| Nonlinear active flutter suppression is a very important aspect in aeroelasticity.The active flutter suppression by changing the deflection of airfoil's control surfaces is expected to be used in engineering,and the research on control strategy for active flutter suppression have attracted more and more attention of researchers.When there exist problems such as saturation,uncertainty and constraint in the system,it is very importance to study the nonlinear flutter control strategy with low order,robustness and good stability.Utilizing the nonlinear dynamical theory,the modern control theory as well as intelligent control theory,this dissertation takes nonlinear two-dimensional airfoil in subsonic flow as the research object,several nonlinear active flutter control strategies which can guarantee strong robustness and good performance for system with nonlinear parameter uncertainty,external disturbance,input saturation and state constraints are proposed.The main contents are included as follows:1.Firstly,applying quasi-steady aerodynamic theory,the expressions of aerodynamic for lift and pitching moment acting on airfoil are derived,then aeroelastic model with plunge and pitch motions for an airfoil are established by using the Lagrangian equations.Eigenvalue method based on Routh-Hurwitz criterion is employed to determine flutter frequency and flutter velocity,and the mechanism and classification of the nonlinear limit cycle flutter are discussed.2.The active flutter control strategy of two-dimensional airfoil aeroelastic system with bilinear hysteresis non-linearity is studied.Firstly,a control law based on the state-dependent Riccati equation(SDRE)is derived,then the model is handled into the form which is suitable for SDRE control.By using the SDRE to select the appropriate performance weighting parameters,the optimal state feedback gain is obtained.The local asymptotic stability of closed-loop system is proven by using Lyapunov-based stability analysis.Then,the regular form approach of Sliding Mode Control(SMC)is used for flutter suppression.The system can be transformed into regular form via a change of coordinates defined by an orthogonal matrix,then by using quadratic minimization method,the state feedback matrix is designed.Further,the closed-loop system is asymptotically stable and fastly converges to the origin.Finally,it is also shown through simulation that the proposed algorithm is effective.The effect of time delay between the control input and actuator is discussed,and comparative analysis between the two algorithms is presented.3.For the problem of nonlinear parametric uncertainties in both pitch stiffness and damping for two-dimensional airfoil aeroelastic system,an adaptive controller based on global feedback linearization is derived.Based on Lie derivative,the global feedback linearization was realized.The stability of closed-loop system is proven by using Lyapunov-based stability analysis.Then,a model reference adaptive control(MRAC)law is developed for flutter suppression.The error dynamic equation is introduced to provide the ideal system response,by using Lyapunov function,the parameter estimate update law can be obtained,and the stability of closed-loop system is achieved.Further,the effect of adaptive gain matrix on parameter estimate convergence rate of the system is investigated.Finally,it is also shown through simulation that the proposed algorithm is effective.The stiffness parameter uncertainty on the role of system response and the relationship between the stiffness and damping parameter uncertainty are discussed.4.For the problem of nonlinear parametric uncertainties in both pitch stiffness and gust loads for two-dimensional airfoil aeroelastic system,based on the backstepping technique,an adaptive sliding mode controller with varying boundary layers is derived.The proposed control scheme combining the sliding mode control and backstepping technique,which make the complex nonlinear system is decomposed into several subsystems.At the same time,the Lyapunov function and virtual control variable are designed,and by using the robustness of sliding mode control,the stability of each subsystem can be guaranteed.Then,the uncertainty and disturbance are compensated via introducing the switching control.Besides,based on the adaptive method,the adaptation law of upper bounds for the uncertain parameter is obtained.Then according to the setting of the tracking error threshold,the width of the boundary layer is changed.Further,the closed-loop system is stable and fastly converges to the origin by using Lyapunov stability theorem.Finally,it is also shown through simulation that the proposed algorithm is effective.5.For a two-dimensional nonlinear airfoil model considered here includes state constraints,parameter uncertainties and gust loads,an iterative learning control(ILC)under state alignment condition is derived.In order to solve the problems of traditional Quadratic Lyapunov Function(QLF),a Barrier Lyapunov Function(BLF)is proposed,which is a Lyapunov-like function that grows to infinity as the arguments approach to certain limits.As a result,by keeping the BLF bounded,state constraints can be satisfied.Then,a Composite Energy Function(CEF)approach is adopted to deal with the state tracking problem in the presence of local Lipschitz continuous nonlinearities,whereas contraction mapping solves the tracking problem with global Lipschitz continuous nonlinearities.Further,a Barrier Composite Energy Function(BCEF)scheme that incorporates BLF into CEF,so that under the perturbation of system uncertainties,convergence of state tracking error can be guaranteed,while demand of state constraints can be satisfied.Finally,it is also shown through simulation that the proposed algorithm is effective.6.For a nonlinear aeroelastic airfoil with leading-and trailing-edge control surfaces,from the aspects of robustness and trajectory tracking performance,comparison of different control methods of the former several sections are given. |
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