球板问题的半解析封闭式解法

IF 2.8 4区工程技术 Q2 ENGINEERING, CHEMICAL

Processes Pub Date : 2024-09-13 DOI:10.3390/pr12091977

Remus-Daniel Ene, Nicolina Pop

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引用次数: 0

摘要

要理解复杂系统的动力学行为，数学模型和数值模拟必不可少。这项工作的目的是研究球-板问题的闭式解，考虑到从球-板动力学最优控制问题衍生出的系统。本研究介绍了球和板控制系统的非线性特性。为了对该系统进行半解析求解，我们探索了一个二阶非线性微分方程。因此，我们通过最优参数迭代法（OPIM）只用一次迭代就得到了近似闭式解。分析程序和相应数值程序之间的比较反映了前者的优势。所得结果与数值结果的一致性突出表明，所使用的程序是精确、有效的，并能很好地应用于球-板问题的滑模控制。

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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Semi-Analytical Closed-Form Solutions of the Ball–Plate Problem

Mathematical models and numerical simulations are necessary to understand the dynamical behaviors of complex systems. The aim of this work is to investigate closed-form solutions for the ball–plate problem considering a system derived from an optimal control problem for ball–plate dynamics. The nonlinear properties of ball and plate control system are presented in this work. To semi-analytically solve this system, we explored a second-order nonlinear differential equation. Consequently, we obtained the approximate closed-form solutions by the Optimal Parametric Iteration Method (OPIM) using only one iteration. A comparison between the analytical and corresponding numerical procedures reflects the advantages of the first one. The accordance between the obtained results and the numerical ones highlights that the procedure used is accurate, effective, and good to implement in applications such as sliding mode control to the ball-and-plate problem.

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来源期刊

Processes Chemical Engineering-Bioengineering

CiteScore

5.10

自引率

11.40%

发文量

2239

审稿时长

14.11 days

期刊介绍： Processes (ISSN 2227-9717) provides an advanced forum for process related research in chemistry, biology and allied engineering fields. The journal publishes regular research papers, communications, letters, short notes and reviews. Our aim is to encourage researchers to publish their experimental, theoretical and computational results in as much detail as necessary. There is no restriction on paper length or number of figures and tables.