A robust nonlinear output feedback control method for limit cycle oscillation suppression using synthetic jet actuators

A synthetic jet actuator-based output feedback control method is presented, which achieves asymptotic limit cycle oscillation regulation in small unmanned aerial vehicle wings, where the dynamic model contains uncertainty and unmodeled external disturbances. In addition, the proposed control method compensates for the parametric uncertainty and nonlinearity inherent in the synthetic jet actuator dynamics. Motivated by the limitations characteristic of small unmanned aerial vehicles, the control method is designed to be computationally inexpensive, eliminating the need for time-varying parameter update laws, function approximators, or other computationally heavy techniques. To this end, a computationally minimal robust-inverse control method is utilized, which is proven to compensate for the uncertainties in both the aerial vehicle dynamics and the synthetic jet actuator dynamics. By endowing the robust-inverse control law with a bank of dynamic filters, asymptotic limit cycle oscillation regulation is achieved using only pitching and plunging displacement measurements in the feedback loop. The result is an asymptotic synthetic jet actuator-based limit cycle oscillation regulation control method, which does not require velocity measurements, adaptive laws, or function approximators in the feedback loop. To achieve the result, a detailed mathematical model of the limit cycle oscillation dynamics is utilized, which includes nonlinear stiffness effects, unmodeled external disturbances, and dynamic model uncertainty, in addition to the parametric uncertainty in the synthetic jet actuator dynamic model. A rigorous Lyapunov-based stability analysis is utilized to prove asymptotic regulation of limit cycle oscillations, and numerical simulation results are provided to demonstrate the performance of the proposed control law.