Nonlinear Robust Approaches to Study Stability and Postcritical Behavior of an Aeroelastic Plant
MARCOS ESTEBAN, ANDRES
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY
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Two approaches to tackle the nonlinear robust stability problem of an aerospace system are compared. The first employs a combination of the describing function method and \mu analysis, while the second makes use of integral quadratic constraints (IQCs). The model analyzed consists of an open-loop wing's airfoil subject to freeplay and linear time-invariant parametric uncertainties. The key steps entailed by the application of the two methodologies and their main features are critically discussed. Emphasis is put on the available insight on the nonlinear postcritical behavior known as limit cycle oscillation. It is proposed a strategy to apply IQCs, typically used to find absolute stability certificates, in this scenario, based on a restricted sector bound condition for the nonlinearity. Another contribution of this paper is to understand how the conservatism usually associated with the IQCs multipliers selection can be overcome by using information coming from the first approach. Nonlinear time-domain simulations showcase the prowess of these approaches in estimating qualitative trends and quantitative response's features. © 1993-2012 IEEE.
describing functions (dfs) integral quadratic constraints (iqcs) nonlinear uncertain systems robust stability (rs) analytical models describing functions integral equations linear systems oscillators (electronic) robustness (control systems) system stability time domain analysis uncertainty analysis describing function methods integral quadratic constraints limit cycle oscillation (lco) nonlinear time domain simulations nonlinear uncertain systems parametric uncertainties robust stability uncertainty stability criteria