Further experimental results on modelling and algebraic control of a delayed looped heating-cooling process under uncertainties

Libor Pekař; Radek Matušů; Petr Dostálek; Mengjie Song

doi:10.1016/j.heliyon.2023.e18445

Further experimental results on modelling and algebraic control of a delayed looped heating-cooling process under uncertainties

Heliyon. 2023 Jul 25;9(8):e18445. doi: 10.1016/j.heliyon.2023.e18445. eCollection 2023 Aug.

Authors

Libor Pekař^{1

2}, Radek Matušů¹, Petr Dostálek¹, Mengjie Song³

Affiliations

¹ Faculty of Applied Informatics, Tomas Bata University in Zlín, Nad Stráněmi 4511, 76005, Zlín, Czech Republic.
² Department of Technical Studies, College of Polytechnics Jihlava, Tolstého 1556, 58601, Jihlava, Czech Republic.
³ School of Mechanical Engineering, Beijing Institute of Technology, No. 5, Zhongguancun South Street, Haidian District, Beijing, 100081, China.

Abstract

The aim of this research is to revise and substantially extend experimental modelling and control of a looped heating-cooling laboratory process with long input-output and internal delays under uncertainties. This research follows and extends the authors' recent results. As several significant improvements regarding robust modelling and control have been reached, the obtained results are provided with a link and comparison to the previous findings. First, an infinite-dimensional model based on mathematical-physical heat and mass transfer principles is developed. All important heat-fluid transport and control-signal delays are considered when assembling the model structure and relations of quantities. Model parameter values optimization based on the measurement data follows. When determining static model parameter values, all variations in steady-state measured data are taken into account simultaneously, which enhances previously obtained models. Values of dynamic model parameters and delays are further obtained by least mean square optimization. This innovative model is compared to two recently developed process models and to the best-fit model that ignores the measured variations. Controller structures are designed using algebraic tools for all four models. The designed controllers are robust in the sense of robust stability and performance. Both concepts are rigorously assessed, and the obtained conditions serve for controller parameter tuning. Two different control systems are assumed: the standard closed-loop feedback loop and the two-feedback-controllers control system. Numerous experimental measurements for nominal conditions and selected perturbations are performed. Obtained results are further analyzed via several criteria on manipulated input and controlled temperature. The designed controllers are compared to the Smith predictor structure that is well-established for time-delay systems control. An essential drawback of the predictor regarding disturbance rejection is highlighted.

Keywords: Algebraic control design; Long delays; Looped heating-cooling process; Robustness; Smith predictor; Uncertainties.