A Practical Approach to Robustness Analysis with by Gilles Ferreres
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 merely inside of a frequency band, in order that approximately not anything will be acknowledged 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 frequently no longer completely identified in perform. this is often e.g. the case in aeronautical platforms: for instance, the ae- dynamic version of an plane is derived from the flight mechanics eq- tions. while synthesizing the plane keep watch over legislation, it's then essential to take into consideration 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 characterize the be- vior of the genuine 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 ignored 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
E. 10). is most generally a mixed model perturbation, containing parametric uncertainties and neglected dynamics. e. : The robust performance problem consists in computing the maximal amount of uncertainties, for which closed loop performance is still achieved. 4 that this robust performance problem can be equivalently transformed into an augmented robust stability problem, involving an additional fictitious full complex block (which is called a fictitious performance block). Chapter 7 will moreover illustrate that the robust performance problem is a skewed problem rather than a classical 4.
Q: pitch rotational rate. 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.
These transfer matrices are chosen so that the singular values reflect the design objectives. 4). A controller is obtained, which stabilizes the augmented plant. The final controller is K(s) = Note that the above robust stabilization procedure presents special properties, since it tries as much as possible to keep the desired open loop shaping while enforcing a stability closed loop constraint. 2 APPLICATION The choice of the compensators is not detailed, the interested reader is referred to (Ferreres and M’Saad, 1996) for a related work.