引用本文: | 许宇宏,李创,唐荣年,陈阳泉.分数阶电路的设计简化与零极点变化规律[J].控制理论与应用,2025,42(6):1142~1151.[点击复制] |
XU Yu-hong,LI Chuang,TANG Rong-nian,CHEN Yang-quan.Simplification of fractional order circuits and zero-pole change rule[J].Control Theory & Applications,2025,42(6):1142~1151.[点击复制] |
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分数阶电路的设计简化与零极点变化规律 |
Simplification of fractional order circuits and zero-pole change rule |
摘要点击 87 全文点击 11 投稿时间:2024-03-29 修订日期:2025-05-04 |
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DOI编号 10.7641/CTA.2024.40183 |
2025,42(6):1142-1151 |
中文关键词 分数阶算子近似函数 零极点变化规律 频率扩展 分数阶电路设计 |
英文关键词 fractional order operator zero-pole setting frequency expansion fractional order circuit design |
基金项目 海南省重大科技项目(ZDKJ2020013), 国家重点研发计划项目(2021YFB1507104), 国家自然科学基金项目(61803131)资助. |
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中文摘要 |
分数阶算子的传递函数一般由近似算法得到, 本文通过调整传递函数的零极点值, 对CFE近似函数的有效
频率区间进行了扩展, 提高了Oustaloup方法的近似精度. 选择参数可调的 OTA元件设计了两种分数阶电路结构. 在
设计高阶算子时, 传递函数式电路的结构相对简单, 零极点式电路的参数设计方便. 本文提出了传递函数式电路结
构的参数设计规则, 将电路传递函数进行了简化. 在电路仿真与实验部分, 使用SPICE模型搭建电路, 设计了两种结
构在不同分数阶算子下的电路参数, 本文进行了仿真与实际电路的对比验证. 根据频率响应结果, 所设计的两种电
路结构能较好的模拟分数阶算子的特性, 电路的工作频率可扩展至原本的1000倍. |
英文摘要 |
The transfer function of fraction-order operators is generally obtained by the approximation algorithm. In
this paper, by adjusting the zero-pole value of the transfer function, the effective frequency interval of continued fraction
expansion (CFE) approximation function is extended and the approximate precision of Oustaloup method is improved.
Operational transconductance amplifier (OTA) elements with adjustable parameters are selected to design two fractional
order circuit structures. In the case of designing higher order operators, the circuit structure of the transfer function is
relatively simple, the parameters of the zero-pole circuit structure are easy to design. In this paper, the parameter design
rules of transfer function circuit structure are presented, which can simplify the circuit transfer function. In the circuit
simulation and experiment part, circuit structure is built by simulation program with integrated circuit emphasis (SPICE)
model, the circuit parameters of the two structures under different fractional order operators are designed, and the simulation
results are compared with the actual circuit. According to the results of frequency response, the two circuit structures can
simulate the characteristics of fractional order operators, and the operating frequency of the circuit is extended 1000 times. |
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