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


In view of the degradation of predictive control performance caused by model mismatch, a multi-variable, semi-adaptive zone predictive control system framework is presented. The proposed framework changes the traditional control mode to testing mode and turns set-point to zone control, thereby realizing the constraint satisfaction of the output variables of the test process. For the constraint zone model's predictive control in the integrated testing mode, the amplitude strength of testing input signals is introduced to realize the constraint guarantee function and signal-to-noise ratio maximization. The framework implements the open-loop test to improve test efficiency under the premise of production on the rails. The signal-to-noise ratio of the testing process is ensured by maximizing the test signal amplitude. Furthermore, the framework is extended from constrained to two-layer model predictive control, and the benefit balance coefficient is introduced to realize the balance between economic benefit and testing. The method proposed in the paper is a type of on-line open-loop identification, which solves the problem of the correlation between input signals and noises in closed-loop identification. The simulation results verify the effectiveness of the method.

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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 (%) $\bigg[{37.0\atop~54.8} {20.5\atop~29.9}\bigg]$ $\bigg[{44.9\atop~20.8} {42.8\atop~53.0}\bigg]$ $\bigg[{22.7\atop~55.5} {79.9\atop~68.2}\bigg]$

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