多边时滞脉冲反馈方法控制SAS的混沌与降低损失率
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摘要
开关时间为0的开关到达系统(SAS)经常用于模拟研究工业控制系统。为更接近工业生产实际,将开关时间改为大于0。这样不仅使系统产生混沌现象,而且产生损失。为此,首先介绍开关到达系统的数学模型及开关时间,说明当开关时间大于0时系统产生损失的原因,接着利用庞加莱截面(PS)定义周期轨道。选定1-周期轨为控制目标,利用无需预先获取目标周期轨道具体位置的多边时滞脉冲反馈控制(M-SDIFC)方法,并针对开关时间大于0的情况加以改变。数值模拟比较有无实施控制情况下的系统轨迹和损失率,以及开关时间是否存在情况下周期轨道的探测。改进方法不仅能控制混沌现象,还能降低系统损失率,同时还能探测周期轨道具体位置。
The switched arrival system(SAS) featuring switched time of 0 is often used to simulate industrial control systems.In order to be closer to industrial production,the switched time is changed to be greater than 0.Thus,the system not only produces chaos but also brings loss.Therefor, first the mathematical model and the switched time of switched arrival system are introduced; and the causes of the loss of the system when the switched time is greater than 0 are explained; then the period orbit is defined by using the Poincare section(PS).The period-1 orbit is selected as control target.the multi-sided delayed impulsive feedback control(M-SDIFC) is adopted for switched time greater than 0,which does not need pre-acquisition of the specific location of the target period orbit.The system track and loss rate with or without control,and the detection of period orbit with or without switched time are compared by numerical simulation.The improved method not only controls chaos,but also reduces the system loss rate,while detecting the specific position of the period orbit.
The switched arrival system(SAS) featuring switched time of 0 is often used to simulate industrial control systems.In order to be closer to industrial production,the switched time is changed to be greater than 0.Thus,the system not only produces chaos but also brings loss.Therefor, first the mathematical model and the switched time of switched arrival system are introduced; and the causes of the loss of the system when the switched time is greater than 0 are explained; then the period orbit is defined by using the Poincare section(PS).The period-1 orbit is selected as control target.the multi-sided delayed impulsive feedback control(M-SDIFC) is adopted for switched time greater than 0,which does not need pre-acquisition of the specific location of the target period orbit.The system track and loss rate with or without control,and the detection of period orbit with or without switched time are compared by numerical simulation.The improved method not only controls chaos,but also reduces the system loss rate,while detecting the specific position of the period orbit.
引文
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[2] TIAN Y P.Delayed feedback control of chaos in a switched arrival system[J].Physics Letters A,2005,339(6):446- 454.
[3] 刘玉良,姚齐国.非线性动力学系统的混沌控制与反控制[M].上海:上海交通大学出社,2013.
[4] TIAN Y P.Detecting unstable period orbit in switched arrival system[J].Proceedings of the 42nd IEEE Conference on Decision and Control,2003(11):1884- 1888.
[5] 陈明,李威.多边时滞脉冲反馈方法控制开关到达系统的混沌[J].北京化工大学学报,2008,35(6):102- 106.
[6] LUAN B L,KONISHI K,HARA N.Design and experimental verification of multiple delay feedback control for time- delay nonlinear oscillators[J].Nonlinear Dynamics,2012(2):1407- 1418.
[7] 李宁,袁惠群,孙海义,等.一类离散混沌系统的脉冲时滞反馈控制[J].控制与决策,2014,29(8):1527- 1531.
[8] 张恩培,李星,吴呈良,等.具有连续时滞的反馈控制合作系统的持久性[J].沈阳大学学报,2016,28(5):425- 428.
[9] 何梅丽.混沌时滞系统控制的算法研究[D].天津:天津工业大学,2018.
[10]吕晓晓,曹进德.脉冲控制系统理论进展综述[J].山东师范大学学报(自然科学版),2018,33(1):1- 11.
[11]梁志清,曾夏萍,周泽文,等.状态反馈脉冲控制Holling- Tanner系统周期解的存在性[J].数学物理学报,2018,38(1):174- 189.
[12]蒋亮亮,江虹,曾闵.基于混沌Duffing振子的BPSK信号均方值解调方法[J].自动化仪表,2018,39(2):45- 49.
[13]杨乐.分散控制系统信息安全方案探讨[J].石油化工自动化,2017,53(3):1- 4.