A mixed H2/H∞ scheduling control scheme for a two degree-of-freedom aeroelastic system under varying airspeed and gust conditions

This article investigates the control of a two degree-of-freedom aeroelastic system with a torsional stiffness nonlinearity. The dynamics are transformed into a Linear Fractional Representation (LFR) such that the nonlinear effects of airspeed on the dynamics act as a gain feedback to the nominal system. A controller in LFR, which allows it to schedule with airspeed, is then synthesised using Linear Matrix Inequalities (LMIs). The performance objectives of the controller are the minimisation of the H2 norm from a gust input to the pitch and plunge outputs, and the minimisation of an H∞ norm that corresponds to the systematic method of H∞ loop-shaping. This method has a rigorous mathematical background that allows upper limits on these criteria to be established. The nonlinear system and controller are simulated under a variety of varying airspeed and gust conditions and is shown to exhibit both good robustness and rejection of gust disturbances.