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Nonlinear model‐predictive control: Closed‐loop stability analysis
Author(s) -
Sistu Phani B.,
Bequette B. Wayne
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.690421210
Subject(s) - discretization , control theory (sociology) , nonlinear system , mathematics , continuous stirred tank reactor , lyapunov function , model predictive control , controller (irrigation) , stability (learning theory) , computer science , engineering , mathematical analysis , control (management) , physics , agronomy , artificial intelligence , chemical engineering , machine learning , biology , quantum mechanics
A method to analyze the closed‐loop stability of a system composed of a nonlinear process and a discrete controller is developed. The closed‐loop system is described by a set of difference equations resulting from the discretization of the continuous‐time model. A commonly used method of discretization (forward difference) offers an incorrect relative order compared to exact discretization. The state and input sensitivity equations of the continuous‐time model are used in computing the nominal closed‐loop stability criteria. The nominal stability analysis is extended to the important cases of unmeasured states and uncertain model parameters. A numerical Lyapunov function is used to estimate closed‐loop regions of attraction. A simulation example (a CSTR with input multiplicity) presented illustrates the analysis methods and closed‐loop behavior.