| 离散变结构控制系统的二阶趋近律方法 |
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| 引用本文： | 刘珑龙,崔静,马明姣.离散变结构控制系统的二阶趋近律方法[J].中国海洋大学学报(自然科学版),2020,50(7):153-158. |
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| 作者姓名： | 刘珑龙 崔静 马明姣 |
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| 作者单位： | 中国海洋大学数学科学学院,山东 青岛 266100;中国海洋大学数学科学学院,山东 青岛 266100;中国海洋大学数学科学学院,山东 青岛 266100 |
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| 基金项目： | 山东省自然科学基金项目 |
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| 摘 要： | 本文研究了应用于离散变结构控制系统的一种新的趋近律方法,即一个二阶递推的趋近律方法。利用新趋近律方法设计了一个和当前时刻相关的前两个样本点的递推二阶控制器;基于Lyapunov函数法,利用提出的二阶趋近律方法证明了离散变结构控制系统的渐近稳定性和滑模的有限时间可达性;说明了此方法在不确定离散变结构控制系统中的稳定性研究中的可行性。新方法可大幅度消弱抖振,使系统运动最终趋于原点,还能使系统的准滑动模态保持步步穿越切换面,较好的改善了趋近过程。
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| 关 键 词： | 离散系统 变结构控制 趋近律方法 LYAPUNOV稳定性 |
Two Order Approach Law for Discrete Variable Structure Control Systems |
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| LIU Long-Long,CUI Jing,MA Ming-Jiao.Two Order Approach Law for Discrete Variable Structure Control Systems[J].Periodical of Ocean University of China,2020,50(7):153-158. |
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| Authors: | LIU Long-Long CUI Jing MA Ming-Jiao |
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| Institution: | (School of Mathematical Science,Ocean University of China, Qingdao 266100, China) |
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| Abstract: | In this paper,a new approach law was applied to discrete variable structure control systems,which was a two order recursive approach law.The new approach law was applied to find a recursive two order controller for the first two sample points associated with the current moment.Lyapunov Stability Theory was used in this study.The validity of this method in discrete variable structure control system was proved theoretically,and the theoretical feasibility of this method in uncertain discrete variable structure control system was further illustrated.Then,the system′s state motion tended to the origin,and the quasi sliding mode of the system kept moving through the basic attributes of the switching surface,and the approach process was improved.We used the new two order reaching law proposed in the discrete variable structure control system to find the variable structure controller,and got a recursive two order controller with the two time points related to the current time.The control input had good continuity,good continuous performance and better reflected the smoothness of the sliding mode function,the reaching law method could make the motion state of discrete time system asymptotically stable at the origin,which could last,back and forth cross the switching surface,rapidly approach the origin,and quickly eliminat chattering.In this paper,the two order reaching law method was further analyzed,especially for the two order reaching law,and the theoretical feasibility of the method in uncertain discrete variable structure control system was proved. |
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| Keywords: | discrete system variable structure control approach law method Lyapunov stability theory |
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