Multi-objective Optimal Antiwindup Compensation of Discrete-Time Nonlinear Systems Under Input Saturation

IF 2.9 4区 综合性期刊 Q1 Multidisciplinary Arabian Journal for Science and Engineering Pub Date : 2024-08-06 DOI:10.1007/s13369-024-09385-9
Faisal Iqbal, Muhammad Rehan, Muntazir Hussain, Ijaz Ahmed, Muhammad Khalid
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Abstract

This paper deals with the discrete-time antiwindup compensator (AWC) synthesis for nonlinear discrete-time systems under input saturation. The proposed method considers the objective of an optimal AWC design for fast convergence and for improved performance against the saturation nonlinearity. A discrete-time full-order AWC architecture is presented for nonlinear discrete-time systems to achieve an improved performance against the saturation nonlinearity. Additionally, an equivalent decoupled AWC architecture for nonlinear discrete-time system is derived through algebraic analysis and transformation of saturation to dead-zone function. To achieve fast convergence, a more generic Lyapunov function has been applied for the AWC design by incorporating an exponential term in the Lyapunov function. Then, new conditions for the AWC synthesis are revealed by application of the resultant decoupled discrete-time architecture, nonlinearity condition, a modified quadratic-exponential Lyapunov function, optimally exponential \(L_{2}\) approach, and input saturation properties. The design conditions are provided for both global and local design scenarios, which can be applied to both stable and unstable plants. Compared with the conventional methods, the proposed approach deals with nonlinear systems, can be more practical due to discrete-time scenario, provides an optimal design for both fast convergence and performance, and applicable to both stable and unstable plants. A simulation example has been provided to demonstrate the efficacy of the proposed nonlinear AWC design.

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输入饱和状态下离散时间非线性系统的多目标最优防逆风补偿
本文论述了输入饱和状态下非线性离散时间系统的离散时间反逆风补偿器(AWC)合成。所提出的方法考虑的目标是优化 AWC 设计,以实现快速收敛并提高抗饱和非线性性能。针对非线性离散时间系统,提出了一种离散时间全阶 AWC 架构,以提高对抗饱和非线性的性能。此外,通过代数分析和饱和到死区函数的变换,还推导出了非线性离散时间系统的等效解耦 AWC 架构。为了实现快速收敛,通过在 Lyapunov 函数中加入指数项,在 AWC 设计中应用了更通用的 Lyapunov 函数。然后,通过应用由此产生的解耦离散时间架构、非线性条件、改进的二次-指数 Lyapunov 函数、最优指数 \(L_{2}\) 方法和输入饱和特性,揭示了 AWC 综合的新条件。为全局和局部设计方案提供了设计条件,既适用于稳定工厂,也适用于不稳定工厂。与传统方法相比,所提出的方法可以处理非线性系统,由于采用了离散时间方案,因此更加实用,同时提供了快速收敛和性能的最优设计,并适用于稳定和不稳定的工厂。我们提供了一个仿真实例来证明所提出的非线性 AWC 设计的有效性。
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来源期刊
Arabian Journal for Science and Engineering
Arabian Journal for Science and Engineering 综合性期刊-综合性期刊
CiteScore
5.20
自引率
3.40%
发文量
0
审稿时长
4.3 months
期刊介绍: King Fahd University of Petroleum & Minerals (KFUPM) partnered with Springer to publish the Arabian Journal for Science and Engineering (AJSE). AJSE, which has been published by KFUPM since 1975, is a recognized national, regional and international journal that provides a great opportunity for the dissemination of research advances from the Kingdom of Saudi Arabia, MENA and the world.
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