By Gilles Ferreres
1. MOTIVATION in lots of actual events, 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 basically within a frequency band, in order that approximately not anything might be acknowledged in regards to 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 often now not completely identified in perform. this can be e.g. the case in aeronautical structures: for example, the ae- dynamic version of an aircraft is derived from the flight mechanics eq- tions. whilst synthesizing the plane regulate legislations, it truly is then essential to consider uncertainties within the values of the soundness derivatives, which correspond to the actual coefficients of the aerodynamic version. furthermore, this plane version doesn't completely characterize the be- vior of the true airplane. As an easy instance, the flight keep watch over approach or the autopilot are typically synthesized simply utilizing the aerodynamic version, therefore with out accounting for the versatile mechanicalstructure: the c- responding dynamics are certainly regarded as excessive frequency missed 1 dynamics, with recognize to the dynamics of the inflexible version .
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Extra info for A Practical Approach to Robustness Analysis with Aeronautical Applications
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. Let (A, B, C, 0) a state-space model of M(s).
Pitch moment of inertia. Q: dynamic pressure. S: reference area. d: missile diameter. 1 35 THE NONLINEAR MODEL A nonlinear longitudinal missile model is extracted from (Reichert, 1992). The control input is the tail deflection while the outputs used by the autopilot are the acceleration and rate outputs The state vector is where is the angle of attack. The missile behavior can be described by the following nonlinear equations: whereas the normal acceleration output is given by: This model is essentially parameterized by the Mach number M (between 2 and 4).
20). v. , so that a lower bound of the robustness margin is finally obtained as: In the context of a robust stability problem in the presence of parametric uncertainties, closed loop stability can thus be guaranteed inside the hypercube in the space of uncertain parameters. e. there exists a real model perturbation with singular (in the context of a robust stability problem, is a destabilizing model perturbation). The usefulness of a lower bound is twofold. As a first point, gives a measure of the conservatism of the upper bound by examining the tightness of the interval which contains the exact value of As a second point, an associated worst-case model perturbation is usually provided with by the computational algorithm.