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
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
Qin, S.J., Badgwell, T.A.: A Survey of Industrial Model Predictive Control Technology. Control Engineering Practice 11(7), 733–764 (2003)
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)
Richalet, J., Rault, A., Testud, J.L., et al.: Model Predictive Heuristic Control: Applications to Industrial Processes. Automatica 14(5), 413–428 (1978)
Clarke, D.W., Mohtadi, C., Tuffs, P.S.: Generalized Predictive Control-Part I. The Basic Algorithm. Automatica 23(2), 137–148 (1987)
Skogestad, S., Postlethwaite, I.: Multivariable Feedback Control: Analysis and Design, New York (1996)
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)
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)
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)
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)
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)
Nikandrov, A., Swartz, C.L.E.: Sensitivity Analysis of LP-MPC Cascade Control Systems. Journal of Process Control 19(1), 16–24 (2009)
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)
Wu-zhong, L.: Singular Perturbation of Linear Algebraic Equations with Application to Stiff Equations. Applied Mathematics and Mechanics 8(6), 513–522 (1987)
Jun-liang, W., Fei, L.: Control Model of Ill-linear System and it Iterative Solution Method. Control and Decision 19(11), 1315–1317 (2004)
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)
Sanliturk, K.Y., Cakar, O.: Noise Elimination from Measured Frequency Response Functions. Mechanical Systems and Signal Processing 19(3), 615–631 (2005)
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)
Zou, T., Ding, B.-C., Zhang, R.: MPC-An Introduction to Industrial Applications (2010)
Ying, C., Zhen, C., Shu-liang, W.: Modified IMM Algorithm for Unmatched Dynamic Models. Systems Engineering and Electronics 33(12), 2593–2597 (2011)
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)
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)
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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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