快速反正切跟踪微分器设计
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摘要
针对反正切跟踪微分器存在整定参数困难和在平衡点附近收敛慢等问题,设计了一种快速收敛的反正切跟踪微分器。在反正切函数中引入线性函数和终端吸引子函数构造了快速反正切跟踪微分器,并证明了其稳定性,使系统在远离平衡点和接近平衡点都能快速并稳定地向平衡点收敛。这种线性与非线性组合的连续函数形式,提高了系统的跟踪能力,并且有效地抑制了噪声。可实现对信号快速而精确的微分和跟踪,且形式简单、易于实现。仿真结果表明快速反正切跟踪微分器具有优良的性能。
In order to solve the problem that the arctangent tracking differentiator has difficulty in setting parameters and slow convergence near the equilibrium, the author has designed a fast convergence arctangent tracking differentiator. A rapid arctangent tracking differentiator is constructed by introducing linear functions and terminal attractor functions into the arctangent function and its stability is proved, which makes the system far from the equilibrium and close to the equilibrium point convergence rapidly and stably to the equilibrium point. This continuous function form of linear and nonlinear combination enhances the tracking ability of the system, and effectively suppresses the noise, which can realize fast and precise signal differential and tracking,and the form is simple and easy to implement. The simulation results show that the rapid arctangent tracking differentiator has excellent performance.
In order to solve the problem that the arctangent tracking differentiator has difficulty in setting parameters and slow convergence near the equilibrium, the author has designed a fast convergence arctangent tracking differentiator. A rapid arctangent tracking differentiator is constructed by introducing linear functions and terminal attractor functions into the arctangent function and its stability is proved, which makes the system far from the equilibrium and close to the equilibrium point convergence rapidly and stably to the equilibrium point. This continuous function form of linear and nonlinear combination enhances the tracking ability of the system, and effectively suppresses the noise, which can realize fast and precise signal differential and tracking,and the form is simple and easy to implement. The simulation results show that the rapid arctangent tracking differentiator has excellent performance.
引文
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[14]Zhicheng Qiu,Sima Zhang.Fuzzy fast terminal sliding mode vibration control of a two-connected flexible plate using laser sensors[J].Journal of Sound and Vibration(s0022-460X),2016,380(13):51-77.
[15]V Nekoukar,A Erfanian.Adaptive fuzzy terminal sliding mode control for a class of MIMO uncertain nonlinear systems[J].Fuzzy Sets and Systems(S0165-0114),2011,179(1):34-49.
[16]蒲明,吴庆宪,姜长生,等.高阶滑模微分器的分析与改进[J].控制与决策,2011,26(8):1136-1146.Pu M,Wu Q X,Jiang C S,et al.Analysis and improvement of higher-order sliding mode diffierentiator[J].Control and Decision,2011,26(8):1136-1146.)
[17]蒲明,吴庆宪,姜长生,等.快速高阶滑模微分器[J].控制与决策,2012,27(9):1415-1420.Pu M,Wu Q X,Jiang C S,et al.Fast higher-order sliding mode diffierentiator[J].Control and Decision,2012,27(9):1415-1420.
[18]王新华,刘金琨.微分器设计与应用-信号滤波与求导[M].北京:电子工业出版社,2010:53-106.Wang X H,Liu J K.Differentiator Design and Application-Signal Filtering and Differentiation[M].Beijing:Publishing House of Electronics Industry,2010:53-106.
[2]Arie Levant.Principles of 2-sliding mode design[J].Automatica(S0005-1098),2007,43(4):576-586.
[3]齐国元,陈增强,袁著祉.非线性系统高阶微分反馈控制[J].中国工程科学,2003,5(8):35-63.Qi G Y,Chen Z Q,Yuan Z Z.High Order Differentia Feedback Control for Nonlinear Systems[J].Engineering Sciences,2003,5(8):35-63.
[4]Tian Dapeng,Shen Honghai,Dai Ming.Improving the Rapidity of Nonlinear Tracking Differentiator via Feedforward[J].IEEETransactions on Industrial Electronics(S0278-0046),2014,61(7):3736-3743.
[5]王新华,陈增强,袁著祉.全程快速非线性跟踪-微分器[J].控制理论与应用,2003,20(6):875-878.Wang X H,Chen Z Q,Yuan Z Z.Nonlinear tracking-differentiator with high speed in whole course[J].Control Theory&Applications,2003,20(6):875-878.
[6]史永丽,侯朝桢.改进的非线性跟踪微分器设计[J].控制与决策,2008,23(6):647-650.Shi Y L,Hou C Z.Design of improved nonliear tracking differentiator[J].Control and Decision,2008,23(6):647-650.
[7]赵鹏,姚敏立,陆长捷,等.高稳快速非线性_线性跟踪微分器设计[J].西安交通大学学报,2011,45(8):43-48.Zhao P,Yao M L,Lu C J,et al.Design of Nonlinear-Linear Tracking Differentiator with High Stability and High Speed[J].Journal of Xi'an Jiaotong University,2011,45(8):43-48.
[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 X M,Zhang P.Design and phase plane analysis of an arctangent-based tracking differentiator[J].Control Theory&Applications,2010,27(4):533-537.
[9]卜祥伟,吴晓燕,马震,等.改进的反正切跟踪微分器设计[J].上海交通大学学报,2015,49(2):164-168.Bu X W,Wu X Y,Ma Z,et al.Design of a Modified Arctangent-Based Tracking Diffierentiator[J].Journal of Shanghai Jiaotong University,2015,49(2):164-168.
[10]卜祥伟,吴晓燕,张蕊,等.双曲正弦非线性跟踪微分器设计[J].西安交通大学学报,2015,49(1):107-138.Bu X W,Wu X Y,Zhang R,et al.Design of AHyperbolic-Sine-Based Nonlinear Tracking Diffierentiator[J].Journal of Xi'an Jiaotong University,2015,49(1):107-138.
[11]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 T.Tracking differentiator based on inverse hyperbolic sine function[J].Control and Decision,2014,29(6):1239-1242.
[12]陆启韶.常微分方程的定性方法和分叉[M].北京:北京航空航天大学出版社,2002:182-230.LU Q S.Qualitative Methods and Bifurcations for Ordinary Differential Equations[M].Beijing:Beijing University of Aeronautics and Astronautics Press,2002:182-230.
[13]陆启韶.常微分方程与动力系统[M].北京:北京航空航天大学出版社,2010:182-230.Lu Q S.Ordinary Differential Equations and Dynamical Systems[M].Beijing:Beijing University of Aeronautics and Astronautics Press,2010:160-188.
[14]Zhicheng Qiu,Sima Zhang.Fuzzy fast terminal sliding mode vibration control of a two-connected flexible plate using laser sensors[J].Journal of Sound and Vibration(s0022-460X),2016,380(13):51-77.
[15]V Nekoukar,A Erfanian.Adaptive fuzzy terminal sliding mode control for a class of MIMO uncertain nonlinear systems[J].Fuzzy Sets and Systems(S0165-0114),2011,179(1):34-49.
[16]蒲明,吴庆宪,姜长生,等.高阶滑模微分器的分析与改进[J].控制与决策,2011,26(8):1136-1146.Pu M,Wu Q X,Jiang C S,et al.Analysis and improvement of higher-order sliding mode diffierentiator[J].Control and Decision,2011,26(8):1136-1146.)
[17]蒲明,吴庆宪,姜长生,等.快速高阶滑模微分器[J].控制与决策,2012,27(9):1415-1420.Pu M,Wu Q X,Jiang C S,et al.Fast higher-order sliding mode diffierentiator[J].Control and Decision,2012,27(9):1415-1420.
[18]王新华,刘金琨.微分器设计与应用-信号滤波与求导[M].北京:电子工业出版社,2010:53-106.Wang X H,Liu J K.Differentiator Design and Application-Signal Filtering and Differentiation[M].Beijing:Publishing House of Electronics Industry,2010:53-106.