Systems Science & Control Engineering (Jan 2020)

Statistical accuracy analysis for virtual reference feedback tuning with two degrees of freedom controllers*

  • Liu Qianming,
  • Wang Jianhong,
  • Wang Yanxiang

Journal volume & issue
Vol. 8, no. 1
pp. 462 – 476


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Virtual reference feedback tuning is one of data-driven control method, as only input–output data are used to design two degrees of freedom controller directly, i.e. feed-forward and feedback controller. Given two desired closed-loop transfer functions, virtual input and virtual disturbance are constructed, respectively to obtain one cost function, whose decision variables correspond to the two unknown controller parameters. Then after formulating the cost function as a linear regression form, the classical least squares algorithm is applied to identify the unknown parameter estimators. To quantify the quality or approximation error of the parameter estimators, statistical accuracy analysis is studied for virtual reference feedback tuning control. The detailed computational process about the asymptotic variance matrix is given by using some knowledge from probability theory and matrix theory. Based on our obtained asymptotic variance matrix, two applications of optimal input design and model structure validation are used to illustrate how to use the obtained asymptotic variance matrix. Finally, one simulation example has been performed to demonstrate the effectiveness of the theories proposed in this paper.