Computation of Decoupling Precompensators for Linear Multi-Variable System Models

Abstract

In this paper system models which are stable, linear, multi-variable and time invariant, expressed in the form of a transfer matrix in the Laplace variable, will be considered. The spectral form of the transfer matrix will be used to show that if the number of coupled right-hand plane zeros is less than or equal to the number of inputs to the system then proper, stable, realizable decoupling precompensators for the system exist. Thereafter algorithms which give the number of decoupling realizations in the set are derived and demonstrations of the wide range of options afforded by these variations to the system designer are presented. To emphasize the flexibility and generality of the result the decoupling precompensators for a simple multi-variable system are computed together with the resulting non-interacting system/compensator combination. Selection of the ‘best’ configuration is then made on the basis of the pole-zero pattern associated with each interfaced system. Finally, the design may be completed by way of the Nyquist array method using the preferred decoupling precompensator as a starting point in the search for a low-order realization, producing diagonal dominance rather than non-interacting characteristics.