model predictive control, linear-quadratic cost functional, state space model, control system


Background. Model predictive control (MPC) approach is the basic feedback scheme, combined with high adaptive properties, which determines its successful use in the practice of design and operation of control systems. These advantages allow managing multidimensional objects with a complex structure, including nonlinearity, optimizing processes in real time within the constraints on controlled and managed variables, taking into account uncertainties in the task of objects and perturbations.

Objective. The purpose of the paper is to design and analyse control system of carbon monoxide oxidation in the convector cavity based on MPC with linear-quadratic cost functional with constraint.

Methods. The design of MPC is based on mathematical model of an object (relatively simple). At the current step, the prediction of object dynamic response on some final period of time (prediction horizon) is carried out; control optimization is performed, the purpose of which is to approximate the control variables of the prediction model to the corresponding setpoint on the predict horizon. The found optimal control is applied and measurement of an actual state of object at the end of a step is carried out. The prediction horizon is shifted one step further, and this algorithm are repeated.

Results. The results of modeling the automatic control system show that the MPC approach provides maintenance of carbon dioxide content when changing oxygen consumption and overshoot caused by introduction bulk does not exceed 0.6 % that meets the technological requirements of the process.

Conclusions. A fuse of the MPC and the quadratic functional given the constraints on the input signals is proposed. The problems of control degree of carbon oxidation in the convector cavity include non-stationarity, so the use of classical control methods is difficult. The MPC approach minimizes the cost function that characterizes the quality of the process. The predicted behaviour of a dynamic system will usually differ from its actual motion. The obtained quadratic functional is optimized to find the optimal control of degree of CO oxidation to CO2.


J. Richalet et al., “Model predictive heuristic control,” Automatica, vol. 14, no. 5, pp. 413–428, 1978. doi: 10.1016/0005-1098(78)90001-8

C.R. Cutler and B.L. Ramaker, “Dynamic matrix control - A computer control algorithm,” in Proc. Joint Automatic Control Conf., Houston, TX, 1980.

S.J. Qin and T.A. Badgwell, “A survey of industrial model predictive control technology,” Control Eng. Pract., vol. 11, no. 7, pp. 733–764, 2003. doi: 10.1016/S0967-0661(02)00186-7

O. Stepanets and Yu. Mariiash, “Analysis of influence of technical features of a pidcontroller implementation on the dynamics of automated control system,” Eastern-Europ. J. Enterpr. Technol., vol. 3, no. 2 (93), pp. 60–69, 2018. doi: 10.15587/1729-4061.2018.132229

S. Dubljevic and J.P. Humaloja, “Model predictive control for regular linear systems,” Automatica, vol. 119, p. 109066, 2020. doi: 10.1016/j.automatica.2020.109066

F. D. Palma and L. Magni, “A multi-model structure for model predictive control,” Ann. Rev. Control, vol. 28, no. 1, pp. 47–52, 2004. doi: 10.1016/j.arcontrol.2004.01.004

M.M. Morato et al., “Model predictive control design for linear parameter varying systems: A survey,” Ann. Rev. Control, vol. 49, pp. 64–80, 2020. doi: 10.1016/j.arcontrol.2020.04.016

P. Tatjewski and M. Ławryńczuk, “Algorithms with state estimation in linear and nonlinear model predictive control,” Comput. & Chem. Eng., vol. 143, p. 107065, 2020. doi: 10.1016/j.compchemeng.2020.107065

Y. Iino and T. Shigemasa, “Model predictive control with multi-objective cost function considering stabilization and linear cost optimization,” IFAC Proc. Vol., vol. 30, no. 9, pp. 547–552, 1997. doi: 10.1016/S1474-6670(17)43206-X

L. Böhler et al., “Fuzzy model predictive control for small-scale biomass combustion furnaces,” Appl. Energy, vol. 276, p. 115339, 2020. doi: 10.1016/j.apenergy.2020.115339

Y. Shin et al., “Development of model predictive control system using an artificial neural network: A case study with a distillation column,” J. Cleaner Production, vol. 277, p. 124124, 2020. doi: 10.1016/j.jclepro.2020.124124

L. Keviczky and Cs. Bányász, “Optimal structure for model predictive control,” IFAC Proc. Vol., vol. 37, no. 12, pp. 621–626, 2004. doi: 10.1016/S1474-6670(17)31538-0

M. Chen et al., “Cooperative distributed model predictive control based on topological hierarchy decomposition,” Control Eng. Pract., vol. 103, p. 104578, 2020. doi: 10.1016/j.conengprac.2020.104578

A. Maxim et al., “An industrially relevant formulation of a distributed model predictive control algorithm based on minimal process information,” J. Process Control, vol. 68, pp. 240–253, 2018. doi: 10.1016/j.jprocont.2018.06.004

L. Hewing et al., “Learning-based model predictive control: Toward safe learning in control,” Annual Rev. Control, Robotics, Autonom. Syst., vol. 3, no. 1, pp. 269–296, 2020. doi: 10.1146/annurev-control-090419-075625

O. Stepanets and Yu. Mariiash, “Model predictive control application in the energy saving technology of basic oxygen furnace,” Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska, vol. 10, no. 2, pp. 70–74, 2020. doi: 10.35784/iapgos.931