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Nonlinear performance of a PI controlled missile: an explanation
Author(s) -
Fromion V.,
Scorletti G.,
Ferreres G.
Publication year - 1999
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/(sici)1099-1239(19990715)9:8<485::aid-rnc417>3.0.co;2-4
Subject(s) - nonlinear system , missile , norm (philosophy) , control theory (sociology) , robustness (evolution) , stability (learning theory) , small gain theorem , weighting , quadratic equation , mathematical optimization , mathematics , computer science , control (management) , engineering , law , artificial intelligence , physics , geometry , quantum mechanics , aerospace engineering , medicine , biochemistry , chemistry , radiology , machine learning , political science , gene
The primary aim of this paper is to investigate the practical interest of the incremental norm approach for analysing (realistic) nonlinear dynamical systems. In this framework indeed, incremental stability, a stronger notion than ℒ 2 ‐gain stability, ensures suitable qualitative and quantitative properties. On the one hand, the qualitative properties essentially correspond to (steady‐state) input/output properties, which are not necessarily obtained when ensuring only ℒ 2 ‐gain stability. On the other hand, it is possible to analyse quantitative robustness performance properties using the notion of (nonlinear) incremental performance, the latter being defined in the continuity of the (linear) H ∞ performance (i.e. through the use of a weighting function). As testing incremental properties is a difficult problem, stronger, but computationally more attractive, notions are introduced, namely quadratic incremental stability and performance. Testing these properties reduces indeed to solving convex optimization problems over Linear Matrix Inequalities (LMIs). As an illustration, we consider a classical missile problem, which was already treated using several (linear and nonlinear) approaches. We focus here on the analysis of the nonlinear behavior of this PI controlled missile: using the notions of quadratic incremental stability and performance, the closed loop nonlinear missile is proved to meet desirable control specifications. Copyright © 1999 John Wiley & Sons, Ltd.