Digital algorithm for adaptive control of controlled variables in a given range
DOI:
https://doi.org/10.21638/spbu10.2025.111Abstract
The article is devoted to the issues of a digital control system synthesis for an arbitrary nonlinear object, including taking into account the delay. An important feature is the absence of a reference signal, the purpose of control is to maintain the controlled variables in a given range. The problem under consideration is solved based on the control method with a predictive model and a special quality functional. It is shown that the optimal control problem at each step is reduced to a nonlinear optimization problem, while the admissible set is never empty due to the use of auxiliary variables. This approach allows changing the restrictions on the control and measured variables in real time. Another important feature is the ability to turn on and off the variables of the control object during its operation, as well as to adjust the prediction for cases where the model is not known exactly. The efficiency of the proposed approach is demonstrated using the example of experiments with a computer model of a rectification column for refining petroleum products.
Keywords:
digital control, adaptivity, control in a given range
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References
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Burdick D. L., Leffler W. L. Petrochemicals in nontechnical language. Ed. 4. Oklahoma, USA, PennWell Corp. Publ., 2010, 460 p.
Lahiri S. K. Multivariable predictive control: Applications in industry. Hoboken, USA, John Wiley & Sons Publ., 2017, 304 p.
Kouvaritakis B., Cannon M. Model predictive control: Classical, robust and stochastic. Cham, Springer International Publishing, 2016, 397 p.
Camacho E. F., Bordons C. Model predictive control. Ed. 2. London, Springer-Verlag, 2007, 427 p.
Faulwasser T., Müller M. A., Worthmann K. Recent advances in model predictive control: Theory, algorithms, and applications. Cham, Springer, 2021, 253 p.
Sotnikova M. Plasma stabilization based on model predictive control. International Journal of Modern Physics A, 2009, vol. 24, no. 5, pp. 999–1008.
Sotnikova M. Ship dynamics control using predictive models. IFAC Proceedings Volumes (IFAC-PapersOnline), 2012, vol. 45, no. 27, pt 1, pp. 250–255.
Corriou J. P. Process control: Theory and applications. Cham, Springer, 2018, 883 p.
Zhabko N. A., Karelin V. V., Provotorov V. V., Sergeev S. M. The method of penalty functions in the analysis of optimal control problems of Navier — Stokes evolutionary systems with a spatial variable in a network-like domain. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2023, vol. 19, iss. 2, pp. 162–175. https://doi.org/10.21638/11701/spbu10.2023.203
Sotnikova M. V. Sintez cifrovogo upravleniya s prognozom dlya uderzhaniya kontroliruemyh peremennyh v zadannom diapazone [Digital control design based on predictive models to keep the controlled variables in a given range]. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2019, vol. 15, iss. 3, pp. 397–409. https://doi.org/10.21638/11701/spbu10.2019.309 (In Russian)
Sotnikova M. V., Sevostyanov R. A. Cifrovoe upravlenie kontroliruemymi peremennymi v zadannom diapazone s uchetom zapazdyvaniya [Digital control of output variables in a given range considering delay]. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2021, vol. 17, iss. 4, pp. 449–463. https://doi.org/10.21638/11701/spbu10.2021.412 (In Russian)
Sotnikova M., Sevostyanov R. Optimal control of output variables within a given range based on a predictive model. Mathematical Optimization Theory and Operations Research: Recent Trends. MOTOR 2022. Communications in Computer and Information Science, 2022, vol. 1661, pp. 272–285.
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