Robust passivity-based continuous sliding-mode control for under-actuated nonlinear wing sections

The stability of an under-actuated nonlinear aeroelastic wing section is addressed using a robust passivity-based continuous sliding-mode control approach. The controller is shown to be capable of stabilising the system in the presence of large matched and mismatched uncertainties and large input disturbance. It is demonstrated in theory that within known bounds on the input disturbance and nonlinearity uncertainty, the controller is able to stabilise the system globally. A numerical example, based on the Texas A&M University experimental rig, is used to demonstrate the stabilisation of the system with a fully-developed limit cycle oscillation and a flap deflection limited to 20 degrees. This is of practical interest because it shows that the system is at least stabilised locally, whereas global stability is a concept limited to theoretical studies and is impossible to demonstrate in practice.