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Tuning of fractional complex‐order direct current motor controller using frequency domain analysis
Mathematical Methods in the Applied Sciences ( IF 2.9 ) Pub Date : 2020-06-29 , DOI: 10.1002/mma.6653
Min Zheng 1, 2 , Guangfeng Zhang 1 , Tao Huang 1
Affiliation  

For the speed control of direct current motor, a fractional complex‐order controller (FCOC) is proposed in this paper. The FCOC is an extension of the fractional‐order controller. It is known that fractional‐order controllers exhibit strong robustness to open‐loop gain variations. However, in actual situations, due to external interference, the phase angle and gain of the system may change at the same time. The FCOC proposed in this paper adds an additional parameter, which makes the system show strong robustness when the phase angle and gain change simultaneously. Existing methods for parameter tuning of FCOCs only consider the preset gain crossover frequency and the expected phase margin. This may not allow the system to exhibit good dynamic and stable performance. In this paper, based on the frequency domain analysis, the parameters of the FCOC are tuned by integrating the gain crossover frequency, cutoff frequency, phase margin, and amplitude margin. The optimal solution satisfying a set of constraint equations is obtained by optimization algorithm. Finally, the simulation results are compared with those of the fractional‐order controller and the integer‐order controller. At the same time, the robustness of the system under disturbance is analyzed. The results show that the complex fractional‐order control presented in this paper has better dynamic performance and robustness.

中文翻译:

使用频域分析微分复数阶直流电动机控制器

对于直流电动机的速度控制,本文提出了分数阶复阶控制器(FCOC)。FCOC是分数阶控制器的扩展。众所周知,分数阶控制器对开环增益变化表现出很强的鲁棒性。但是,在实际情况下,由于外部干扰,系统的相位角和增益可能会同时变化。本文提出的FCOC增加了一个附加参数,当相角和增益同时变化时,该系统显示出强大的鲁棒性。现有的FCOC参数调整方法仅考虑预设增益交叉频率和预期相位裕量。这可能不允许系统表现出良好的动态和稳定性能。本文基于频域分析,通过集成增益交叉频率,截止频率,相位裕度和幅度裕度来调整FCOC的参数。通过优化算法获得了满足一组约束方程的最优解。最后,将仿真结果与分数阶控制器和整数阶控制器的仿真结果进行比较。同时,分析了系统在干扰下的鲁棒性。结果表明,本文提出的复杂分数阶控制具有更好的动态性能和鲁棒性。将仿真结果与分数阶控制器和整数阶控制器的仿真结果进行比较。同时,分析了系统在干扰下的鲁棒性。结果表明,本文提出的复杂分数阶控制具有更好的动态性能和鲁棒性。仿真结果与分数阶控制器和整数阶控制器的仿真结果进行了比较。同时,分析了系统在干扰下的鲁棒性。结果表明,本文提出的复杂分数阶控制具有更好的动态性能和鲁棒性。
更新日期:2020-06-29
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