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 simply inside of a frequency band, in order that approximately not anything could be acknowledged concerning the habit of the true plant at excessive frequencies. nevertheless, 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 identified in perform. this can be e.g. the case in aeronautical platforms: for instance, the ae- dynamic version of an plane is derived from the flight mechanics eq- tions. whilst synthesizing the plane regulate legislation, it truly is then essential to bear in mind uncertainties within the values of the soundness derivatives, which correspond to the actual coefficients of the aerodynamic version. furthermore, this aircraft version doesn't completely signify the be- vior of the true airplane. As an easy instance, the flight regulate method 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 missed 1 dynamics, with admire to the dynamics of the inflexible version .
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Additional info for A Practical Approach to Robustness Analysis with Aeronautical Applications
E. 1 PRINCIPLE OF LOOP SHAPING 37 AUTOPILOT CONTROL In the case of a SISO system, the very classical Bode method shapes the magnitude and phase of the open loop frequency response where K(s) and G(s) respectively represent the controller and plant model. As an extension to the case of a MIMO plant G(s), the singular values of the open loop transfer or can be shaped (McFarlane and Glover, 1990; McFarlane and Glover, 1992). To this aim, pre- and post-compensators and are added at the plant inputs and outputs.
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. 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.
Actual tail deflection angle. commanded tail deflection angle. 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.