北京航空航天大学学报 ›› 2016, Vol. 42 ›› Issue (7): 1536-1542.doi: 10.13700/j.bh.1001-5965.2015.0486

• 论文 • 上一篇    下一篇

基于高阶奇异值分解的LPV鲁棒控制器设计

孙斌, 杨凌宇, 张晶   

  1. 北京航空航天大学 自动化科学与电气工程学院, 北京 100083
  • 收稿日期:2015-07-20 出版日期:2016-07-20 发布日期:2016-07-29
  • 通讯作者: 杨凌宇,Tel.: 010-82316873 E-mail: yanglingyu@buaa.edu.cn E-mail:yanglingyu@buaa.edu.cn
  • 作者简介:孙斌 男,硕士研究生。主要研究方向:先进飞行器控制。E-mail: sun1990bin@qq.com Tel.: 010-82316873;杨凌宇 男,博士,副教授,硕士生导师。主要研究方向:先进飞行器控制,容错控制,先进布局飞机多操纵控制方法。E-mail: yanglingyu@buaa.edu.cn Tel.: 010-82316873
  • 基金资助:
    国家自然科学基金(61273099);航空科学基金(20135851041)

Robust LPV control design based on HOSVD

SUN Bin, YANG Lingyu, ZHANG Jing   

  1. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
  • Received:2015-07-20 Online:2016-07-20 Published:2016-07-29

摘要: 针对高超声速飞行器线性变参数(LPV)模型建模中准确度与复杂度之间的矛盾性,提出了一种基于网格化张量及高阶奇异值分解(HOSVD)的凸多胞LPV模型建模及控制方法。首先基于雅可比线性化给出了大包线网格化模型的张量描述形式,然后提出了一种基于HOSVD的多胞LPV模型生成算法,将网格化模型表述为有限个线性时不变(LTI)顶点及权重函数的组合,并基于舍弃的奇异值给出了建模误差的指标,最后结合某航天飞机再入段六自由度非线性模型进行了大包线鲁棒LPV控制器设计与仿真验证,结果表明该方法可获得计算复杂度低且保证建模精度的LPV模型,设计的鲁棒变增益控制器能够使系统快速跟踪姿态角指令信号,并能够保证系统的稳定性和鲁棒性。

关键词: 高超声速飞行器, 飞行包线, 多胞线性变参数(LPV)系统, 鲁棒变增益控制, 高阶奇异值分解(HOSVD)

Abstract: Considering the trade-off between the accuracy and complexity of the linear parameter varying (LPV) modeling of hypersonic vehicles, a novel polytopic LPV modelling technique based on grid tensors and higher-order singular value decomposition (HOSVD) was developed. Firstly, through Jacobian linearization, the grid tensor description of a hypersonic vehicle with large flight envelopes was introduced, and a polytopic LPV model was constructed using HOSVD. The resulting model was described by a linear combination of vertices of linear time invariant (LTI) models and corresponding weighting functions. The discarded singular values were treated as a modeling error index. A robust variable gain controller which combines a robust controller and gain scheduling technique was then designed for the 6 degree-of-freedom nonlinear model of the hypersonic vehicle. Simulation results demonstrate that the proposed method not only reduces the computational complexity, but also guarantees the modeling accuracy. Furthermore, under the proposed controller, the closed loop system can track the attitude commands rapidly, and good stability and robustness are achieved.

Key words: hypersonic vehicle, flight envelope, polytopic linear parameter varying (LPV) system, robust variable gain control, higher-order singular value decomposition (HOSVD)

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