Design of robust fuzzy iterative learning control for nonlinear batch processes

Wei Zou; Yanxia Shen; Lei Wang; Wei Zou; Yanxia Shen; Lei Wang

doi:10.3934/mbe.2023897

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 11: 20274-20294. doi: 10.3934/mbe.2023897

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Research article

Design of robust fuzzy iterative learning control for nonlinear batch processes

1.
Engineering Research Center of Internet of Things Technology Applications, Ministry of Education, Jiangnan University, Wuxi 214122, China
2.
School of Automation, Wuxi University, Wuxi 214105, China

Academic Editor: Yang Kuang

Received: 06 August 2023 Revised: 17 October 2023 Accepted: 25 October 2023 Published: 07 November 2023

In this paper, a two-dimensional (2D) composite fuzzy iterative learning control (ILC) scheme for nonlinear batch processes is proposed. By employing the local-sector nonlinearity method, the nonlinear batch process is represented by a 2D uncertain T-S fuzzy model with non-repetitive disturbances. Then, the feedback control is integrated with the ILC scheme to be investigated under the constructed model. Sufficient conditions for robust asymptotic stability and 2D $ H_\infty $ performance requirements of the resulting closed-loop fuzzy system are established based on Lyapunov functions and some matrix transformation techniques. Furthermore, the corresponding controller gains can be derived from a set of linear matrix inequalities (LMIs). Finally, simulations on the three-tank system and the highly nonlinear continuous stirred tank reactor (CSTR) are carried out to prove the feasibility and efficiency of the proposed approach.
- fuzzy iterative learning control,
- nonlinear batch processes,
- uncertain T-S fuzzy model,
- robust asymptotic stability,
- 2D $ H_\infty $ performance
Citation: Wei Zou, Yanxia Shen, Lei Wang. Design of robust fuzzy iterative learning control for nonlinear batch processes[J]. Mathematical Biosciences and Engineering, 2023, 20(11): 20274-20294. doi: 10.3934/mbe.2023897

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Abstract

In this paper, a two-dimensional (2D) composite fuzzy iterative learning control (ILC) scheme for nonlinear batch processes is proposed. By employing the local-sector nonlinearity method, the nonlinear batch process is represented by a 2D uncertain T-S fuzzy model with non-repetitive disturbances. Then, the feedback control is integrated with the ILC scheme to be investigated under the constructed model. Sufficient conditions for robust asymptotic stability and 2D $ H_\infty $ performance requirements of the resulting closed-loop fuzzy system are established based on Lyapunov functions and some matrix transformation techniques. Furthermore, the corresponding controller gains can be derived from a set of linear matrix inequalities (LMIs). Finally, simulations on the three-tank system and the highly nonlinear continuous stirred tank reactor (CSTR) are carried out to prove the feasibility and efficiency of the proposed approach.

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