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Inversion and zero dynamics in nonlinear multivariable control
Author(s) -
Daoutidis Prodromos,
Kravaris Costas
Publication year - 1991
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690370406
Subject(s) - nonlinear system , linearization , control theory (sociology) , invertible matrix , mathematics , zero (linguistics) , inversion (geology) , multivariable calculus , inverse , mimo , feedback linearization , inverse system , computer science , control (management) , physics , engineering , geometry , control engineering , beamforming , philosophy , structural basin , artificial intelligence , linguistics , biology , paleontology , quantum mechanics , statistics , pure mathematics
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.