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Applied Mathematicsematics

A Practical Approach to Robustness Analysis with by Gilles Ferreres

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 simply within a frequency band, in order that approximately not anything may be stated in regards to 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 identified in perform. this can be 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 plane keep watch over legislation, it truly 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. furthermore, this plane version doesn't completely characterize the be- vior of the true plane. 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 appreciate to the dynamics of the inflexible version .

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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.

The third subsection presents the flexible model, which is to be added to the aerodynamic model in order to obtain a complete aircraft model. The fourth subsection presents the design of the new flight control system. Glossary sideslip angle. roll angle. yaw rotational rate. roll rotational rate. acceleration output. aileron deflection. 29 30 A PRACTICAL APPROACH TO ROBUSTNESS ANALYSIS rudder deflection. angle of attack. pitch angle. inertial speed. acceleration due to gravity. 1 THE AERODYNAMIC MODEL Let the state vector, whereas the output vector is denotes the control input vector.

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. 2 that a template is to be determined for each block of neglected dynamics. 8, with only two parametric uncertainties and The zero point corresponds to the nominal values of the uncertain parameters: remember that the nominal closed loop system is asymptotically stable.

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