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By Gilles Ferreres

1. MOTIVATION in lots of actual occasions, 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 in simple terms within a frequency band, in order that approximately not anything might be stated in regards to the habit of the genuine 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 now not completely identified 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 airplane keep an eye on legislations, it's then essential to take note of uncertainties within the values of the soundness derivatives, which correspond to the actual coefficients of the aerodynamic version. additionally, this aircraft version doesn't completely characterize the be- vior of the genuine plane. As an easy instance, the flight regulate approach or the autopilot tend to be synthesized simply utilizing the aerodynamic version, therefore with no accounting for the versatile mechanicalstructure: the c- responding dynamics are certainly regarded as excessive frequency ignored 1 dynamics, with admire to the dynamics of the inflexible version .

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The third subsection presents the flexible model, which is to be added to the aerodynamic model in order to obtain a complete aircraft model. The fourth subsection presents the design of the new flight control system. Glossary sideslip angle. roll angle. yaw rotational rate. roll rotational rate. acceleration output. aileron deflection. 29 30 A PRACTICAL APPROACH TO ROBUSTNESS ANALYSIS rudder deflection. angle of attack. pitch angle. inertial speed. acceleration due to gravity. 1 THE AERODYNAMIC MODEL Let the state vector, whereas the output vector is denotes the control input vector.

17). v. over the frequency range). 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).

Along the border of to find the minimal size real model perturbation, which shifts one closed loop pole on this border. 9). Performance is indeed defined in this context by minimal values and for the damping ratio and the degree of stability To some extent, these specifications correspond to requirements on the rise time and overshoot of the closed loop step response, or on the time needed to reject an unmeasured disturbance or a non zero initial condition. 2 the degree of stability of a state-space matrix A is defined as is an eigenvalue of A.

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