By Gilles Ferreres
1. MOTIVATION in lots of actual occasions, a plant version is usually supplied with a qualitative or quantitative degree of linked version uncertainties. at the one hand, the validity of the version is assured in basic terms within a frequency band, in order that approximately not anything will be acknowledged concerning 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 frequently now not completely recognized in perform. this can be 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 regulate legislations, it really is then essential to have 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 characterize the be- vior of the genuine plane. As an easy instance, the flight regulate approach 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 ignored 1 dynamics, with recognize to the dynamics of the inflexible version .
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Additional resources for A Practical Approach to Robustness Analysis with Aeronautical Applications
16, the sensitivity with 26 A PRACTICAL APPROACH TO ROBUSTNESS ANALYSIS respect to is strictly positive, whereas the sensitivity with respect to is zero. , 1991). v. , 1994), so that the computational burden of the algorithms, which compute the exact value of is necessarily an exponential function of the size of the problem. It is consequently impossible to compute the exact value of for large dimension problems. A usual solution is to compute upper and lower bounds instead of the exact value. The associated algorithms can be exponential time (like the algorithms which compute the exact value of ), or more interestingly polynomial time.
E. V. is now split as where structured perturbations. 1 illustrates that it is possible under mild conditions to 3 An other reason for handling repeated complex scalars is historical: during the Eighties, the real repeated scalars were often assumed to be complex, because the real nature of parametric uncertainties could not be taken into account by existing computational algorithms. Introduction to and LFTs 19 compute the exact value of (resp. of ) by computing recursively the exact value of (resp.
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. e. 10). is most generally a mixed model perturbation, containing parametric uncertainties and neglected dynamics.
A Practical Approach to Robustness Analysis with Aeronautical Applications by Gilles Ferreres