Abstract
The paper is concerned with development and analysis of the Dynamic Matrix Control (DMC) discrete-time model predictive control algorithm with parametrisation of the control input trajectories by sets of Laguerre functions. First the appropriate formulation of the algorithm is developed. The main difference between it and the standard DMC formulation is that coefficients of the approximation by the Laguerre functions, instead of control input values, are the decision variables of the DMC optimization problem. Then the proposed DMCL (DMC with Laguerre functions) algorithm is applied to a multivariable benchmark problem to investigate its properties and to provide a concise comparison with the standard DMC algorithm.
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References
Blevins, T.L., McMillan, G.K., Wojsznis, W.K., Brown, M.W.: Advanced Control Unleashed. The ISA Society, Research Triangle Park (2003)
Blevins, T.L., Wojsznis, W.K., Nixon, M.: Advanced Control Foundation. The ISA Society, Research Triangle Park (2013)
Camacho, E., Bordons, C.: Model Predictive Control. Springer, London (1999)
Ławryńczuk, M.: Computationally Efficient Model Predictive Control Algorithms: A Neural Network Approach, Studies in Systems, Decision and Control, vol. 3. Springer, Heidelberg (2014)
Ławryńczuk, M.: Nonlinear model predictive control for processes with complex dynamics: parametrisation approach using Laguerre functions. Int. J. Appl. Math. Comput. Sci. 30(1), 35–46 (2020)
Maciejowski, J.: Predictive Control. Prentice Hall, Harlow (2002)
Qin, S., Badgwell, T.: A survey of industrial model predictive control technology. Control Eng. Pract. 11, 733–764 (2003)
Rawlings, J.B., Mayne, D.Q.: Model Predictive Control: Theory and Design. Nob Hill Publishing, Madison (2009)
Rossiter, J.: Model-Based Predictive Control. CRC Press, Boca Raton (2003)
Tatjewski, P.: Advanced Control of Industrial Processes. Springer, London (2007)
Tatjewski, P.: Advanced control and on-line process optimization in multilayer structures. Ann. Rev. Control 32, 71–85 (2008)
Valencia-Palomo, G., Rossiter, J.: Using Laguerre functions to improve efficiency of multi-parametric predictive control. In: Proceedings of the 2010 American Control Conference, Baltimore (2010)
Wahlberg, B.: System identification using the Laguerre models. IEEE Trans. Autom. Control 36(5), 551–562 (1991)
Wang, L.: Discrete model predictive controller design using Laguerre functions. J. Process Control 14, 131–142 (2004)
Wang, L.: Model Predictive Control System Design and Implementation using MATLAB. Springer, London (2009)
Wood, R., Berry, M.: Terminal composition control of a binary distillation column. Chem. Eng. Sci. 28(9), 1707–17 (1973)
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Tatjewski, P. (2020). DMC Algorithm with Laguerre Functions. In: Bartoszewicz, A., Kabziński, J., Kacprzyk, J. (eds) Advanced, Contemporary Control. Advances in Intelligent Systems and Computing, vol 1196. Springer, Cham. https://doi.org/10.1007/978-3-030-50936-1_84
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DOI: https://doi.org/10.1007/978-3-030-50936-1_84
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