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Feedback control of hyperbolic PDE systems
Author(s) -
Christofides Panagiotis D.,
Daoutidis Prodromos
Publication year - 1996
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.690421108
Subject(s) - control theory (sociology) , distributed parameter system , hyperbolic partial differential equation , partial differential equation , state space , state (computer science) , feedback control , output feedback , computer science , tracking (education) , control (management) , mathematics , control engineering , engineering , mathematical analysis , algorithm , psychology , pedagogy , statistics , artificial intelligence
This article deals with distributed parameter systems described by first‐order hyperbolic partial differential equations (PDEs), for which the manipulated input, the controlled output, and the measured output are distributed in space. For these systems, a general output‐feedback control methodology is developed employing a combination of theory of PDEs and concepts from geometric control. A concept of characteristic index is introduced and used for the synthesis of distributed state‐feedback laws that guarantee output tracking in the closed‐loop system. Analytical formulas of distributed output‐feedback controllers are derived through combination of appropriate distributed state observers with the developed state‐feedback controllers. Theoretical analogies between our approach and available results on stabilization of linear hyperbolic PDEs are also identified. The developed control methodology is implemented on a nonisothermal plug‐flow reactor and its performance is evaluated through simulations.