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 acknowledged concerning 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 often no longer completely identified in perform. this is often e.g. the case in aeronautical structures: to illustrate, the ae- dynamic version of an plane is derived from the flight mechanics eq- tions. while synthesizing the plane keep watch over 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. in addition, this aircraft version doesn't completely characterize the be- vior of the true plane. As an easy instance, the flight regulate method or the autopilot tend to be synthesized simply utilizing the aerodynamic version, hence with out 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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Additional resources for A Practical Approach to Robustness Analysis with Aeronautical Applications
The actuators and filters poles are not to be moved. 2. The 6 closed loop flexible modes are chosen as: The damping ratios of the 4 critical flexible modes are increased up to 30 %. The two other flexible modes are left unchanged. Summarizing, the closed loop poles, corresponding to the state-feedback controller, are: 34 A PRACTICAL APPROACH TO ROBUSTNESS ANALYSIS An observer is now to be built. Since the states of the filters are available, the new design model is the same as the one for the state feedback, except that it does not include the filters.
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 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.
3 as a specific interconnection of two LFTs. 2 CHENG AND DE MOOR’S METHOD As said at the beginning of this chapter, an LFT model can be computed when the coefficients of the state space model or transfer matrix are most generally rational functions of the parametric uncertainties. The aim of this subsection is to illustrate this by detailing the method by (Cheng and DeMoor, 1994). This technique uses the fact that an interconnection of LFTs is also an LFT. The idea is to realize separately the linear and nonlinear parts of the model.