SCIENCE CHINA Information Sciences, Volume 64 , Issue 7 : 172210(2021) https://doi.org/10.1007/s11432-020-3078-1

Parametric output regulation using observer-based PI controllers with applications in flexible spacecraft attitude control

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  • ReceivedMay 15, 2020
  • AcceptedOct 1, 2020
  • PublishedMay 18, 2021



This work was supported by Major Program of National Natural Science Foundation of China (Grant Nos. 61690210, 61690212), Self-Planned Task of State Key Laboratory of Robotics and System (HIT) (Grant No. SKLRS201716A), and National Natural Science Foundation of China (Grant No. 61333003). The authors are very grateful to the anonymous associate editor and reviewers for their meaningful suggestions and comments.


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  • Figure 1

    Control system structure.

  • Figure 2

    Structure of classic PID controller.

  • Figure 3

    (Color online) The index values $J_{\mathrm{sen}}$ under the two control methods.

  • Figure 4

    (Color online) Dynamic responses. (a) Pitch angle; (b) pitch anglular velocity; (c) control input.

  • Table 1  

    Table 1Symbols

    Symbol Meaning
    $\lambda~_{i}(~M~)$textThe $i$text-th eigenvalue of matrix $M$
    $\mathrm{trace}(~M~)$textSum of diagonal elements of matrix $M$
    $\mathrm{blockdiag}\left(~M_{1},M_{2},\ldots,M_{n}\right)$textBlock diagonal matrix with $M_{1},M_{2},\ldots,M_{n}$text as diagonal elements
    $\mathrm{vec}(~[ \begin{array}{cccc} \eta~_{1}~&~\eta~_{2}~&~\cdots~&~\eta~_{n} \end{array} ]~)$$[ \begin{array}{cccc} \eta~_{1}^{\mathrm{T}}~&~\eta~_{2}^{\mathrm{T}}~&~\cdots~&~\eta~_{n}^{\mathrm{T} } \end{array} ]~^{\mathrm{T}}$
    $\mathrm{unvec}(~[ \begin{array}{cccc} \eta~_{1}^{\mathrm{T}}~&~\eta~_{2}^{\mathrm{T}}~&~\cdots~&~\eta~_{n}^{\mathrm{T} } \end{array} ]~^{\mathrm{T}})$$[ \begin{array}{cccc} \eta~_{1}~&~\eta~_{2}~&~\cdots~&~\eta~_{n} \end{array} ] $
    $A\otimes~B$ $\text{Kronecker~product~of~}A\text{~and~}B$
    $I_{n}$ $\text{Identity~matrix~of~$n$-order~}$
    $\mathrm{eig}(~M~)$ $\text{Set~of~eigenvalues~of~matrix~}M$

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