抑制POGO振动的滑模控制及其多项式系数方法
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- 英文论文题名：A Polynomial Coefficients Method on Sliding-mode Control for POGO Vibration Suppression
- 论文作者：吕宁 ; 郝盛强 ; 刘佳琦 ; 高晓智
- 英文论文作者：Ning Lyu ; Shengqiang Hao ; Jiaqi Liu ; Xiaozhi Gao ; School of Automation ; Harbin University of Science and Technology ; Department of Electrical Engineering and Automation ; Aalto University
- 年：2017
- 作者机构：哈尔滨理工大学自动化学院;芬兰Aalto大学电子工程与自动化系;
- 论文关键词：POGO振动 ; 滑模控制 ; 控制系统降阶 ; 特征多项式
- 英文论文关键词：POGO Vibration ; Sliding-mode Control ; Control System Reduction ; Characteristic Polynomials
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：中文
- 分类号：V249.1
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：298k
- 原文格式：D
- 会议级别：全国
摘要
充液飞行器的POGO振动是一种挠性机体弹性振动和控制力矩脉动耦合作用而产生的闭环不稳定现象,在飞行器姿态控制任务中需要特别关注。本文设计一类基于姿态四元数信息的自适应滑模控制方法,不同于大多数的控制方法仅保证全局渐进稳定性,本文通过构造Lyapunov函数并将其用于有限时间收敛的姿态跟踪控制器设计中。为了降低滑模控制器的设计难度,对具有POGO振动飞行器的高维数控制系统进行降阶,由于秩约束使得控制系统设计成为一类非凸优化问题,进而导致数值算法难以应用,并且降阶控制系统性能也无法保证。为此本文通过把控制系统秩约束转变为特征多项式系数的形式并设计出一种选频保结构降阶方法,通过构造Gram矩阵实现降阶控制系统在POGO振动特定频率内逼近原始系统。最后将该方法用于具有POGO振动的飞行器姿态控制任务,验证基于所提方法设计的降阶控制系统的有限时间稳定跟踪性能。
The POGO vibration in the liquid-filled aircraft is taken for coupling effect of elastic vibration and pulsing control torque that might affects the closed-loop instability, which should be paid attention on the attitude controller design. An adaptive sliding mode control strategy is designed based on the attitude quaternion. Furthermore, a proper Lyapunov function is constructed and then the controller can realize the attitude tracking error to zero with finite time convergence. A polynomial coefficient method for solving optimization problem of unmanageably large demands on computational resources is considered which that rank constraints are rewritten into a characteristic polynomial equation of the elements. By constructing block matrix of controllable and observable Gram functions, the reduction control system has the ability to maintain second-order structure and closely approximates the original system in the specified frequency range. Finally, the numerical simulations illustrate that the proposed low order finite-time control system can suppress the POGO vibration and keep the aircraft high pointing precision.
The POGO vibration in the liquid-filled aircraft is taken for coupling effect of elastic vibration and pulsing control torque that might affects the closed-loop instability, which should be paid attention on the attitude controller design. An adaptive sliding mode control strategy is designed based on the attitude quaternion. Furthermore, a proper Lyapunov function is constructed and then the controller can realize the attitude tracking error to zero with finite time convergence. A polynomial coefficient method for solving optimization problem of unmanageably large demands on computational resources is considered which that rank constraints are rewritten into a characteristic polynomial equation of the elements. By constructing block matrix of controllable and observable Gram functions, the reduction control system has the ability to maintain second-order structure and closely approximates the original system in the specified frequency range. Finally, the numerical simulations illustrate that the proposed low order finite-time control system can suppress the POGO vibration and keep the aircraft high pointing precision.
引文
[1]赵治华.液体火箭POGO振动的多体动力学建模及稳定性分析.北京:清华大学博士学位论文,2011.
[2]B.W.Oppenheim,S.Rubin.Advanced POGO Stability Analysis for Liquid Rockets.Journal of Spacecraft and Rockets,30(3):360-373,1993.
[3]Y.Feng,F.Han,X.Yu.Chattering free full-order sliding-mode control,Automatica,50(4):1310-1314,2014.
[4]S.Gugercin.An iterative SVD-Krylov based method for model reduction of large-scale dynamical systems.Linear Algebra and its Applications,428(8-9):1964-1986,2008.
[5]P.Apkarian,D.Noll.Nonsmooth H_∞synthesis.IEEE Trans,on Automatic Control,51(1):71-86,2006.
[6]P.Apkarian P,D.Noll.Controller design via nonsmooth multidirectional search.SIAM Journal on Control and Optimization.44(6):1923-1949,2006.
[7]孟占峰,韩潮.柔性空间结构选频二阶保结构平衡降阶.航空学报,32(3):410-420,2011.
[8]W.Gawronski,J.Juang.Grammians and model reduction in limited time and frequency intervals.Guidance,Navigation and Control Conference Minneapolis,MN,USA.2013:275-280.
[9]W.Gawronski,J.Juang.Model Reduction for Flexible Structures.Journal of Guidance Control&Dynamics,36(1):143-222,2015.
[10]D.Ankelhed,A.Helmersson,A.Hansson.A partially augmented lagrangian method for low order H-Infinity controller synthesis using rational constraints.IEEE Trans.on Automatic Control,57(11):2901-2905,2012.
[11]胡鹏翔.液体火箭的多体动力学建模与仿真研究.北京:清华大学博士学位论文,2013.
[12]梅生伟,申铁龙,刘康志.现代鲁棒控制理论与应用(2版).北京:清华大学出版社,2008.
[13]Cheng Y,Dai S L,Ren G X.A hybrid finite segment/finite element modeling and experiment on a flexible deployment system.Journal of Sound and Vibration,258(5):931-949,2002.
[14]丁世宏,李世华.有限时间控制问题综述.控制与决策,26(2):161-169,2011.
[15]耿洁,吕楠,王韬,宫经刚.航天器的有限时间时变滑模姿态控制方法设计.空间控制技术与应用,42(4):30-35,2016.
[16]康宇,奚宏生,季海波.有限时间快速收敛滑模变结构控制.控制理论与应用,21(4):623-626,2004.
[17]李家文.大型捆绑火箭姿态控制系统的建模、设计与分析.长沙:国防科学技术大学博士学位论文,2011.
[2]B.W.Oppenheim,S.Rubin.Advanced POGO Stability Analysis for Liquid Rockets.Journal of Spacecraft and Rockets,30(3):360-373,1993.
[3]Y.Feng,F.Han,X.Yu.Chattering free full-order sliding-mode control,Automatica,50(4):1310-1314,2014.
[4]S.Gugercin.An iterative SVD-Krylov based method for model reduction of large-scale dynamical systems.Linear Algebra and its Applications,428(8-9):1964-1986,2008.
[5]P.Apkarian,D.Noll.Nonsmooth H_∞synthesis.IEEE Trans,on Automatic Control,51(1):71-86,2006.
[6]P.Apkarian P,D.Noll.Controller design via nonsmooth multidirectional search.SIAM Journal on Control and Optimization.44(6):1923-1949,2006.
[7]孟占峰,韩潮.柔性空间结构选频二阶保结构平衡降阶.航空学报,32(3):410-420,2011.
[8]W.Gawronski,J.Juang.Grammians and model reduction in limited time and frequency intervals.Guidance,Navigation and Control Conference Minneapolis,MN,USA.2013:275-280.
[9]W.Gawronski,J.Juang.Model Reduction for Flexible Structures.Journal of Guidance Control&Dynamics,36(1):143-222,2015.
[10]D.Ankelhed,A.Helmersson,A.Hansson.A partially augmented lagrangian method for low order H-Infinity controller synthesis using rational constraints.IEEE Trans.on Automatic Control,57(11):2901-2905,2012.
[11]胡鹏翔.液体火箭的多体动力学建模与仿真研究.北京:清华大学博士学位论文,2013.
[12]梅生伟,申铁龙,刘康志.现代鲁棒控制理论与应用(2版).北京:清华大学出版社,2008.
[13]Cheng Y,Dai S L,Ren G X.A hybrid finite segment/finite element modeling and experiment on a flexible deployment system.Journal of Sound and Vibration,258(5):931-949,2002.
[14]丁世宏,李世华.有限时间控制问题综述.控制与决策,26(2):161-169,2011.
[15]耿洁,吕楠,王韬,宫经刚.航天器的有限时间时变滑模姿态控制方法设计.空间控制技术与应用,42(4):30-35,2016.
[16]康宇,奚宏生,季海波.有限时间快速收敛滑模变结构控制.控制理论与应用,21(4):623-626,2004.
[17]李家文.大型捆绑火箭姿态控制系统的建模、设计与分析.长沙:国防科学技术大学博士学位论文,2011.
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