Active Suppression ofAerofoil Flutter via Neural-Network-Based Adaptive Nonlinear Optimal Control

Abstract

This thesis deals with active flutter suppression (AFS) on aerofoils via adaptive nonlinear optimal control using neural networks (NNs). Aeroelastic flutter can damage aerofoils if not properly controlled. AFS not only ensures flutter-free flight but also enables the use of aerodynamically more efficient lightweight aerofoils. However, existing optimal controllers for AFS are generally susceptible to modelling errors while other controllers less prone to uncertainties do not provide optimal control. This thesis, thus, aims to reduce the impact of the dilemma by proposing new solutions based on nonlinear optimal control online synthesis (NOCOS) according to online updated dynamics. Existing NOCOS methods, with NNs as essential elements, require a separate initial stabilising control law for the overall system, an additional stabilising tuning loop for the actor NN, or an additional stabilising term in the critic NN tuning law, to guarantee the closed-loop stability for unstable and marginally stable systems. The resulting complexity is undesired in AFS applications due to computational concerns in real-time implementation. Moreover, the existing NOCOS methods are confined to locally nonlinear systems, while aeroelastic systems under consideration are globally nonlinear. These make all the existing NOCOS algorithms inapplicable to AFS without modification and improvement. Therefore, this thesis solves the aforementioned problems through the following step-by-step approaches. Firstly, a four degrees-of-freedom (4-DOF) aeroelastic model is considered, where leading- and trailing-edge control surfaces of the aerofoil are used to actively suppress flutter. Accordingly, a virtual stiffness-damping system (VSDS) is developed to simulate physical stiffness in the aeroelastic system. The VSDS, together with a scaled-down typical aerofoil section placed in a wind tunnel, serve as an experimental 4-DOF aeroelastic test-bed for synthesis and validation of proposed AFS controllers that follow. Secondly, a Modified form of NN-based Value Function Approximation (MVFA), tuned by gradient-descent learning, is proposed for NOCOS to address the closedloop stability in a compact controller configuration suitable for real-time implementation. Its validity and efficacy are examined by the Lyapunov stability analysis and numerical studies. Thirdly, a systematic procedure based on linear matrix inequalities is further proposed for synthesising a scheduled parameter matrix to generalise the MVFA to to globally nonlinear cases, so that the new NN controller suits AFS applications. In addition, the extended Kalman filter (EKF) is proposed for the new NN controller for fast parameter convergence. An identifier NN is also derived to capture and update aeroelastic dynamics in real time to mitigate the impact of modelling errors. Wind-tunnel experiments were conducted for validation. Finally, a non-quadratic functional is introduced to generalise the performance index to tackle the problem where control inputs are constrained. The feasibility of including the non-quadratic cost function under the proposed control scheme based on the MVFA is examined via the Lyapunov stability analysis and was also experimentally evaluated through the wind-tunnel testings. The proposed NN controllers are compact in structure and shown capable of maintaining the closed-loop stability while eliminating the need for a separate initial stabilising control law for the overall system, an additional tuning loop for the actor NN, and an additional stabilising term in the critic NN tuning law. Under the new control schemes, online synthesised nonlinear control laws are optimal in the cases with and without constraints in control. Comparisons drawn with a popular linear-parameter-varying (LPV) controller in the form of the widely used linear quadratic regulator (LQR) in experiments show that the proposed NN controllers outperform the LPV-LQR algorithm and improve AFS from the optimal control perspective. Specifically, the proposed NN controllers can effectively mitigate the impact of modelling errors, successfully solving the mentioned dilemma involved in AFS. The results also confirm that the proposed NN controllers are suitable for real-time implementation.