By Gilles Ferreres
1. MOTIVATION in lots of actual events, 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 purely within a frequency band, in order that approximately not anything could be stated in regards to 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 can be e.g. the case in aeronautical platforms: for example, the ae- dynamic version of an aircraft is derived from the flight mechanics eq- tions. whilst synthesizing the airplane regulate legislation, it's then essential to bear in mind 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 characterize the be- vior of the true plane. As an easy instance, the flight keep an eye on method or the autopilot are typically synthesized simply utilizing the aerodynamic version, hence with no 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 info for A Practical Approach to Robustness Analysis with Aeronautical Applications
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).
Is defined as the inverse of the size of this model perturbation. v. along the imaginary axis: Introduction to and LFTs 13 The principle is thus to detect the crossing of one of the closed loop poles through the imaginary axis. corresponds to the size of the smallest parametric uncertainty which brings one closed loop pole on the imaginary axis. v. ). 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.
In the context of this new and difficult problem, chapter 10 proposes a method for computing a reliable estimate of as a function of 28 A PRACTICAL APPROACH TO ROBUSTNESS ANALYSIS Chapter 2 APPLICATIVE EXAMPLES The first section describes the rigid and flexible models of the transport aircraft, while the second section describes the nonlinear and linearized missile models. These two sections also present the design of associated controllers. 1 % for the damping ratio of the bending modes for the telescope, about 1 % for the aircraft).