具有时变输出约束的柔性机翼非线性自适应控制

Nonlinear adaptive control for a flexible wing with time-varying outputconstraints

具有弯曲和扭转变形的柔性翼系统由一个四阶偏微分方程(PDE)与一个二阶常微分方程(ODE)描述,其中各个通道的干扰和参考轨迹来自于一个未知外系统.此时所有干扰和参考轨迹的系数均未知,且由于外系统初值未知,扰动和参考轨迹的时变状态也未知.首先,将柔性翼系统的鲁棒输出调节问题转化为跟踪误差系统的镇定问题,此时来自于干扰和参考轨迹的时变未知项被进一步转化为未知系数与已知时变信号的组合;然后,提出非线性自适应控制,其中非线性对数项用于保证时变输出约束,自适应律用于估测未知干扰的系数;最后,基于Barrier Lyapunov函数证明闭环系统跟踪误差的收敛性,以及跟踪误差的时变约束特性,通过Matlab数值仿真进一步验证该控制方法的有效性.

A flexible wing system of bending and twisting deformations is described by a fourth-order partial differential equation(PDE)and a second-order partial differential equation(ODE),where the disturbances in all channels and references are supposed to be from an unknown exosystem.In this sense,all the disturbances and references are composed of uncertain coefficients and time-varying states due to unknown initial values.Firstly,the robust output regulation is firstly transformed into a stabilization problem of the tracking error system,where the unknown time-varying terms from disturbances and references are rewritten into unknown coefficients but known time-varying terms.Then,adaptive nonlinear controls are proposed where adaption laws are used to estimate the unknown coefficients and nonlinear terms are used to guarantee the output constraint.Based on a Barrier Lyapunov function,the tracking errors of the closed-loop system are proved to converge toward zero,and are further restrained by time-varying constraints.Two numerical simulations are provided to show the effectiveness of the adaptive controls.