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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[1] Strutzel F A M, Bogle I D L. Assessing plant design with regard to MPC performance. Comput Chem Eng, 2016, 94: 180-211 CrossRef Google Scholar

[2] Zou T, Ding B C, Zhang D. MPC: An Introduction to Industrial Applications. Beijing: Chemical Industry Press, 2010. 94, 100--106. Google Scholar

[3] Zhang K K, Ji G L, Zhu Y C. A method of MIMO model error detection for MPC systems. J Process Control, 2012, 22: 535--542. Google Scholar

[4] Heirung T A N, Foss B, Ydstie B E. MPC-based dual control with online experiment design. J Process Control, 2015, 32: 64-76 CrossRef Google Scholar

[5] Heirung T A N, Ydstie B E, Foss B. Dual adaptive model predictive control. Automatica, 2017, 80: 340-348 CrossRef Google Scholar

[6] Darby M L, Nikolaou M. Identification test design for multivariable model-based control: An industrial perspective. Control Eng Practice, 2014, 22: 165-180 CrossRef Google Scholar

[7] Genceli H, Nikolaou M. New approach to constrained predictive control with simultaneous model identification. AIChE J, 1996, 42: 2857-2868 CrossRef Google Scholar

[8] Záceková E, Prívara S, P?olka M. Persistent excitation condition within the dual control framework. J Process Control, 2013, 23: 1270-1280 CrossRef Google Scholar

[9] Potts A S, Romano R A, Garcia C. Improving performance and stability of MPC relevant identification methods. Control Eng Practice, 2014, 22: 20-33 CrossRef Google Scholar

[10] Marafioti G, Bitmead R R, Hovd M. Persistently exciting model predictive control. Int J Adaptive Control Signal Process, 2014, 45: 536--552. Google Scholar

[11] Heirung T A N, Erik Ydstie B, Foss B. Towards Dual MPC. IFAC Proc Volumes, 2012, 45: 502-507 CrossRef Google Scholar

[12] Bustos G A, Ferramosca A, Godoy J L. Application of Model Predictive Control suitable for closed-loop re-identification to a polymerization reactor. J Process Control, 2016, 44: 1-13 CrossRef Google Scholar

[13] González A H, Ferramosca A, Bustos G A. Model predictive control suitable for closed-loop re-identification. Syst Control Lett, 2014, 69: 23-33 CrossRef Google Scholar

[14] Anderson A, Gonzalez A H, Ferramosca A. Probabilistic Invariant Sets for Closed-Loop Re-Identification. IEEE Latin Am Trans, 2016, 14: 2744-2751 CrossRef Google Scholar

[15] Sotomayor O A Z, Odloak D, Moro L F L. Closed-loop model re-identification of processes under MPC with zone control. Control Eng Practice, 2009, 17: 551-563 CrossRef Google Scholar

[16] Zhu Y, Patwardhan R, Wagner S B. Toward a low cost and high performance MPC: The role of system identification. Comput Chem Eng, 2013, 51: 124-135 CrossRef Google Scholar

[17] Forssell U, Ljung L. Closed-loop identification revisited. Automatica, 1999, 35: 1215-1241 CrossRef Google Scholar

[18] Qin S J, Badgwell T A. An overview of industrial model predictive control technology. Control Eng Pract, 1997, 93: 232--256. Google Scholar

[19] González A H, Odloak D. A stable MPC with zone control. J Process Control, 2009, 19: 110-122 CrossRef Google Scholar

[20] Pang Z H, Cui H. System Identification and Adaptive Control MATLAB Simulation. Beijing: Beihang University Press, 2013. 20. Google Scholar

[21] Isermann R, Münchhof M. Identification of Dynamic Systems. Berlin: Springer, 2011. 184--190. Google Scholar

[22] Pintelon R, Schoukens J. System Identification: A Frequency Domain Approach. Piscataway: IEEE Press, 2001. 304--306. Google Scholar

[23] Beal L D R, Park J, Petersen D. Combined model predictive control and scheduling with dominant time constant compensation. Comput Chem Eng, 2017, 104: 271-282 CrossRef Google Scholar

[24] Li S Q, Ding B C. An overall solution to double-layered model predictive control based on dynamic matrix control. Acta Autom Sin, 2015, 41: 1857--1866. Google Scholar

[25] Darby M L, Nikolaou M, Jones J. RTO: An overview and assessment of current practice. J Process Control, 2011, 21: 874-884 CrossRef Google Scholar

[26] Prett D M, Morari M. The Shell Process Control Workshop. Boston: Butterworths, 1987. Google Scholar

  • 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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