A Practical Approach to Robustness Analysis with by Gilles Ferreres

By Gilles Ferreres

1. MOTIVATION in lots of actual occasions, a plant version is usually supplied with a qualitative or quantitative degree of linked version uncertainties. at the one hand, the validity of the version is assured in basic terms inside of a frequency band, in order that approximately not anything could be acknowledged concerning the habit of the true plant at excessive frequencies. nonetheless, if the version is derived at the foundation of actual equations, it may be parameterized as a functionality of some actual parameters, that are often now not completely recognized in perform. this is often e.g. the case in aeronautical platforms: for example, the ae- dynamic version of an plane is derived from the flight mechanics eq- tions. whilst synthesizing the airplane keep watch over legislations, it really is then essential to keep in mind uncertainties within the values of the soundness derivatives, which correspond to the actual coefficients of the aerodynamic version. in addition, this aircraft version doesn't completely signify the be- vior of the genuine plane. As an easy instance, the flight keep an eye on approach or the autopilot tend to be synthesized simply utilizing the aerodynamic version, therefore with out accounting for the versatile mechanicalstructure: the c- responding dynamics are certainly regarded as excessive frequency overlooked 1 dynamics, with appreciate to the dynamics of the inflexible version .

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At each point of a frequency gridding The robustness margin is deduced as: When choosing a sufficiently fine frequency gridding, good results are obtained in many practical examples. 17). v. over the frequency range). In the context of this new and difficult problem, chapter 10 proposes a method for computing a reliable estimate of as a function of 28 A PRACTICAL APPROACH TO ROBUSTNESS ANALYSIS Chapter 2 APPLICATIVE EXAMPLES The first section describes the rigid and flexible models of the transport aircraft, while the second section describes the nonlinear and linearized missile models.

This qualitative presentation will be completed by a technical presentation of the associated methods in chapter 3. These techniques will be moreover applied to the aeronautical examples in chapter 4. v. is then introduced in a qualitative way in the second section. More precisely, we first focus on the problem of robust stability inside the left half plane. v. e. parametric uncertainties and neglected dynamics). v. provides a general framework for analyzing the robustness properties of a closed loop subject to model uncertainties.

18 A PRACTICAL APPROACH TO ROBUSTNESS ANALYSIS Remark: for the sake of completeness, the model perturbation above can also contain repeated complex scalars. Nevertheless, in many control problems, only contains real (possibly repeated) scalars and full complex blocks. g. (Doyle and Packard, 1987) 3. Note finally that a non repeated complex scalar can also be considered as a one dimensional full complex block. v. e. V. is now split as where structured perturbations. 1 illustrates that it is possible under mild conditions to 3 An other reason for handling repeated complex scalars is historical: during the Eighties, the real repeated scalars were often assumed to be complex, because the real nature of parametric uncertainties could not be taken into account by existing computational algorithms.

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