基于反双曲正弦函数的自抗扰控制器

利用反双曲正弦函数分别设计了三阶跟踪微分器和三阶扩张状态观测器,并利用该函数和设定输入的二阶微分信号设计控制律,从而构造了一种新型自抗扰控制器.通过李雅普诺夫函数证明了自抗扰控制系统在平衡点处渐近稳定.仿真实验表明,采用该自抗扰控制器的二阶系统能有效抑制内部和外部非线性扰动的影响,实现对方波信号和正弦信号的高精度跟踪,同时,扩张状态观测器能较准确地估计系统内部和外部扰动信号.

An Active Disturbance Rejection Controller Based on Inverse Hyperbolic Sine Function

Abstract： A third-order tracking differentiator and a third-order extended state observer (ESO) with an inverse hyperbolic sine function were proposed in this paper. The control law was designed with this function and the second-order derivative of the desired input signal. A new active disturbance rejection controller(ADRC) was constructed. Moreover, the asymptotic stability at the equilibrium point of the ADRC system was proved with the Lyapunov function. Finally, the simulation experiments demonstrate that the ADRC second-order system can track the square wave signal and sine signal in higher precision by rejecting the inner and outer nonlinear disturbance， and the ESO can accurately estimate the inner and outer disturbance.