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Design of robust fuzzy iterative learning control for nonlinear batch processes.

Wei Zou1, Yanxia Shen1, Lei Wang2

  • 1Engineering Research Center of Internet of Things Technology Applications, Ministry of Education, Jiangnan University, Wuxi 214122, China.

Mathematical Biosciences and Engineering : MBE
|December 5, 2023
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Summary
This summary is machine-generated.

A novel composite fuzzy iterative learning control (ILC) scheme stabilizes nonlinear batch processes using a 2D fuzzy model. This robust control method ensures stability and performance, validated through simulations.

Keywords:
2D $ H_\infty $ performancefuzzy iterative learning controlnonlinear batch processesrobust asymptotic stabilityuncertain T-S fuzzy model

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Area of Science:

  • Control Engineering
  • Fuzzy Systems
  • Nonlinear Systems

Background:

  • Nonlinear batch processes present control challenges due to their complex dynamics and disturbances.
  • Iterative learning control (ILC) is effective for repetitive tasks but requires adaptation for nonlinear systems.
  • Fuzzy systems offer a powerful framework for modeling and controlling nonlinear uncertainties.

Purpose of the Study:

  • To propose a two-dimensional (2D) composite fuzzy iterative learning control (ILC) scheme for nonlinear batch processes.
  • To address non-repetitive disturbances and ensure robust asymptotic stability and 2D $H_\infty$ performance.
  • To develop a controller design method based on linear matrix inequalities (LMIs).

Main Methods:

  • Representing the nonlinear batch process using a 2D uncertain Takagi-Sugeno (T-S) fuzzy model via the local-sector nonlinearity method.
  • Integrating feedback control with the ILC scheme under the developed fuzzy model.
  • Establishing sufficient conditions for stability and performance using Lyapunov functions and matrix transformations.

Main Results:

  • Sufficient conditions for robust asymptotic stability and 2D $H_\infty$ performance of the closed-loop fuzzy system were derived.
  • Controller gains were obtained by solving a set of linear matrix inequalities (LMIs).
  • Simulations on a three-tank system and a continuous stirred tank reactor (CSTR) demonstrated the approach's feasibility and efficiency.

Conclusions:

  • The proposed 2D composite fuzzy ILC scheme effectively controls nonlinear batch processes with non-repetitive disturbances.
  • The method guarantees robust stability and achieves desired performance levels.
  • The LMI-based design provides a practical approach for controller synthesis.