An Active Disturbance Rejection Controller Based on Inverse Hyperbolic Sine Function

Abstract

Abstract:

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.

Key words: inverse hyperbolic sine function, tracking differentiator, extended state observer, active disturbance rejection controller（ADRC）, Lyapunov function

CLC Number:

TP 273

ZHOU Tao. An Active Disturbance Rejection Controller Based on Inverse Hyperbolic Sine Function[J]. Journal of Shanghai Jiaotong University, 2015, 49(08): 1186-1190.

References

［1］韩京清. 自抗扰控制技术——估计补偿不确定因素的控制技术［M］.北京：国防工业出版社，2008.

［2］XIA Yuanqing, LIU Bo, FU Mengyin. Active disturbance rejection control for power plant with a single loop［J］. Asian Journal of Control，2010，14(1)：239250.

［3］黄一，薛文超. 自抗扰控制：思想、应用及理论分析［J］.系统科学与数学，2012，32(10)：12871307.

HUANG Yi, XUE Wenchao. Active disturbance rejection control: idea, application and theoretical analysis［J］. Journal of Systems Science and Mathematical Sciences，2012，32(10)：12871307.

［4］周林阳，王生捷. 基于反正切非线性函数的自抗扰控制［J］.上海交通大学学报，2013，47(7)： 10431048.

ZHOU Linyang, WANG Shengjie. An improved ADRC based on nonlinear arctangent function［J］. Journal of Shanghai Jiaotong University，2013，47(7)：10431048.

［5］XIA Yuanqing, FU Mengyin, DENG Zhihong,et al. Recent developments in sliding mode control and active disturbance rejection control［J］. Control Theory & Applications，2013，30(2)：137147.

［6］周涛. 基于反双曲正弦函数的跟踪微分器［J］. 控制与决策，2014，29(6)：12391242.

ZHOU Tao. Tracking differentiator based on inverse hyperbolic sine function［J］. Control and Decision， 2014，29(6)：12391242.

［7］周涛.基于反双曲正弦函数的扩张状态观测器［J］.控制与决策，2015，30(5)：943946.

ZHOU Tao. Extended state observer based on inverse hyperbolic sine function［J］. Control and Decision, 2015，30(5)：943946.

［8］董小萌，张平. 反正切形式跟踪微分器设计及相平面分析［J］. 控制理论与应用，2010，27(4)：533537.

DONG Xiaomeng, ZHANG Ping. Design and phase plane analysis of an arctangentbased tracking differentiator［J］. Control Theory & Applications，2010，27(4)：533537.

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