一种固定时间收敛模型参考终端滑模控制方法

张骁骏; 袁夏明; 王向阳; 朱纪洪; 李春文

doi:10.16383/j.aas.c190273

一种固定时间收敛模型参考终端滑模控制方法

doi: 10.16383/j.aas.c190273

1.
清华大学自动化系北京 100084
2.
清华大学计算机科学与技术系北京 100084
3.
清华大学精密仪器系北京 100084

基金项目: 国家自然科学基金(61673240, 61603210)资助

详细信息

作者简介:
张骁骏：清华大学自动化系硕士研究生. 主要研究方向为非线性控制和飞行控制. E-mail: z-xj17@mails.tsinghua.edu.cn

袁夏明：清华大学博士后. 2015年于清华大学计算机科学与技术系获得博士学位. 主要研究方向为飞行控制, 非线性控制, 信息融合. E-mail: summersbright@126.com

王向阳：清华大学博士后. 2014年于清华大学航天航空学院获得博士学位. 主要研究方向为飞/推综合控制, 非线性控制, 动力学建模. E-mail: wangxy668@rtsinghua.edu.cn

朱纪洪：清华大学计算机科学与技术系教授. 主要研究方向为飞行控制与导航, 鲁棒控制和非线性控制. 本文通信作者. E-mail: jihong_zhu@hotmail.com

李春文：清华大学自动化系教授. 主要研究方向为非线性控制和逆系统控制. E-mail: lcw@tsinghua.edu.cn

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出版历程
- 收稿日期: 2019-04-01
- 录用日期: 2019-07-30
- 网络出版日期: 2022-01-28
- 刊出日期: 2022-03-25

A Model Reference Terminal Sliding Mode Control Method With Fixed-time Convergence

1.
Department of Automation, Tsinghua University, Beijing 100084
2.
Department of Computer Science and Technology, Tsinghua University, Beijing 100084
3.
Department of Precision Instrument, Tsinghua University, Beijing 100084

Funds: Supported by National Natural Science Foundation of China (61673240, 61603210)

More Information

Author Bio:
ZHANG Xiao-Jun　Master student in the Department of Automation, Tsinghua University. His research interest covers nonlinear control and flight control

YUAN Xia-Ming　Postdoctoral at Tsinghua University. He received his Ph.D. degree in the Department of Computer Science and Technology, Tsinghua University in 2015. His research interest covers fight control, nonlinear control, and information fusion

WANG Xiang-Yang　Postdoctoral at Tsinghua University. He received his Ph.D. degree at the School of Aerospace, Tsinghua University in 2014. His research interest covers integrated flight/propulsion control, dynamic modeling, and nonlinear control

ZHU Ji-Hong　Professor in the Department of Precision Instrument, Tsinghua University. His research interest covers fight control and navigation, robust control, and nonlinear control. Corresponding author of this paper

LI Chun-Wen　Professor in the Department of Automation, Tsinghua University. His research interest covers nonlinear control and inverse system control

摘要

摘要: 针对一类具有模型不确定性和外部扰动的时变非线性系统, 基于模型参考控制方法, 设计了具有固定时间收敛特性的终端滑模控制器. 首先, 提出一种带有输入饱和限幅和补偿信号滤波的模型参考控制结构; 然后针对广义误差信号, 采用新型终端滑模面设计了补偿控制器, 较好地平衡靠近和远离平衡点的收敛速度. 基于李雅普诺夫方法证明了闭环系统的稳定性和固定时间收敛特性, 并给出了收敛时间上界. 最后将该方法应用到含有极限环的非线性系统跟踪控制中, 仿真结果验证了该方法的有效性.
- 固定时间收敛 /
- 模型参考控制 /
- 终端滑模控制 /
- 时变非线性系统
Abstract: Based on model reference method, a nonsingular terminal sliding-mode control method with fixed time convergence is proposed for a class of time-varying nonlinear systems with model uncertainties and external disturbances. Firstly, a model reference controller structure considering input saturation and compensation signal filtering is proposed. Then a sliding mode controller based on a novel nonlinear terminal sliding mode manifold is constructed for generalized errors, which balances the convergence speed near and away from the equilibrium point. The fixed time convergence and stability of closed-loop system are proved with the Lyapunov method, and the upper bound of convergence time is obtained. Finally, the method proposed is applied to tracking control of nonlinear systems with limit cycle.The simulation results verify its effectiveness.
- Fixed-time convergence /
- model reference control /
- terminal sliding mode control /
- time-varying nonlinear systems

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图 1 模型参考控制器结构

Fig. 1 Structure of the model reference controller proposed

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图 2 标量系统收敛过程

Fig. 2 Convergence process of the scalar system

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图 3 基准模型跟踪误差曲线

Fig. 3 Tracking error curve of the benchmark model

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图 4 误差系统相平面图

Fig. 4 Phase plane plots of error dynamic

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图 5 模型C开环响应极限环

Fig. 5 Open-loop response of Model C exhibiting limit cycle

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图 6 不同初值模型A闭环响应

Fig. 6 Closed-loop response of Model A for several initial

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图 7 不同迎角模型C闭环响应

Fig. 7 Closed-loop response of Model C for several angle of attack

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图 8 模型A对阶跃信号跟踪响应

Fig. 8 Closed-loop response to step signal tracking of Model A

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图 9 模型(43)开环响应特性

Fig. 9 Open-loop response of model (43)

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图 10 闭环系统对阶跃信号跟踪响应

Fig. 10 Response to step signal tracking of closed-loop system

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表 1 标量系统参数和收敛时间 (s)

Table 1 Coefficients and convergence time (s) of the scalar system

参数	$\beta $	$q $	$\alpha $	$p $	$T $
1	1	5/9	0	5/9	1.08
2	1	5/9	1	5/9	0.80
3	3	5/9	1	5/9	0.34
4	1	3/9	1	5/9	0.68
5	1	5/9	3	5/9	0.56
6	1	5/9	1	3/9	0.75

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表 2 模型A的气动数据

Table 2 Aerodynamic coefficients for Model A

$\alpha\;{\rm{(rad)}}$	$\hat a_0$	$ \hat a_1 $	$ \hat a_2 $	$ \hat a_3 $	$ \hat a_4 $
0.4363	0.00543	−0.01426	0.41336	−0.00465	0.00263
0.4800	0.00594	−0.01765	0.38793	−0.00487	0.01689
0.5236	0.00657	−0.02040	0.38008	−0.00537	0.02596
0.5672	0.00732	−0.03104	0.53884	−0.00623	0.04189
0.6109	0.00794	−0.03137	0.53455	−0.00751	0.05144
0.6545	0.00914	−0.00246	0.00105	−0.01059	0.03736
0.6981	0.00902	−0.01881	0.62351	−0.01187	0.06119
0.7418	0.00999	−0.03219	1.51180	−0.02862	0.06867
0.7854	0.01135	−0.03712	2.42520	−0.08113	0.02935

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表 3 模型C的气动数据

Table 3 Aerodynamic coefficients for Model C

$\alpha\;{\rm{(rad)}}$	$\hat a_0$	$ \hat a_1 $	$ \hat a_2 $	$ \hat a_3 $	$ \hat a_4 $
0.4363	0.00615	−0.02644	0.82603	−0.00940	0.04934
0.4800	0.00310	−0.00057	1.00250	−0.01157	−1.19080
0.5236	0.00523	−0.00406	0.09998	−0.00167	−0.00183
0.5672	0.00729	−0.01260	0.33063	−0.00506	−0.00378
0.6109	0.00591	−0.03024	1.07030	−0.00285	−0.03726
0.6545	−0.00406	−0.00588	1.0840	0.03646	−0.15374
0.6981	0.00574	−0.00771	−0.03172	−0.01095	0.16302
0.7418	−0.0040	−0.03261	2.3447	0.13848	0.90542
0.7854	−0.00089	−0.02071	0.8361	0.13752	2.8685

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