Interaction analysis for multivariable systems

Two interaction indices for multivariable systems and an algorithm for designing two static compensators that minimize the destructive interactions while enhancing the constructive ones are discussed. An interaction has a constructive effect if the result of the interaction augments the control effort. An interaction is said to have a negative effect if the result of the interaction either destabilizes the system or degrades its performance. The first interaction index tells quantitatively whether the interactions that result as the feedback loops are closed are constructive or destructive. This index is independent of the order in which the feedback loops are closed. The second interaction index tells quantitatively whether the interactions that result as the inputs are applied to the system are constructive or destructive. This index is independent of the order in which the inputs are applied