Quadratic weights for large scale regulators

A large-scale model is reduced to a low-order robust model by using principal component analysis. The low-order model is partitioned into (decoupled) subsystems by projecting the directions of strong influence in individual input(s) and output(s) on the state space of the reduced model. Quadratic weights are determined for the individual decoupled subsystems. These weights are used in the quadratic performance index for the reduced model. The quadratic weights for the original large-order model can easily be determined from the reduced performance index. The reduced performance index is sufficient to determine a robust low-order optimal controller for the large-order system. A ninth-order model of a chemical reactor having four inputs and three outputs is considered as an example