Discrete natural logarithmic barrier function-based prescribed performance backstepping control for MEMS resonator

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-24 DOI:10.1016/j.cnsns.2025.108910

Le Zhao, Guanci Yang, Yang Li, Kexin Luo, Junxing Zhang, Ling He

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引用次数: 0

Abstract

The prescribed performance control is able to optimize both the transient and static performance of the controlled object by pre-set performance indicators, thereby ensuring that the output error remains within a predetermined small range despite any interference or uncertainty within the system. Considering this, aiming at the discrete micro-electromechanical system (MEMS) resonator, we design a discrete natural logarithmic barrier function-based prescribed performance backstepping controller. Among them, firstly, the discrete interval type-3 fuzzy logic system (IT3FLS) and discrete tracking differentiator are constructed to approximate the virtual control input and unknown nonlinear function. Secondly, a prescribed performance adaptive fuzzy backstepping controller based on the constructed discrete natural logarithmic barrier function is designed to constrain the output errors of the system, and enhance transient and static performances of the controller. Then, a discrete event-triggered mechanism based on the switch threshold is constructed and integrated into the designed controller to release unnecessary resource occupation and controller computational burden on the premise of ensuring tracking accuracy. Furthermore, through the mean-square stability criterion, we demonstrate that all signals of this system are exponentially mean-square stable, and tracking errors fall within the prescribed constraint region. Finally, simulation and comparative experiment results display that the designed controller performs well in the transient performance, static performance and robustness.

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基于离散自然对数势垒函数的MEMS谐振器规定性能反步控制

规定的性能控制是通过预先设定的性能指标来优化被控对象的暂态和静态性能，从而保证在系统内部存在干扰或不确定性的情况下，输出误差保持在预定的小范围内。考虑到这一点，针对离散微机电系统（MEMS）谐振器，设计了一种基于离散自然对数势垒函数的规定性能反步控制器。其中，首先构造离散区间3型模糊逻辑系统（IT3FLS）和离散跟踪微分器来逼近虚拟控制输入和未知非线性函数；其次，基于所构造的离散自然对数障碍函数设计了一种规定性能的自适应模糊反步控制器，以约束系统的输出误差，提高控制器的暂态和静态性能；然后，构建基于开关阈值的离散事件触发机制，并将其集成到所设计的控制器中，在保证跟踪精度的前提下，释放不必要的资源占用和控制器计算负担。进一步，通过均方稳定性判据，证明了该系统的所有信号都是指数均方稳定的，跟踪误差落在规定的约束区域内。仿真和对比实验结果表明，所设计的控制器具有良好的暂态性能、静态性能和鲁棒性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.