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 merely inside of a frequency band, in order that approximately not anything should be acknowledged 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 frequently no longer completely identified in perform. this can be e.g. the case in aeronautical structures: as an instance, the ae- dynamic version of an aircraft is derived from the flight mechanics eq- tions. whilst synthesizing the plane keep an eye on legislation, it really is then essential to keep in mind uncertainties within the values of the steadiness derivatives, which correspond to the actual coefficients of the aerodynamic version. furthermore, this plane version doesn't completely characterize the be- vior of the genuine 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 admire to the dynamics of the inflexible version .
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Additional resources for A Practical Approach to Robustness Analysis with Aeronautical Applications
Commanded acceleration. actual acceleration. M: Mach number. V: missile velocity. Mass: missile mass. pitch moment of inertia. Q: dynamic pressure. S: reference area. d: missile diameter. 1 35 THE NONLINEAR MODEL A nonlinear longitudinal missile model is extracted from (Reichert, 1992). The control input is the tail deflection while the outputs used by the autopilot are the acceleration and rate outputs The state vector is where is the angle of attack. The missile behavior can be described by the following nonlinear equations: whereas the normal acceleration output is given by: This model is essentially parameterized by the Mach number M (between 2 and 4).
In the case of a real model perturbation, a first solution is to study the robustness of the location of the closed loop poles despite parametric uncertainties. In the general context of a mixed model perturbation, a second and more classical solution consists in checking whether a frequency domain template on a closed loop transfer matrix remains satisfied despite model uncertainties. In the first case, performance is rather defined in the time domain, whereas it is defined in the frequency domain in the second one.
In the same way, the flexible LFT model contains the physical inputs and outputs and additional inputs and outputs with the fictitious feedback The complete LFT model of the aircraft, is computed as an interconnection of the two above LFTs. 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.
A Practical Approach to Robustness Analysis with Aeronautical Applications by Gilles Ferreres