Inversion and zero dynamics in nonlinear multivariable control

Abstract

This work concerns general multiple-input/multiple-output (MIMO) nonlinear systems with nonsingular characteristic matrix. For these systems, the problem of inversion is revisited and explicit formulas are derived for the full-order and the reduced inverse system. The reduced inverse naturally leads to an explicit calculation of the unforced zero dynamics of the system and the definition of a concept of forced zero dynamics. These concepts generalize the notion of transmission zeros for MIMO linear systems in a nonlinear setting. Chemical engineering examples are given to illustrate the calculation of zero dynamics. Input/output linearization is then interpreted as canceling the forced zero dynamics of the system, and precise internal stability conditions are derived for the closed-loop system.