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一类MIMO系统连续状态空间模型的参数辨识频域方法

鲁兴举 郑志强

鲁兴举, 郑志强. 一类MIMO系统连续状态空间模型的参数辨识频域方法. 自动化学报, 2016, 42(1): 145-153. doi: 10.16383/j.aas.2016.c150150
引用本文: 鲁兴举, 郑志强. 一类MIMO系统连续状态空间模型的参数辨识频域方法. 自动化学报, 2016, 42(1): 145-153. doi: 10.16383/j.aas.2016.c150150
LU Xing-Ju, ZHENG Zhi-Qiang. Identification of Continuous State-space Model Parameters for a Class of MIMO Systems:A Frequency Domain Approach. ACTA AUTOMATICA SINICA, 2016, 42(1): 145-153. doi: 10.16383/j.aas.2016.c150150
Citation: LU Xing-Ju, ZHENG Zhi-Qiang. Identification of Continuous State-space Model Parameters for a Class of MIMO Systems:A Frequency Domain Approach. ACTA AUTOMATICA SINICA, 2016, 42(1): 145-153. doi: 10.16383/j.aas.2016.c150150

一类MIMO系统连续状态空间模型的参数辨识频域方法

doi: 10.16383/j.aas.2016.c150150
基金项目: 

国家自然科学基金 61203095, 61403407

详细信息
    作者简介:

    鲁兴举 国防科技大学机电工程与自动化学院博士研究生.主要研究方向为飞行器制导与控制.E-mail:luxingju@163.com

    通讯作者:

    郑志强 国防科技大学机电工程与自动化学院教授.主要研究方向为飞行器制导与控制,机器人控制.本文通信作者.E-mail:zqzheng@nudt.edu.cn

Identification of Continuous State-space Model Parameters for a Class of MIMO Systems:A Frequency Domain Approach

Funds: 

National Natural Science Foundation of China 61203095, 61403407

More Information
    Author Bio:

    Ph. D. candidate at the College of Mechatronic Engineering and Automation, National University of Defense Technology. His research interest covers aircraft guidance and control

    Corresponding author: ZHENG Zhi-Qiang Professor at the College of Mechatronic Engineering and Automation, National University of Defense Technology. His research interest covers aircraft guidance and control, and robot control. Corresponding author of this paper
  • 摘要: 在连续时间状态空间模型的参数辨识中,针对系统状态微分项获取困难这一问题,对输入、状态及输出序列应用离散傅里叶变换,得到复数域线性回归方程,并给出了不同形式的最小二乘解估计式.以飞行器多输入多输出(Multiple-input multiple-output, MIMO)状态空间模型为例,设计正交多正弦信号对系统进行多通道同时激励,在一次激励的情况下就可以辨识出所有模型参数,从而提高辨识实验效率.仿真实验证明了方法的有效性和结果的准确性.
  • 图  1  正交多正弦信号频谱分布

    Fig.  1  Spectral distribution of orthogonal multi-sine signals

    图  2  正交多正弦信号的时间历程(采样点数= 1000)

    Fig.  2  Plots of orthogonal multi-sine signals (Samples =1000)

    图  3  F-16飞机纵向通道输入及响应时间历程

    Fig.  3  Plots of input and response of F-16 aircraft longitudinal channel

    图  4  系统输入及状态变量的DFT曲线

    Fig.  4  DFT plots of system input and states

    图  5  单输入系统参数辨识结果的误差及其置信区间

    Fig.  5  Error and confidence interval of identification results for a single-input system

    图  6  频域最小二乘算法计算时间

    Fig.  6  Time consumption of frequency domain least-squares algorithm

    图  7  Multi-sine多输入激励及系统响应

    Fig.  7  Multiple multi-sine inputs and system response

    图  8  3-2-1-1多输入激励及系统响应

    Fig.  8  Multiple 3-2-1-1 inputs and system response

    图  9  MIMO 系统参数辨识结果的误差及置信区间

    Fig.  9  Error and con¯dence interval of identi¯cation results for a MIMO system

    表  1  不同频域最小二乘算法的结果比较

    Table  1  Comparison of results with different frequency domain least-square algorithms

    LS algorithm ${\hat{A}_{{\text{lon}}}}$ $\hat{B}_{{\rm{lon}}}$
    LS_Re -0.0161 -3.8292 -1.0548 -32.0137 10.1047
    -0.0003 -0.7514 0.9272 -0.0020 -0.1613
    -0.0004 -4.1575 -1.3190 -0.1572 -14.1069
    0.0009 -0.0693 1.0046 0.0579 0.0139
    LS_Im -0.0175 -3.7048 -1.0633 -32.1205 10.0944
    -0.0002 -0.7543 0.9274 0.0005 -0.1609
    0.0026 -4.3783 -1.3070 0.0307 -14.0746
    0.0019 -0.1118 1.0048 0.0929 0.0298
    LS_EAM -0.0165 -3.7773 -1.0591 -32.0588 10.1050
    -0.0002 -0.7523 0.9273 -0.0012 -0.1613
    0.0002 -4.2252 -1.3142 -0.0985 -14.1047
    0.0010 -0.0655 1.0036 0.0544 0.0161
    下载: 导出CSV
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出版历程
  • 收稿日期:  2015-03-31
  • 录用日期:  2015-09-06
  • 刊出日期:  2016-01-01

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