二阶非线性系统自抗扰控制的全局渐近稳定性
Global and asymptotical stability of active disturbance rejection control for second-order nonlinear systems

自抗扰技术应用已十分广泛, 但其稳定性和收敛性分析仍是一个核心问题. 因此, 基于二阶非线性动态系 统, 设计了线性自抗扰控制器, 并利用李雅普诺夫函数方法, 通过理论分析和数学证明得到了系统大范围渐近稳定 时的控制参数可行域. 当被控对象的动态模型已知时, 只要系统总扰动的导数满足利普希茨条件, 控制参数可以从 得到的可行域内任意选择. 当被控对象的动态模型未知时, 还需满足总扰动关于输入和外扰的二阶导数等于零这个 条件. 然后针对不同的利普希茨常数绘制了参数可行域, 并对系统进行了数值仿真, 体现了自抗扰控制技术的强鲁 棒性. 这些分析都建立在扩张状态观测器和控制器相结合的基础上.
Active disturbance rejection control technique has been widely used, but the analysis on stability and convergence is still the core issue. So based on the second-order nonlinear dynamic systems, this paper constructs the linear active disturbance rejection controller, and obtains the feasible region of control parameters for the global and asymptotic stability through theoretical analysis and mathematical proof by means of Lyapunov function method. To be specific, when dynamic model of plant is given, the control parameters can be chosen arbitrarily from the feasible region as long as the derivative of disturbance satisfies a Lipschitz condition. When dynamic model of plant is unknown, it is necessary to satisfy another condition that the second derivative of total disturbance with respect to the input and the external disturbance is equal to zero. Then the feasible region is presented for different Lipschitz constants, and numerical simulations are carried out which show the great robustness of active disturbance rejection controller. All of these studies are based on the combination of extended state observer and the controller