Decoupling Control

Abstract

A characteristic property of multivariable systems is that the input–output behaviour is coupled, i.e., a change in one input affects several outputs. By designing a decoupled reference transfer behaviour each output variable is affected by only one reference signal. Therefore, each input–output pair can then be controlled by a SISO controller. A precise definition of this diagonal decoupling problem using static state feedback was first given in [48]. Later, a necessary and sufficient condition for the solvability of diagonal decoupling was established in [17]. If this condition is not satisfied or if the system is completely decouplable, but not in a stable scheme, at least partial decoupling can be achieved (for an overview see, e.g., [66]). In this chapter a partial decoupling using static state feedback is considered, such that the reference transfer matrix contains one or more coupled rows. These coupled rows have non-zero elements outside the main diagonal, so that the corresponding output is affected by several inputs. Using the parametric approach this decoupling problem has been solved in the time domain in [44]. A frequency-domain formulation of this approach is presented in this chapter.