Decoupling of Measurable Signals via Self-Bounded Controlled Invariant Subspaces: Minimal Unassignable Dynamics of Feedforward Units for Prestabilized Systems

A dynamic feedforward scheme allows measurable signal decoupling to be solved independently of other problems simultaneously present in the design of a control system like, e.g., stabilization, robustness, insensitivity to disturbances. The synthesis procedure, based on the properties of self-bounded controlled invariant subspaces, ensures the minimal complexity of the feedforward unit, in terms of minimal unassignable dynamics and minimal dynamic order, in the case of left-invertible systems and, on some specific conditions, also in the case of non-left-invertible systems. The output dynamic feedback set up to guarantee stability (or, more generally, robustness or insensitivity properties) does not affect the complexity of the feedforward unit, since the peculiar layout where the feedback unit receives an additional input from the precompensator preserves, in the extended system, exactly the same set of unassignable internal eigenvalues of the minimal self-bounded controlled invariant subspace as that defined for the original system. The overall control structure turns out to be a two-degree-of-freedom controller completely devised in the geometric context.