract 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.