By Gilles Ferreres
1. MOTIVATION in lots of actual occasions, a plant version is frequently 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 within a frequency band, in order that approximately not anything could be stated concerning the habit of the genuine plant at excessive frequencies. however, if the version is derived at the foundation of actual equations, it may be parameterized as a functionality of some actual parameters, that are frequently now not completely recognized in perform. this can be e.g. the case in aeronautical structures: as an instance, the ae- dynamic version of an plane is derived from the flight mechanics eq- tions. while synthesizing the plane regulate legislations, it truly is then essential to have 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 characterize the be- vior of the genuine plane. As an easy instance, the flight regulate process or the autopilot are typically synthesized simply utilizing the aerodynamic version, hence with no accounting for the versatile mechanicalstructure: the c- responding dynamics are certainly regarded as excessive frequency ignored 1 dynamics, with recognize to the dynamics of the inflexible version .
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1. MOTIVATION in lots of actual events, a plant version is frequently supplied with a qualitative or quantitative degree of linked version uncertainties. at the one hand, the validity of the version is assured simply within a frequency band, in order that approximately not anything could be stated concerning the habit of the genuine plant at excessive frequencies.
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Additional info for A Practical Approach to Robustness Analysis with Aeronautical Applications
The transfer between and z). e. the one corresponding to • Assume isthatasymptotically stable. The issue is to determine the max- imal amount of neglected dynamics, for which the closed loop remains stable. A simple solution is provided by the small gain theorem, which gives a necessary and sufficient condition of stability of the closed loop at frequency possible choice of the weighting function W(s) is finally illustrated in •theA context of a simple example. Consider the case of a large dimension plant model Gcomplete(s).
Even if the gap between the bounds can not be guaranteed a priori when using polynomial time algorithms, good results can be obtained in realistic examples: this will be illustrated in the following. , 1995). Conversely, methods which compute a lower bound are generally heuristic, and the computational burden is required to be low. The most classical solution consists in solving in an heuristic way a non convex optimization problem: a lower bound corresponds indeed to a local optimum of this non convex optimization problem, whereas the exact value of corresponds to the global optimum of this optimization problem.
Other regions of the complex plane will be considered in the following section. For the sake of clarity, the first subsection presents the special case of a closed loop subject to parametric uncertainties. The general case of parametric uncertainties and neglected dynamics is treated in the second subsection. The third subsection is devoted to a technical, but practically important issue, namely the choice of the weights on the model uncertainties. v. e. 1 A PRELIMINARY RESULT For the sake of simplicity, M(s) is assumed to be a strictly proper transfer matrix.
A Practical Approach to Robustness Analysis with Aeronautical Applications by Gilles Ferreres