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Summary: This article presents a nonlinear closed‐loop active flow control (AFC) method, which achieves asymptotic regulation of a fluid flow velocity field in the presence of actuator uncertainty and sensor measurement limitations. To achieve the result, a reduced‐order model of the flow dynamics is derived, which utilizes proper orthogonal decomposition (POD) to express the Navier‐Stokes equations as a set of nonlinear ordinary differential equations. The reduced‐order model formally incorporates the actuation effects of synthetic jet actuators (SJA). Challenges inherent in the resulting POD‐based reduced‐order model include (1) the states are not directly measurable, (2) the measurement equation is in a nonstandard mathematical form, and (3) the SJA model contains parametric uncertainty. To address these challenges, a sliding mode observer (SMO) is designed to estimate the unmeasurable states in the reduced‐order model of the actuated flow field dynamics. A salient feature of the proposed SMO is that it formally compensates for the parametric uncertainty inherent in the SJA model. The SMO is rigorously proven to achieve local finite‐time estimation of the unmeasurable state in the presence of the parametric uncertainty in the SJA. The state estimates are then utilized in a nonlinear control law, which regulates the flow field velocity to a desired state. A Lyapunov‐based stability analysis is provided to prove local asymptotic regulation of the flow field velocity. To illustrate the performance of the proposed estimation and AFC method, comparative numerical simulation results are provided, which demonstrate the improved performance that is achieved by incorporating the uncertainty compensator. [ABSTRACT FROM AUTHOR]

Summary: Novel sliding mode observer (SMO) and robust nonlinear control methods are presented, which are shown to achieve finite‐time state estimation and asymptotic regulation of a fluid flow system. To facilitate the design and analysis of the closed‐loop active flow control (AFC) system, proper orthogonal decomposition–based model order reduction is utilized to express the Navier‐Stokes partial differential equations as a set of nonlinear ordinary differential equations. The resulting reduced‐order model contains a measurement equation that is in a nonstandard mathematical form. This challenge is mitigated through the detailed design and analysis of an SMO. The observer is shown to achieve finite‐time estimation of the unmeasurable states of the reduced‐order model using direct sensor measurements of the flow field velocity. The estimated states are utilized as feedback measurements in a closed‐loop AFC system. To address the practical challenge of actuator bandwidth limitations, the control law is designed to be continuous. A rigorous Lyapunov‐based stability analysis is presented to prove that the closed‐loop flow estimation and control method achieves asymptotic regulation of a fluid flow field to a prescribed state. Numerical simulation results are also provided to demonstrate the performance of the proposed closed‐loop AFC system, comparing 2 different designs for the SMO. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The flight trajectory of unmanned aerial vehicles (UAVs) can be significantly affected by external disturbances such as turbulence, upstream wake vortices, or wind gusts. These effects present challenges for UAV flight safety. Hence, addressing these challenges is of critical importance for the integration of unmanned aerial systems (UAS) into the National Airspace System (NAS), especially in terminal zones. This work presents a robust nonlinear control method that has been designed to achieve roll/yaw regulation in the presence of unmodeled external disturbances and system nonlinearities. The data from NASA-conducted airport experimental measurements as well as high-fidelity Large Eddy Simulations of the wake vortex are used in the study. Side-by-side simulation comparisons between the robust nonlinear control law and both linear H ∞ and PID control laws are provided for completeness. These simulations are focused on applications involving small UAV affected by the wake vortex disturbance in the vicinity of the ground (which models the take-off or landing phase) as well as in the out-of-ground zone. The results demonstrate the capability of the proposed nonlinear controller to asymptotically reject wake vortex disturbance in the presence of the nonlinearities in the system (i.e., parametric variations, unmodeled, time-varying disturbances). Further, the nonlinear controller is designed with a computationally efficient structure without the need for the complex calculations or function approximators in the control loop. Such a structure is motivated by UAV applications where onboard computational resources are limited. [ABSTRACT FROM AUTHOR]