为分数顺序系统的特定情况设计不超射的分数顺序PI控制器
1Department of Electrical Engineering, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran.
ISA transactions
|August 14, 2025
概括
本研究引入了一种新的分数顺序比例积分 (FOPI) 控制器设计,该设计保证了分数顺序系统 (FOS) 的不超射单位步骤响应 (USR). 该方法确保了单调的大小频率响应 (MFR),提高了系统的稳定性和性能.
科学领域:
- 控制系统工程 控制系统工程
- 应用数学 应用数学 应用数学
- 机械电子学是什么意思 机械电子学
背景情况:
- 对于许多控制应用来说,实现一个不超射的步骤响应至关重要.
- 现有的分数顺序比例积分 (FOPI) 控制器不能保证闭环系统的单位步骤响应 (USR) 不超过.
- 分数顺序系统 (FOS) 由于其复杂的动态,在控制器设计中存在独特的挑战.
研究的目的:
- 为FOS设计新型非超射FOPI控制器,采用一个和两个分数订单.
- 建立一个条件,以实现闭环系统的单调大小频率响应 (MFR).
- 确保稳定性和优化性能指标,如阶段边际 (PM) 和循环增益交叉频率 (GCF).
主要方法:
- 控制器参数被选择以确保单调的MFR,导致不超射或极小超射的USR.
- 一个关键的发现是,当FOPI控制器的分数顺序和FOS的最大顺序的和等于1时,就会实现单调的MFR.
- 比例增益和集成器时间常数计算以满足所需的PM和GCF,稳定性经过严格验证.
主要成果:
- 拟议的FOPI控制器设计成功地实现了FOS的不超射USR.
- 数字模拟验证了在干扰和模型不确定性下控制器的有效性.
- 对比模拟表明设计的FOPI控制器在现有方法上的优势.
结论:
- 开发的FOPI控制器提供了一个强大的解决方案,用于在FOS中实现非超射步骤响应.
- 该控制器的实用性进一步通过其在控制离子聚合物-金属复合执行器的成功实施来得到证实.
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