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 basically inside of a frequency band, in order that approximately not anything could be stated 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 now not completely recognized in perform. this is often e.g. the case in aeronautical platforms: for example, the ae- dynamic version of an aircraft is derived from the flight mechanics eq- tions. while synthesizing the airplane keep an eye on legislation, it's then essential to bear in mind 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 signify the be- vior of the true airplane. As an easy instance, the flight regulate procedure 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 missed 1 dynamics, with recognize to the dynamics of the inflexible version .
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Extra resources for A Practical Approach to Robustness Analysis with Aeronautical Applications
Bendix pivots are represented by feedbacks of stiffness and friction and The order of the augmented system is equal to N + 6, where N is the order of (40 if the full order identified model is used) and 6 represents the 2 Bendix states and the 4 sensor states. , 1996; Madelaine, 1998) for the design of the control law. 7, a 59th closed loop flexible system is obtained. In this example, the issue will be to analyze the robustness properties of this controller with respect to uncertainties in the natural frequencies of the bending modes (see chapter 10).
In the second one, which is far less standard, a flexible airplane is considered. The aerodynamic model is presented in the first subsection. A simple static control law is synthesized for this rigid model in the second subsection. 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.
Yaw rotational rate. roll rotational rate. acceleration output. aileron deflection. 29 A PRACTICAL APPROACH TO ROBUSTNESS ANALYSIS 30 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. The lateral state-space equations of the aircraft are (see appendix A for numerical data): This model is obtained as the linearization of a nonlinear model at the trim value The acceleration at the center of gravity is: At a point of coordinates x and z (with respect to the center of gravity), the acceleration is: Uncertainties are introduced in the 14 coefficients which characterize the aerodynamic model, namely the stability derivatives and As an example, the coefficient is rewritten as: represents the nominal value of the coefficient.
A Practical Approach to Robustness Analysis with Aeronautical Applications by Gilles Ferreres