Probabilistic Control Optimization of Aeroservoelastic Systems with Uncertainty

Aprobabilistic-based control optimizationmethod is developed for aeroservoelastic systems with parameter uncertainties. Genetic algorithms are used to find optimal feedback control gains that simultaneously assign a mean flutter speed andmaximize a defined worst-case speed. In the proposed approach, a surrogatemodel of the flutter speed response surface is constructed so that the critical flutter speed is represented in terms of the uncertain parameters. The surrogate model is created in two ways: 1) by linearization of the response surface using local sensitivities, and 2) by a polynomial chaos expansion. The surrogate model is then sampled to find the worst-case flutter speed, which is defined probabilistically by the inverse cumulative distribution function. The method is applied to a three-degree-of-freedom aeroservoelastic system that uses an unsteady, two-dimensional potential flow and explicitly contains the control and actuator dynamics. Case studies with uncertainty in the pitch and plunge stiffness parameters are presented. It is demonstrated that the control gains have a strong influence on the shape of the response surface and that it is possible to control not only the expectation, but also the variance of the flutter speed.