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首页> 外文期刊>Journal of the Franklin Institute >Design of optimal PID controller for multivariable time-varying delay discrete-time systems using non-monotonic Lyapunov-Krasovskii approach
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Design of optimal PID controller for multivariable time-varying delay discrete-time systems using non-monotonic Lyapunov-Krasovskii approach

机译：使用非单调Lyapunov-krasovskii方法设计多变量时变离散时间系统最优PID控制器的设计

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摘要

This paper is concerned with stability analysis and stabilization of time-varying delay discrete-time systems in Lyapunov-Krasovskii stability analysis framework. In this regard, a less conservative approach is introduced based on non-monotonic Lyapunov-Krasovskii (NMLK) technique. The proposed method derives time-varying delay dependent stability conditions based on Lyapunov-Krasovskii functional (LKF), which are in the form of linear matrix inequalities (LMI). Also, a PID controller designing algorithm is extracted based on obtained NMLK stability condition. The stability of the closed loop system is guaranteed using the designed controller. Another property that is important along with the stability, is the optimality of the controller. Thus, an optimal PID designing technique is introduced in this article. The proposed method can be used to design optimal PID controller for unstable multi-input multi-output time-varying delay discrete-time systems. The proposed stability and stabilization conditions are less conservative due to the use of non-monotonic decreasing technique. The novelty of the paper comes from the consideration of non-monotonic approach for stability analysis of time-varying delay discrete-time systems and using obtained stability conditions for designing PID controller. Numerical examples and simulations are given to evaluate the theoretical results and illustrate its effectiveness compared to the existing methods.
机译：本文涉及Lyapunov-Krasovskii稳定性分析框架中时变延迟离散时间系统的稳定性分析和稳定性。在这方面，基于非单调Lyapunov-Krasovskii（NMLK）技术来引入更少保守的方法。该方法基于Lyapunov-Krasovskii功能（LKF）来衍生出时变延迟依赖性稳定性条件，其是线性矩阵不等式（LMI）的形式。此外，基于获得的NMLK稳定性条件提取PID控制器设计算法。使用设计的控制器可以保证闭环系统的稳定性。另一种与稳定性相同的属性是控制器的最优性。因此，本文介绍了最佳PID设计技术。该方法可用于为不稳定的多输入多输出时变延迟离散时间系统设计最佳PID控制器。由于使用非单调降低技术，所提出的稳定性和稳定性条件较少。本文的新颖性来自考虑时间变化延迟离散时间系统的稳定性分析的非单调方法，并使用所获得的PID控制器的稳定性条件。给出了数值示例和模拟来评估理论结果并说明与现有方法相比的有效性。

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  • 来源
    《Journal of the Franklin Institute》 |2021年第13期|6634-6665|共32页
  • 作者

    Younes Solgi; Alireza Fatehi; Amirhossein Nikoofard; Ala Shariati;

  • 作者单位

    APAC Research Group Faculty of Electrical Engineering K.N. Toosi University of Technology Seyyed-Khandan Tehran Iran;

    APAC Research Group Faculty of Electrical Engineering K.N. Toosi University of Technology Seyyed-Khandan Tehran Iran;

    APAC Research Group Faculty of Electrical Engineering K.N. Toosi University of Technology Seyyed-Khandan Tehran Iran;

    APAC Research Group Faculty of Electrical Engineering K.N. Toosi University of Technology Seyyed-Khandan Tehran Iran;

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