分布参数系统源控制系统设计

周笔锋; 罗毅平; 唐果宁

doi:10.16383/j.aas.c190612

分布参数系统源控制系统设计

doi: 10.16383/j.aas.c190612

周笔锋^{1, 2,},
罗毅平^3,,
唐果宁^1,

1.
湖南科技大学机电工程学院湘潭 411101
2.
湖南电气职业技术学院湘潭 411101
3.
湖南工程学院电气信息学院湘潭 411101

基金项目: 国家自然科学基金(11972156), 湖南省教育厅科学研究项目(19C0418)资助

详细信息

作者简介:
周笔锋：湖南科技大学博士研究生. 2015年获得湖南工程学院硕士学位. 主要研究方向为复杂网络系统, 分布参数系统, 永磁同步电机退磁振动. E-mail: zhoubifeng99@163.com

罗毅平：湖南工程学院教授. 2006年获得华南理工大学博士学位. 主要研究方向为神经网络, 模式识别, 复杂网络系统, 分布参数系统. 本文通信作者.E-mail: lyp8688@sohu.com

唐果宁：湖南科技大学教授. 主要研究方向为永磁同步电机退磁振动, 超细振动磨机研究.E-mail: tangguoning99@163.com

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出版历程
- 收稿日期: 2019-09-02
- 录用日期: 2019-12-23
- 网络出版日期: 2020-01-02
- 刊出日期: 2022-12-23

Distributed Parameter Systems of Source Control

1.
School of Mechanical Engineering, Hunan University of Science and Technology, Xiangtan 411101
2.
Hunan Electrical College of Technology, Xiangtan 411101
3.
College of Electrical Information, Hunan Institute of Engineering, Xiangtan 411101

Funds: Supported by National Natural Science Foundation of China (11972156) and Science Research Projects of Hunan Province Educa-tion Department (19C0418)

More Information

Author Bio:
ZHOU Bi-Feng　Ph.D. candidate at Hunan Univer-sity of Science and Technology. He received his master degree in power engineering from Hunan Institute of Engineering in 2015. His research interest covers complex networks, distributed parameter systems, and demagnetization vibration of PMSM

LUO Yi-Ping　Professor at Hunan Institute of Engin-eering. He received his Ph.D. degree from South China University of Technology. His research interest covers neural network, pattern recognition, complex network, and distributed parameter systems. Corresponding author of this paper

TANG Guo-Ning　Professor at Hunan University of Science and Technology. His research interest covers demagnetization vibration of PMSM and ultra-fine vibration mill

摘要

摘要: 针对一类分布参数系统(Distributed parameter system, DPS), 提出了源控制方法. 将构成分布参数系统的空间分成若干分, 每份为一个节点, 在所有的节点中, 将能产生量变源头的节点定义为源节点, 跟随源节点变化的节点为跟随节点, 以此构建分布参数系统模型. 对于源节点, 根据经验函数结合反馈偏差调节设计控制器, 对跟随节点考虑源节点控制的逸散作用控制. 利用Lyapunov稳定性理论并结合线性矩阵不等式(Linear matrix inequality, LMI)处理方法, 得出了分布式参数系统稳定源控制器存在的充分条件. 最后结合所给条件, 给出一个数值仿真说明其有效性.
- 分布参数系统 /
- 源控制 /
- Lyapunov /
- 线性矩阵不等式
Abstract: The stability problem of distributed parameter systems (DPSs) is investigated. For this purpose, a source controller is developed for such a system. The space is divided into several parts, and each part is considered a node. The source of the node that produces quantitative changes is defined as the source node. The nodes that follow the change of source nodes are defined as the subsequent nodes. On the basis of these definitions, the distributed parameter system model is constructed. The designed controller for the source nodes is the empirical function combined with the feedback adjustment and that for the subsequent nodes considers the diffusion control action of the source nodes. Numerous sufficient conditions with stable source controller for distributed parameter systems are derived using Lyapunovs stability theory and the method of linear matrix inequality (LMI). A numerical simulation illustrates the effectiveness of the method under given conditions.
- Distributed parameter systems (DPSs) /
- source control /
- Lyapunov /
- linear matrix inequality (LMI)

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图 1 系统源节点$W_{L}(x,t)$状态图

Fig. 1 The system state of source nodes $W_{L}(x,t)$

下载: 全尺寸图片幻灯片

图 2 系统跟随节点$W_{g}(x,t)$状态图

Fig. 2 The system state of following nodes $W_{g}(x,t)$

下载: 全尺寸图片幻灯片

参考文献(19)

[1]	Ray W H. Advanced Process Control. New York: McGraw-Hill, 1981.
[2]	Christofides P D. Nonlinear and Robust Control of PDE Systems. Boston: Birkhauser Boston, 2001.
[3]	Deng H, Li H X, Chen G R. Spectral approximation based intelligent modeling for distributed thermal processes[J]. IEEE Transactions on Control Systems Technology, 2005, 13:686-700. doi: 10.1109/TCST.2005.847329
[4]	Padhi R, Ali S F. An account of chronological developments in control of distributed parameter systems[J]. Annual Reviews in Control, 2009, 33:59-68. doi: 10.1016/j.arcontrol.2009.01.003
[5]	Baillieul J. Linearized models for the control of rotating beams. In: Proceedings of the 27th IEEE Conference on Decision and Control. Austim, TX, USA: IEEE, 1988: 1726−1731
[6]	Najar F, Choura S, Abdelrahman E M, et al. Dynamic analysis of variable-geometry electrostatic microactuators[J]. Journal of Micromechanics Microengineering, 2006, 16:2449-2457. doi: 10.1088/0960-1317/16/11/028
[7]	Ly C, Doiron B. Correction: Divisive Gain Modulation with Dynamic Stimuli in Integrate-and-Fire Neurons[J]. Plos Computational Biology, 2009, 5(4):e1000365. doi: 10.1371/journal.pcbi.1000365
[8]	Lan Y H, Wu B, Shi Y X, et al. Iterative learning based consensus control for distributed parameter multi-agent systems with time-delay. Neurocomputing, 2019, 357(10): 77-85.
[9]	Lan Y H, Xia J J, Xia Y P, et al. Iterative learning consensus control for multi-agent systems with fractional order distributed parameter models. Int. J. Control Autom. Syst, 2019, 17(4): 1-11.
[10]	Luo Y P, Xia W H, Liu G R, et al. LMI Approach to Exponential Stabilization of Distributed Parameter Control Systems with Delay[J]. Acta Automatica Sinica, 2009, 35:299-304.
[11]	Ji H H, Cui B T, LiuX Z. Adaptive control of Markov jump distributed parameter systems via model reference[J]. Fuzzy Sets and Systems, 2019.https://doi.org/10.1016/j.fss.2019.06.016 doi: 10.1016/j.fss.2019.06.016
[12]	Wang Z P, Wu H N. Finite dimensional guaranteed cost sampled-data fuzzy control for a class of nonlinear distributed parameter systems[J]. Information Sciences An International Journal, 2016, 327:21-39. doi: 10.1016/j.ins.2015.08.009
[13]	Zhang X M, Wu H N. H∞ boundary control for a class of nonlinear stochastic parabolic distributed parameter systems[J]. International Journal of Robust and Nonlinear Control, 2019, 29(14):4665-4680. doi: 10.1002/rnc.4646
[14]	周延九, 崔宝同. 一类半线性抛物型偏微分方程描述的分布参数系统的边界控制. 控制与决策, 2019, 34(12): 2594−2602 Zhou Yan-Jiu, Cui Bao-Tong. Boundary control of the distributed parameter systems described by a class of semi-linear parabolic partial differential equations. Control and Decision, 2019, 34(12): 2594−2602
[15]	Wang J W, Wu H N, Sun C Y. Local exponential stabilization via boundary feedback controllers for a class of unstable semi-linear parabolic distributed parameter processes[J]. Journal of the Franklin Institute, 2017, 354(13): 5221-5244. doi: 10.1016/j.jfranklin.2017.05.044
[16]	栗小丽, 李凯, 刘飞. 双曲线型分布参数系统边界控制下的干扰解耦[J]. 控制与决策, 2016, 31(2): 256-260. Luan X L, Li K, Liu F. Disturbance decoupling for hyperbolic-type distributed parameter systems with boundary control[J]. Control and Decision, 2016, 31(2):256-260.
[17]	周笔锋, 罗毅平. 时滞分布参数系统中和控制器设计[J]. 自动化学报, 2018, 44(12):2222-2227. Zhou B F, Luo Y P. Distributed parameter systems of neutralization control with delay[J]. Acta Automatica Sinica, 2018, 44(12):2222-2227.
[18]	催宝同, 楼旭阳. 时滞分布参数系统理论及其应用. 北京: 国防工业出版社, 2009. 8−12 Cui Bao-Tong, Lou Xu-Yang. Theory and Application of Time-delay Distributed Parameter System. Beijing: National Defense Industry press, 2009. 8−12
[19]	Song Q, Cao J. On pinning synchronization of directed and undirected complex dynamical networks[J]. IEEE Transactions on Circuits Systems Part I Regular Papers, 2010, 57:672-680. doi: 10.1109/TCSI.2009.2024971