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SCIENTIA SINICA Informationis, Volume 49 , Issue 1 : 57-73(2019) https://doi.org/10.1360/N112017-00190

A framework for multi-variable, semi-adaptive predictive control system

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  • ReceivedDec 25, 2017
  • AcceptedFeb 26, 2018
  • PublishedJan 8, 2019

Abstract


Funded by

国家重点研发计划(2017YFA0700303)

国家重点研发计划(2017YFB0603703)

国家自然科学基金(61773366)

国家自然科学基金(61533015)


References

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  • Figure 1

    Control objective of controlled variable: setpoint, zone, reference trajectory and funnel

  • Figure 2

    Block diagram of the semi-adaptive MPC

  • Figure 3

    Structure of online re-identification based on MPC

  • Figure 4

    Structure of online re-identification based on double-layer MPC

  • Figure 5

    (Color online) Geometric description of “calibration mode". (a) Standard SSTC; (b) SSTC with benefit balance coefficient

  • Figure 6

    (Color online)The input and output curves of process. (a) No controller model updated; (b) controller model updated

  • Figure 7

    (Color online) The orthogonal PRBS signals

  • Figure 8

    (Color online) Inputs and outputs for the online comprehensive testing of the plant. (a) $\lambda=0.8$; (b) $\lambda=0.4$

  • Figure 9

    (Color online) Step response. (a) $\lambda=0.8$; (b) $\lambda=0.4$

  • Table 1   Estimated errors of the MPC model (%)
    $\bigg[{G_{11}~\atop~G_{21}} {G_{12}\atop~G_{22}}\bigg]$ $f=0.015$ Hz $f=0.067$ Hz $f=0.13$ Hz
    Estimated errors (%) $\bigg[{116.3~\atop~99.1} {89.5\atop~66.7}\bigg]$ $\bigg[{70.5~\atop~108.3} {96.0\atop~98.9}\bigg]$ $\bigg[{92.1~\atop~97.4} {98.6\atop~98.0}\bigg]$
  • Table 2   Results corresponding comprehensive testing
    Parameter Actual value $\lambda~=0.8$ $\lambda~=0.4$
    $a\left(1\right)$ $-$1.8930 $-$1.8810 $-$1.8331
    $a\left(2\right)$ 0.8958 0.8845 0.8393
    $b_{11}\left(0\right)$ 0.0000 0.0000 0.0000
    $b_{11}\left(1\right)$ 0.2359 0.2358 0.2359
    $b_{11}\left(2\right)$ $-$0.2244 $-$0.2215 $-$0.2103
    $b_{12}\left(0\right)$ 0.0580 0.0581 0.0580
    $b_{12}\left(1\right)$ $-$0.0264 $-$0.0258 $-$0.0229
    $b_{12}\left(2\right)$ $-$0.0266 $-$0.0261 $-$0.0248
    $b_{21}\left(0\right)$ 0.0000 0.0000 0.0000
    $b_{21}\left(1\right)$ 0.3139 0.3139 0.3138
    $b_{21}\left(2\right)$ $-$0.2986 $-$0.2949 $-$0.2799
    $b_{22}\left(0\right)$ 0.0945 0.0946 0.0945
    $b_{22}\left(1\right)$ 0.0954 0.0964 0.1010
    $b_{22}\left(2\right)$ $-$0.1737 $-$0.1713 $-$0.1625
    ${\rm~Total}\_{\rm~e}^2$ $^{\rm~a)}$ 0.0000 0.0003 0.0075
  • Table 3   Estimated errors of the updated MPC model ($\lambda~=0.8$) (%)
    $\bigg[{G_{11}~\atop~G_{12}} {G_{21}\atop~G_{22}}\bigg]$ $f=0.015~\mathrm{Hz}$ $f=0.067~\mathrm{Hz}$ $f=0.13~\mathrm{Hz}$
    Estimated errors (%) $\bigg[{37.0\atop~54.8} {20.5\atop~29.9}\bigg]$ $\bigg[{44.9\atop~20.8} {42.8\atop~53.0}\bigg]$ $\bigg[{22.7\atop~55.5} {79.9\atop~68.2}\bigg]$