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 in simple terms inside of a frequency band, in order that approximately not anything might be stated in regards to the habit of the genuine 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 frequently now not completely identified in perform. this can be e.g. the case in aeronautical platforms: for instance, the ae- dynamic version of an aircraft is derived from the flight mechanics eq- tions. whilst synthesizing the airplane keep an eye on legislation, it's then essential to take into consideration uncertainties within the values of the soundness derivatives, which correspond to the actual coefficients of the aerodynamic version. furthermore, this aircraft version doesn't completely symbolize the be- vior of the genuine plane. As an easy instance, the flight keep watch over process or the autopilot are typically synthesized simply utilizing the aerodynamic version, therefore 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
Coincides with the maximal singular value (resp. the real spectral radius When is a full complex block, The small gain theorem provides indeed a necessary and sufficient condition of stability in the context of an unstructured model perturbation. In an alternative way, the following result can be used: if A is a complex matrix, the size of the smallest unstructured complex matrix which renders the matrix singular, is In the context of the initial problem, matrix M is assumed to be invertible for the sake of simplicity.
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.
The skewed is defined Introduction to and LFTs 17 in the second one. The can be considered as an extension of classical algebraic notions, namely the spectral radius and the spectral norm (third subsection). The fourth subsection introduces the Main Loop Theorem in the specific context of robust performance problems. The notion of sensitivity is defined in the fifth subsection. The last subsection presents in a qualitative way some difficulties arising when using the framework. , 1991), contains real scalars (which represent the parametric uncertainties), complex scalars and full complex blocks (which represent the neglected dynamics).