Design of multiple-loop feedback control systems

A single-loop design is basic for a two-degree-of-freedom plant, and it is theoretically able to achieve any desired insensitivity to plant variations or rejection of disturbances, if the plant is minimum-phase. In exacting feedback problems where the parameter variations or disturbances are large, the resulting single-loop transmission may require a larger gain and bandwidth than that of the plant. The added feedback compensation networks then have rising frequency characteristics and make the system very sensitive to HF noise in the feedback path. It is shown how a multiple-loop design permits the attainment of the same benefits of feedback, but with considerably less sensitivity to the HF noise. The basic problem is how to divide up the feedback burden most efficiently among the various loop transmission functions. Detailed procedures for this purpose are presented in the paper. The treatment is restricted to cascade-type plants.