Finite Impulse Response Systems for Almost Perfect Decoupling in Nonminimum-Phase Plants

This contribution focuses on decoupling of previewed signals, i.e. the problem of making the output insensitive to input signals which are known a certain amount of time in advance. Inclusion of time delays in the problem formulation enables decoupling with preview to be turned into a causal problem. The solution of this latter problem is then completely set forth in the geometric approach context. Necessary and sufficient constructive conditions for decoupling of previewed signals are provided, where self-bounded controlled invariant subspaces play a key role in connection with internal stability of the devised system. If the minimal self-bounded controlled invariant subspace satisfying the structural constraint is internally stabilizable, decoupling just requires finite preview. Otherwise, infinite preview is demanded. In this latter case, resorting to finite impulse response systems yields a practically implementable solution which approximates the theoretical one with arbitrary accuracy. The procedure is illustrated by a benchmark example consisting of a flexible mechanical structure.