Nonlinear Estimation and Control Methods for Mechanical and Aerospace Systems under Actuator Uncertainty

Air flow velocity field control is of crucial importance in aerospace applications to prevent the potentially destabilizing effects of phenomena such as cavity flow oscillations, flow separation, flow-induced limit cycle oscillations (LCO) (flutter), vorticity, and acoustic instabilities. Flow control is also important in aircraft applications to reduce drag in aircraft wings for improved flight performance. Although passive flow control approaches are often utilized due to their simplicity, active flow control (AFC) methods can achieve improved flight performance over a wider range of time-varying operating conditions by automatically adjusting their level of control actuation in response to real-time sensor measurements. Although several methods for AFC have been presented in recent literature, there remain numerous challenges to be overcome in closed-loop nonlinear AFC design. Additional challenges arise in control design for practical systems with limited onboard sensor measurements and uncertain actuator dynamics. In this thesis, robust nonlinear control methods are developed, which are rigorously proven to achieve reliable control of fluid flow systems under uncertain, timevarying operating conditions and actuator model uncertainty. Further, to address the practical control design challenges resulting from sensor limitations, this thesis research will investigate and develop new methods of sliding mode estimation, which are shown to achieve finite-time state estimation for systems with limited onboard sensing capabilities. The specific contributions presented in this thesis include: 1) the application of proper orthogonal decomposition (POD)-based model order reduction techniques to develop simplified, control-oriented mathematical models of actuated fluid flow dynamic systems; 2) the rigorous development of nonlinear closed-loop active flow control techniques to achieve asymptotic regulation of fluid flow velocity fields; 3) the design of novel sliding mode estimation and control methods to regulate fluid flow velocity fields in the presence of actuator uncertainty; 4) the design of a nonlinear control method that achieves simultaneous fluid flow velocity control and LCO suppression in a flexible airfoil; and 5) the analysis of a discontinuous hierarchical sliding mode estimation method using a differential inclusions-based technique.