By Gilles Ferreres
1. MOTIVATION in lots of actual occasions, 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 within a frequency band, in order that approximately not anything should be stated concerning the habit of the true 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 no longer completely recognized in perform. this is often e.g. the case in aeronautical structures: for instance, the ae- dynamic version of an plane is derived from the flight mechanics eq- tions. whilst synthesizing the plane keep an eye on legislation, it really is then essential to consider uncertainties within the values of the steadiness derivatives, which correspond to the actual coefficients of the aerodynamic version. additionally, this aircraft version doesn't completely symbolize the be- vior of the true plane. As an easy instance, the flight keep watch over method or the autopilot are typically 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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Extra info for A Practical Approach to Robustness Analysis with Aeronautical Applications
V. provides a general framework for analyzing the robustness properties of a closed loop subject to model uncertainties. The framework is finally introduced in a formal way in the last section. v. is first defined. The Main Loop Theorem, which plays a key role in the approach, is then introduced, before being interpreted in a qualitative way in the specific context of robust performance problems. v. instead of the exact value. These difficulties will be further studied in the next chapters. 3 4 A PRACTICAL APPROACH TO ROBUSTNESS ANALYSIS 1.
Is considered as a full block of neglected dynamics. 4 PARAMETRIC UNCERTAINTIES Assume as an example that the parametric uncertainties affine way the state-space equations of the plant l: enter in an 1 T h e parametric uncertainties may enter in practice in numerous other ways the (statespace or input/output) plant model. See chapter 3 for more details. Introduction to and LFTs 9 represents the normalized variation of the ith uncertain parameter. 5). 5). the LFT model of the uncertain plant. 1.
E. 10). is most generally a mixed model perturbation, containing parametric uncertainties and neglected dynamics. e. : The robust performance problem consists in computing the maximal amount of uncertainties, for which closed loop performance is still achieved. 4 that this robust performance problem can be equivalently transformed into an augmented robust stability problem, involving an additional fictitious full complex block (which is called a fictitious performance block). Chapter 7 will moreover illustrate that the robust performance problem is a skewed problem rather than a classical 4.