A comparative study of linear and nonlinear optimal control of a three-tank system. (January 2023)

• Record Type: Journal Article
• Authors: Emebu, Samuel; Kubalčík, Marek; Backi, Christoph Josef; Janáčová, Dagmar
• Is Part Of: ISA transactions. Volume 132(2023)
• Page Start: 419
• Page End: 427
• Publication Date: 2023-01
• Subjects: Linear optimal control -- Nonlinear optimal control -- Hamilton-Jacobi equation -- Three-tank-system -- ACADO; Engineering instruments -- Periodicals; Engineering instruments; Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.isatra.2022.06.002
• Languages: English
• ISSNs: 0019-0578

Abstract

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. Highlights: A Multi-Input | Multi-Output (MIMO) nonlinear three-tank system with experimentally verified valve constants is considered. Discretised linear and nonlinear optimal controllers are designed for the system. The linear optimal controller was designed based on the Jacobian linearisation of the nonlinear system. The two designed controllers were used to control the simulated system and their results were compared. Automatic Control and Dynamic Optimization (ACADO) was also used to compare and validate the nonlinear optimal controllers.