A comparative study of linear and nonlinear optimal control of a three-tank system

Samuel Emebu; Marek Kubalčík; Christoph Josef Backi; Dagmar Janáčová

doi:10.1016/j.isatra.2022.06.002

A comparative study of linear and nonlinear optimal control of a three-tank system

ISA Trans. 2023 Jan:132:419-427. doi: 10.1016/j.isatra.2022.06.002. Epub 2022 Jun 9.

Authors

Samuel Emebu¹, Marek Kubalčík², Christoph Josef Backi³, Dagmar Janáčová⁴

Affiliations

¹ Department of Automation and Control Engineering, Faculty of Applied Informatics, Tomas Bata University in Zlín, Nad Stráněmi 4511, 76005, Zlín, Czech Republic; Department of Chemical Engineering, Faculty of Engineering, University of Benin, PO Box 1154, Benin City, Nigeria. Electronic address: emebu@utb.cz.
² Department of Process Control, Faculty of Applied Informatics, Tomas Bata University in Zlín, Nad Stráněmi 4511, 76005, Zlín, Czech Republic. Electronic address: kubalcik@utb.cz.
³ Department of Chemical Engineering, Faculty of Natural Sciences, Norwegian University of Science and Technology, Høgskoleringen 1, 7491 Trondheim, Norway. Electronic address: christoph.backi@ntnu.no.
⁴ Department of Automation and Control Engineering, Faculty of Applied Informatics, Tomas Bata University in Zlín, Nad Stráněmi 4511, 76005, Zlín, Czech Republic. Electronic address: janacova@utb.cz.

PMID: 35760654
DOI: 10.1016/j.isatra.2022.06.002

Abstract

In this work, a laboratory scaled industrial interconnected nonlinear Multi-Input|Multi-Output (MIMO) three-tank system, was modelled to control the liquid levels. Ensuing the tradition in the process industry to apply linear controller to most control processes, a linear control scheme was developed for this system. However, since linear schemes are proximate to actual process models, they may not be adequate, especially for highly nonlinear systems. Therefore, a nonlinear control scheme was also developed and compared with the linear scheme. Specifically, optimal linear and nonlinear controllers were designed. In summary, the results of the two control schemes showed adequate performance. However, the linear controller had more robust control and required lesser computational demand compared to the nonlinear scheme. To enhance the computational demand of the nonlinear scheme, a third-party MATLAB toolbox, Automatic Control and Dynamic Optimization (ACADO) toolbox, that interfaces MATLAB with C++ to speed up computations was also utilised, and its results compared, and tentatively validate the earlier solved nonlinear control scheme.

Keywords: ACADO; Hamilton-Jacobi equation; Linear optimal control; Nonlinear optimal control; Three-tank-system.