To overcome nonlinear, underactuated and external wind disturbances problems for the 6-DOF (degrees of freedom) quadrotor unmanned aerial vehicle (UAV) system, a backstepping sliding mode control algorithm based on high-order extended state observer (ESO) is proposed. Based on the hierarchical control principle, the quadrotor UAV dynamic system is decomposed into position subsystem and attitude subsystem to facilitate the backstepping control design. Moreover, the EXO is used to estimate the remaining unmeasurable states and the external wind disturbances online. The advantages of the controllers are that they can not only ensure good tracking performance, but also deal with uncertain external disturbances. To imitate the real situation as much as possible, the external wind disturbances are composed of four basic wind models in this paper. The tracking error and estimate error of the design methods are shown to arbitrarily small by using Lyapunov theory. Finally, the effectiveness and superiority of the proposed control algorithm are proved by the simulation.
Uncertainties existing in the acoustic metamaterial may strongly affect its unusual properties. Aiming at this actuality, the interval model is introduced to treat with uncertainties existing in the acoustic metamaterial with Helmholtz resonators. Frequency intervals in which the sound intensity transmission coefficients are certainly less than the required value and the effective bulk moduli are certainly negative are defined as conservative approximations. Frequency intervals in which the sound intensity transmission coefficients may be less than the required value and the effective bulk moduli may be negative are defined as unsafe approximations. The proportion of the conservative approximation and the unsafe approximation is defined as an approximate precision. Based on the quantification of uncertainties of the sound intensity transmission coefficients and the negative effective bulk moduli, an optimization model for the interval acoustic metamaterial with Helmholtz resonators is constructed. Numerical results showed that even suffering from effects of interval parameters, unusual properties of the optimized acoustic metamaterial (such as the bandgap of the sound transmission and the negative effective bulk modulus) could be improved. 相似文献