By Gilles Ferreres
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 basically inside of a frequency band, in order that approximately not anything should be stated concerning the habit of the genuine plant at excessive frequencies. nevertheless, 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 no longer completely identified in perform. this is often e.g. the case in aeronautical platforms: for instance, the ae- dynamic version of an plane is derived from the flight mechanics eq- tions. whilst synthesizing the airplane keep an eye on legislation, 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. furthermore, this plane version doesn't completely symbolize the be- vior of the genuine airplane. As an easy instance, the flight keep an eye on procedure 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 missed 1 dynamics, with appreciate to the dynamics of the inflexible version .
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Additional info for A Practical Approach to Robustness Analysis with Aeronautical Applications
Corresponds to the size of the smallest parametric uncertainty which brings one closed loop pole on the imaginary axis. v. ). v. m. may be infinite (if no structured model perturbation exists, which destabilizes the closed loop). v. e. its spectral norm - see below). 1 to the case of neglected dynamics seems a priori more complex, since is now a dynamic transfer matrix instead of a simple gain matrix. 3 CHOICE OF WEIGHTS ON THE MODEL UNCERTAINTIES An important practical issue is the choice of weights on model uncertainties.
Which is assumed to belong to the interval [1,1], finally represents the normalized parametric uncertainty in The scalar is called in the following "the weight" in the coefficient The weights in the 14 stability derivatives are chosen in the following as 10 %. A second order actuator is added at the control input Applicative examples 31 whereas a third order actuator is added at the control input Remarks: (i) All quantities p, r and are expressed in degree or degree/s. The acceleration output is expressed in (ii) For the sake of simplicity, the acceleration is measured in the following at the center of gravity.
Of ). When computing the exact value of it is moreover possible to use either a fixed point or a dichotomy search. ). Point b/ is deduced from point a/ using Note however that Remark: takes an infinite value if and only if (Fan and Tits, 1992). v. can only take finite values. On the contrary, an infinite value can be obtained for the measure. v. is available. Nevertheless, in the special 20 A PRACTICAL APPROACH TO ROBUSTNESS ANALYSIS case of a single full complex block (resp. v. coincides with the maximal singular value (resp.
A Practical Approach to Robustness Analysis with Aeronautical Applications by Gilles Ferreres
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