带有正定位反控制器的倒置的动态分析大致均溶液.
Galal M Moatimid1, A T El-Sayed2, Hala F Salman3
1Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt. gal_moa@edu.asu.edu.eg.
Scientific reports
|May 31, 2023
概括
这项研究使用非线性控制理论和先进的扰动方法来控制反转 (IP). 结果显示,增加的通用力,刚性和磁场增强了IP稳定性,为非线性系统控制提供了洞察力.
科学领域:
- 非线性控制理论 不线性控制理论
- 分析力学 分析力学
- 振动分析 振动分析
背景情况:
- 倒挂 (IP) 是古典力学和控制理论中的一个基本系统.
- 控制IP的稳定性,特别是在外部力量和共振下,对于各种应用至关重要.
- 现有的方法可能无法完全解决复杂的动态和多次激发场景.
研究的目的:
- 开发和验证反向摆形系统的非线性控制策略.
- 分析系统的动态行为和稳定性在各种条件下,包括多激发力.
- 探索扰动方法和反控制在稳定IP中的有效性.
主要方法:
- 使用古典分析力学推导运动方程.
- 泰勒扩张的应用,用于分析恢复力.
- 使用修改后的同位体扰动方法 (mHPM) 进行近似周期解.
- 采用第四阶Runge-Kutta (RK-4) 方法进行数字验证.
- 开发积极位置反 (PPF) 控制.
- 应用二次多重时间尺度扰动技术 (MSPT) 对两度自由度模型.
- 使用Routh-Hurwitz标准进行稳定性分析.
主要成果:
- 通过使用mHPM获得了IP的令人满意的周期性解决方案,并进行了数值验证.
- PPF控制在多激发力下减轻振动方面是有效的.
- MSPT分析揭示了对系统在初级和1:1内部共振的行为的一些见解.
- 频率响应曲线和数值模拟证实了受控性能.
- 发现增加的通用力,扭曲刚性和磁场可以抑制不稳定性并增强IP稳定性.
结论:
- 提出的非线性控制方法,包括mHPM和PPF,对于稳定反转的摆形是有效的.
- 扰动技术提供了通过数值模拟验证的准确近似解决方案.
- 系统参数如刚度,外力和磁场显著影响稳定性.
- 这些发现对许多其他非线性系统的设计和控制有影响.
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