内模控制中的虚拟参考反馈校正设计

王建宏

系统科学与数学 ›› 2017, Vol. 37 ›› Issue (2) : 355-369.

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系统科学与数学 ›› 2017, Vol. 37 ›› Issue (2) : 355-369. DOI: 10.12341/jssms13068
论文

内模控制中的虚拟参考反馈校正设计

    王建宏
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Virtual Reference Feedback Tuning Design in Internal Model Control

    WANG Jianhong
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摘要

针对内模控制中的真实模型、辨识模型和内模控制器同时出现, 因传统内模控制器的设 计紧紧依赖于真实模型和辨识模型, 从而使得内模控制器设计过程较复杂. 为规避真实模型的建模, 使辨识模型的建模与内模控制器设计可同步实现, 文章将虚拟参考反馈校正思想应用于内模控制中. 虚拟参考反馈校正思想可将辨识模型和内模控制器的求解转化为参数辨识过程. 为建立虚拟参考反馈校正思想与传统自适应控制方法间的等价性, 推导出对输入-输出观测数据作预滤波处理的滤波器. 为衡量内模控制中两类未知参数的辨识精度, 采用渐近性理论推导两类未知参数矢量的渐近方差矩阵式. 以此渐近方差矩阵式的迹运算作为目标函数, 以输入观测数据的功率谱密度作为优化决策变量, 利用初等代数运算求解出内模控制中的最优输入功率谱. 最后用仿真算例验证本文辨识方法的有效性.

Abstract

Because there are three models appear in the internal model control structure which includes the true model, identified model and internal model controller. So the classical internal model controller depends on the true model and identified model. To avoid the process of identifying the true model, we apply the idea of virtual reference feedback tuning into the internal model control in order to identify the identified model and internal model controller simultaneously. The idea of virtual reference feedback tuning formulates the problem into a process of identifying two classes of unknown parameter vectors. To establish the equivalence between the virtual reference feedback tuning and the classical adaptive control, the filter used to filter the input-output observed data is derived. The asymptotic theory is proposed to derive the asymptotic covariance matrices of those two classes of unknown parameter vectors so that the identified accuracy can be evaluated. Then this trace operation of the asymptotic covariance matrices is regarded as the objective function and the optimization decision variable is chosen as the power spectrum of the input signal. The optimal input spectrum in the internal model control structure can be obtained by using some elementary algebra. Finally, the efficiency and possibility of the proposed strategy can be confirmed by the simulation example results.

关键词

内模控制 / 虚拟参考反馈校正 / 滤波器 / 渐近性 / 最优功率谱.

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王建宏. 内模控制中的虚拟参考反馈校正设计. 系统科学与数学, 2017, 37(2): 355-369. https://doi.org/10.12341/jssms13068
WANG Jianhong. Virtual Reference Feedback Tuning Design in Internal Model Control. Journal of Systems Science and Mathematical Sciences, 2017, 37(2): 355-369 https://doi.org/10.12341/jssms13068
中图分类号: 93C40   
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