一类新的二阶滑模控制方法及其在倒立摆控制中的应用

李雪冰; 马莉; 丁世宏

doi:10.16383/j.aas.2015.c140263

一类新的二阶滑模控制方法及其在倒立摆控制中的应用

doi: 10.16383/j.aas.2015.c140263 cstr: 32138.14.j.aas.2015.c140263

1.
江苏大学电气信息工程学院镇江 212013

基金项目:

国家自然科学基金(61203054);江苏省高校优势学科建设工程资助项目(PAPD, 苏政办发(2011)6号;江苏省自然科学基金(BK2012283)资助

详细信息

作者简介:
李雪冰江苏大学电气信息工程学院硕士研究生.主要研究方向为滑模变结构控制理论.E-mail:lxb121619@163.com

通讯作者:
丁世宏江苏大学电气信息工程学院副教授.主要研究主向为非线性系统,高阶滑模控制,DC-DC控制.本文通信作者.E-mail:dsh@ujs.edu.cn

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- 文章访问数: 2970
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- 被引次数: 0
出版历程
- 收稿日期: 2014-04-16
- 修回日期: 2014-07-18
- 刊出日期: 2015-01-20

A New Second-order Sliding Mode Control and Its Application to Inverted Pendulum

1.
School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013

Funds:

Supported by National Natural Science Foundation of China (61203054), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD, (2011)6), and Natural Science Foundation of Jiangsu Province (BK2012283)

摘要

摘要: 二阶滑模作为高阶滑模的特殊情形, 不仅具有传统滑模鲁棒性强、对外界干扰不敏感的特点, 而且能够有效地消弱传统一阶滑模中存在的"抖振"现象. 本文设计了一种新的二阶滑模控制算法. 该算法的优点是假设不确定性是由非负函数限制而不是由常数限定. 因此, 该算法在实际应用中具有更广的应用范围. 此外, 算法中的加幂积分技术保证了系统在有限时间内稳定, 而不是传统二阶滑模中普遍存在的有限时间收敛, 并给出了严格的数学证明. 最后, 在倒立摆控制中的应用验证了该算法的有效性.
- 二阶滑模 /
- 有限时间稳定 /
- 加幂积分 /
- 倒立摆
Abstract: Second-order sliding mode, as a special case of high-order sliding mode, not only has strong robustness and insensitiveness to external disturbance, but also eliminates the chattering phenomenon existing in the traditional first-order sliding mode. A new second-order sliding mode control algorithm is developed in this paper. The advantage of the algorithm lies in that it can be used to handle the uncertainty bounded by a known positive function rather than a positive constant. Consequently, the algorithm can be applied to a more general class of systems. In addition, the adding a power integrator technique guarantees the global finite-time stability rather than the finite-time convergence. Finally, the application to control of an inverted pendulum shows the effectiveness of the algorithm.
- Second-order sliding mode /
- finite-time stability /
- adding a power integrator /
- invented pendulum

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参考文献(30)

[1]	Liu Jin-Kun, Sun Fu-Chun. Research and development on theory and algorithms of sliding mode control. Control Theory and Applications, 2007, 24(3): 407-418 (刘金琨, 孙福春. 滑模变结构控制理论及其算法研究与进展. 控制理论及应用, 2007, 24(3): 407-418)
[2]	Ding S H, Li S H. Stabilization of the attitude of a rigid spacecraft with external disturbances using finite-time control techniques. Aerospace Science and Technology, 2009, 13(4-5): 256-265
[3]	Liu Yue, Ma Shu-Ping. A singular system approach to output feedback sliding mode control for time-delay systems. Acta Automatica Sinica, 2013, 39(5): 594-601 (刘月, 马树萍. 时滞系统的输出反馈滑模控制的一种奇异系统方法. 自动化学报, 2013, 39(5): 594-601)
[4]	Wang He, Li Yao-Feng, Zhang Shou-Long, Dong Chen. Chaotic oscillation control based on adaptive terminal sliding mode. Proceedings of the CSU-EPSA, 2013, 25(3): 152-157 (王鹤, 李耀峰, 张守龙, 董晨. 基于自适应Terminal 滑模的混沌振荡控制. 电力系统及其自动化学报, 2013, 25(3): 152-157)
[5]	Pu Ming, Wu Qing-Xian, Jiang Chang-Sheng, Dian Song-Yi, Wang Yu-Fei. Recursive terminal sliding mode control for higher-order nonlinear system with mismatched uncertainties. Acta Automatica Sinica, 2012, 38(11): 1777-1793 (蒲明, 吴庆宪, 姜长生, 佃松宜, 王宇飞. 非匹配不确定高阶非线性系统递阶Terminal滑模控制. 自动化学报, 2012, 38(11): 1777-1793)
[6]	Utkin V I, Lee H. The chattering analysis. In: Proceedings of the 12th International Power Electronics and Motion Control. Portoroz: IEEE, 2006. 2014-2019
[7]	Slotine J J, Sastry S S. Tracking control of non-linear systems using sliding surfaces with application to robot manipulators. International Journal of Control, 1983, 38(2): 465-492
[8]	Gao Wei-Bing. Theory and design method of variable structure control. BeiJing: Science Press, 1996.(高为炳. 变结构控制的理论及设计方法. 北京: 科学出版社, 1996.)
[9]	Levant A. Sliding order and sliding accuracy in sliding mode control. International Journal of Control, 1993, 58(6): 1247-1263
[10]	Levant A. Principles of 2-sliding mode design. Automatica, 2007, 43(4): 576-586
[11]	Levant A. Higher-order sliding modes, differentiation and output-feedback control. International Journal of Control, 2003, 76(9): 924-941
[12]	Chen Jie, Li Zhi-Ping, Zhang Guo-Zhu. Higher-order sliding-mode controller for a class of uncertain nonlinear systems. Control Theory and Applications, 2010, 27(5): 563-569 (陈杰, 李志平, 张国柱. 不确定非线性系统的高阶滑模控制器设计. 控制理论及应用, 2010, 27(5): 563-569)
[13]	Emelyanov S V, Korovin S K, Levantovskii L V. Higher-order sliding modes in binary control systems. Soviet Physics Doklady, 1986, 31(4): 291-293
[14]	Ma Ke-Mao. Design of higher order sliding mode attitude control laws for large-scale spacecraft. Control and Decision, 2013, 28(2): 201-204(马克茂. 大型空间飞行器的高阶滑模姿态控制律设计. 控制与决策, 2013, 28(2): 201-204)
[15]	Fan Jin-Suo, Zhang He-Xin, Zhang Ming-Kuan, Zhou Xin. Adaptive second-order terminal sliding mode control for aircraft re-entry attitude. Control and Decision, 2012, 27(3): 403-407 (范金锁, 张合新, 张明宽, 周鑫. 基于自适应二阶终端滑模的飞行器再入姿态控制. 控制与决策, 2012, 27(3): 403-407)
[16]	Shi Hong-Yu, Feng Yong. High-order terminal sliding mode flux observer for induction motors. Acta Automatica Sinica, 2012, 38(2): 288-294 (史宏宇, 冯勇. 感应电机高阶终端滑模磁链观测器的研究. 自动化学报, 2012, 38(2): 288-294)
[17]	Hu Yue-Ming, Chao Hong-Min, Li Zhi-Quan, Liang Tian-Pei. High-order sliding mode control of nonlinear affine control systems. Acta Automatica Sinica, 2002, 28(2): 284-289 (胡跃明, 晁红敏, 李志权, 梁天培. 非线性仿射控制系统的高阶滑模控制. 自动化学报, 2002, 28(2): 284-289)
[18]	Boiko I, Fridman L, Pisano A, Usai E. On the transfer properties of the generalized sub-optimal second-order sliding mode control algorithm. IEEE Transactions on Automatic Control, 2009, 54(2): 399-403
[19]	Shtessel Y B, Foreman D C, Tournes C H. Stability margins in traditional and second order sliding mode control. In: Proceedings of the 50th IEEE Conference on Decision and Control and Control Conference. Orlando, FL, USA: IEEE, 2011. 4604-4609
[20]	Pan Y D, Liu G J, Kumar K D. Robust stability analysis of asymptotic second-order sliding mode control system using Lyapunov function. In: Proceedings of the 2010 IEEE International Conference on Information and Automation. Harbin, Heilongjiang, China: IEEE, 2010. 313-318
[21]	Zong Q, Zhao Z S, Zhang J. Brief paper: higher order sliding mode control with self-tuning law based on integral sliding mode. IET Control Theory and Applications, 2010, 4(7): 1282-1289
[22]	Levant A, Michael A. Adjustment of high-order sliding-mode controllers. International Journal of Robust and Nonlinear Control, 2009, 19(15): 1657-1672
[23]	Bartolini G, Pisano A, Usai E. Global stabilization for nonlinear uncertain systems with unmodeled actuator dynamics. IEEE Transactions on Automatic Control, 2001, 46(11): 1826-1832
[24]	Qian C, Lin W. A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Transactions on Automatic Control, 2001, 46(7): 1061-1079
[25]	Ding S H, Li S H, Zheng W X. Nonsmooth stabilization of a class of nonlinear cascaded systems. Automatica, 2012, 48(10): 2597-2606
[26]	Qian C J, Lin W. Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Systems and Control Letters, 2001, 42(3): 185-200
[27]	Bhat S P, Bernstein D S. Finite-time stability of continuous autonomous systems. SIAM Journal on Control and Optimization, 2000, 38(3): 751-766
[28]	Wang X D. Research on Fuzzy Control Algorithm Based on Inverted Pendulum System [Master dissertation], Xidian University, China, 2012.(王旭东. 基于倒立摆系统的模糊控制算法研究[硕士学位论文]. 西安电子科技大学. 中国, 2012.)
[29]	Pei Y L. Inverted Pendulum System Stability Control Algorithm Research [Master dissertation], Chongqing University, China, 2012.(裴月琳. 倒立摆系统稳摆控制算法研究[硕士学位论文].重庆大学. 2012.)
[30]	Moreno J A, Osorio M. A Lyapunov approach to second-order sliding mode controllers and observers. In: Proceedings of the 47th IEEE Conference on Decision and Control. Cancun, Mexico: IEEE, 2008. 2856-2861

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一类新的二阶滑模控制方法及其在倒立摆控制中的应用

doi: 10.16383/j.aas.2015.c140263 cstr: 32138.14.j.aas.2015.c140263

作者简介:
李雪冰江苏大学电气信息工程学院硕士研究生.主要研究方向为滑模变结构控制理论.E-mail:lxb121619@163.com

通讯作者:
丁世宏江苏大学电气信息工程学院副教授.主要研究主向为非线性系统,高阶滑模控制,DC-DC控制.本文通信作者.E-mail:dsh@ujs.edu.cn

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A New Second-order Sliding Mode Control and Its Application to Inverted Pendulum

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留言板

一类新的二阶滑模控制方法及其在倒立摆控制中的应用

doi: 10.16383/j.aas.2015.c140263 cstr: 32138.14.j.aas.2015.c140263

作者简介: 李雪冰 江苏大学电气信息工程学院硕士研究生.主要研究方向为滑模变结构控制理论.E-mail:lxb121619@163.com

通讯作者: 丁世宏 江苏大学电气信息工程学院副教授.主要研究主向为非线性系统,高阶滑模控制,DC-DC控制.本文通信作者.E-mail:dsh@ujs.edu.cn

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出版历程

A New Second-order Sliding Mode Control and Its Application to Inverted Pendulum

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出版历程

目录

作者简介:
李雪冰江苏大学电气信息工程学院硕士研究生.主要研究方向为滑模变结构控制理论.E-mail:lxb121619@163.com

通讯作者:
丁世宏江苏大学电气信息工程学院副教授.主要研究主向为非线性系统,高阶滑模控制,DC-DC控制.本文通信作者.E-mail:dsh@ujs.edu.cn