Controller design for partial decoupling of linear multivariable systems

In the design of feedback control systems for linear multivariable plants, insisting on the elimination of coupling in closed-loop is often achieved at the expense of an increase in the multiplicity of infinite and non-minimum phase zeros beyond those of the plant plant. This behaviour is known as the ‘cost of decoupling’ since these additional zeros are manifested in the time domain by increased rise times and undershoots in step responses. Using partially decoupling controllers, however, it is always possible to obtain closed-loop systems with precisely the same number of infinite and non-minimum phase zeros as the plant, albeit at the expense of a restricted form of transient coupling. This paper uses a generalization of the interactor matrix to generate a class of partially decoupling controllers for square, stable plants in which diagonal decoupling arises as a special case, thereby permitting the designer to trade off speed of response versus the severity of transient interaction.