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International Conference on Intelligent Robotics and Applications

ICIRA 2015: Intelligent Robotics and Applications pp 619–631Cite as

Analysis and Correction of Ill-Conditioned Model in Multivariable Model Predictive Control

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9244))

Abstract

The ill-conditioned model is a common problem in model predictive control. The model ill-conditioned can lead to control performance declining obviously from steady-state model of process in this paper. The direction of output movement is relevant to whether the model is ill-conditioned by simulation and analysis. Model mismatch also leads to model ill-conditioned becoming more serious. The geometry tools and SVD in linear algebra are used to analyze the essential reason of ill-conditioned model, and an offline strategy is proposed which can solve the ill-conditioned model problem together with existing online strategies. Finally, the simulations are used to prove the conclusions which presented in this paper are correct.

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References

  1. Qin, S.J., Badgwell, T.A.: An overview of industrial model predictive control technology. AIChE Symposium Series. American Institute of Chemical Engineers, New York, pp. 1971--2002 (1997). 93(316): 232−256

    Google Scholar 

  2. Qin, S.J., Badgwell, T.A.: A Survey of Industrial Model Predictive Control Technology. Control Engineering Practice 11(7), 733–764 (2003)

    Article  Google Scholar 

  3. Cutler, C.R., Ramaker, B.L.: Dynamic matrix control-A computer control algorithm. In: Proceedings of the Joint Automatic Control Conference, vol. 1, p. Wp5-B. American Automatic Control Council, Piscataway (1980)

    Google Scholar 

  4. Richalet, J., Rault, A., Testud, J.L., et al.: Model Predictive Heuristic Control: Applications to Industrial Processes. Automatica 14(5), 413–428 (1978)

    Article  Google Scholar 

  5. Clarke, D.W., Mohtadi, C., Tuffs, P.S.: Generalized Predictive Control-Part I. The Basic Algorithm. Automatica 23(2), 137–148 (1987)

    Article  MATH  Google Scholar 

  6. Skogestad, S., Postlethwaite, I.: Multivariable Feedback Control: Analysis and Design, New York (1996)

    Google Scholar 

  7. Skogestad, S., Morari, M., Doyle, J.C.: Robust Control of Ill-conditioned Plants: High-Purity Distillation. IEEE Transactions on Automatic Control 33(12), 1092–1105 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  8. Grosdidier, P., Froisy, B., Hammann, M.: The Idcom-M controller. In: Proceedings of the 1988 IFAC workshop on Model Based Process Control, pp. 31−36 (1988)

    Google Scholar 

  9. Marroquin, J., Mitter, S., Poggio, T.: Probabilistic Solution of Ill-Posed Problems in Computational Vision. Journal of the American Statistical Association 82(397), 76–89 (1987)

    Article  MATH  Google Scholar 

  10. Cai, J.F., Candès, E.J., Shen, Z.: A Singular Value Thresholding Algorithm for Matrix Completion. SIAM Journal on Optimization 20(4), 1956–1982 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kassmann, D.E., Badgwell, T.A., Hawkins, R.B.: Robust Steady-State Target Calculation for Model Predictive Control. AIChE Journal 46(5), 1007–1024 (2000)

    Article  Google Scholar 

  12. Nikandrov, A., Swartz, C.L.E.: Sensitivity Analysis of LP-MPC Cascade Control Systems. Journal of Process Control 19(1), 16–24 (2009)

    Article  MATH  Google Scholar 

  13. Limebeer, D.J.N., Kasenally, E.M., Perkins, J.D.: On the Design of Robust Two Degree of Freedom Controllers. Automatica 29(1), 157–168 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wu-zhong, L.: Singular Perturbation of Linear Algebraic Equations with Application to Stiff Equations. Applied Mathematics and Mechanics 8(6), 513–522 (1987)

    Article  MathSciNet  Google Scholar 

  15. Jun-liang, W., Fei, L.: Control Model of Ill-linear System and it Iterative Solution Method. Control and Decision 19(11), 1315–1317 (2004)

    MathSciNet  Google Scholar 

  16. Gui, C., Jiang, Y., Lei, X., Rongjin, Z.: Research on Model-Plant Mismatch Detection Based on Subspace Approach. CIESC Journal 62(9), 2575–2581 (2011)

    Google Scholar 

  17. Sanliturk, K.Y., Cakar, O.: Noise Elimination from Measured Frequency Response Functions. Mechanical Systems and Signal Processing 19(3), 615–631 (2005)

    Article  Google Scholar 

  18. Hu, S.-L.J., Bao, S., Li, H.: Model Order Determination and Noise Removal for Modal Parameter Estimation. Mechanical Systems and Signal Processing 24(6), 1605–1620 (2010)

    Article  Google Scholar 

  19. Zou, T., Ding, B.-C., Zhang, R.: MPC-An Introduction to Industrial Applications (2010)

    Google Scholar 

  20. Ying, C., Zhen, C., Shu-liang, W.: Modified IMM Algorithm for Unmatched Dynamic Models. Systems Engineering and Electronics 33(12), 2593–2597 (2011)

    Google Scholar 

  21. Harrison, C.A., Qin, S.J.: Discriminating between Disturbance and Process Model Mismatch in Model Predictive Control. Journal of Process Control 19(10), 1610–1616 (2009)

    Article  Google Scholar 

  22. Li, R., Fang, Y., Cai, W., et al.: Stability Analysis and a Fast Algorithm for the Predictive Control of Stochastic Systems. Information and Control 2, 000 (2013)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Shenyang Institute of Automation, Chinese Acedemy of Science, Shenyang, 110016, China

    Hao Pan, Hai-Bin Yu, Tao Zou & Dewei Du

  2. University of Chinese Academy of Sciences, Beijing, 100049, China

    Hao Pan & Dewei Du

Authors
  1. Hao Pan
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  2. Hai-Bin Yu
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  3. Tao Zou
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  4. Dewei Du
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Corresponding author

Correspondence to Hao Pan .

Editor information

Editors and Affiliations

  1. University of Portsmouth, Portsmouth, United Kingdom

    Honghai Liu

  2. Tokyo Metropolitan University, Tokyo, Japan

    Naoyuki Kubota

  3. Shanghai Jiao Tong University, Shanghai, China

    Xiangyang Zhu

  4. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Rüdiger Dillmann

  5. University of Portsmouth, Portsmouth, United Kingdom

    Dalin Zhou

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© 2015 Springer International Publishing Switzerland

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Pan, H., Yu, HB., Zou, T., Du, D. (2015). Analysis and Correction of Ill-Conditioned Model in Multivariable Model Predictive Control. In: Liu, H., Kubota, N., Zhu, X., Dillmann, R., Zhou, D. (eds) Intelligent Robotics and Applications. ICIRA 2015. Lecture Notes in Computer Science(), vol 9244. Springer, Cham. https://doi.org/10.1007/978-3-319-22879-2_56

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  • DOI: https://doi.org/10.1007/978-3-319-22879-2_56

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22878-5

  • Online ISBN: 978-3-319-22879-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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