基于D分解的分数阶PID控制器的图形化参数整定

Graphical parameter tuning of fractional order PID controller based on D decomposition

摘要:

针对二自由度分数阶PID控制器设计的参数多，结构复杂等复杂问题，提出了一种基于D分解法和主导极点配置的新型参数整定方法。其基本原理首先基于动态响应指标约束进行主导极点配置，在确保闭环系统的响应特性良好的条件下确定系统超调量和调节时间，由此经过转换得到未知参数之间的函数关系。其次，使用D分解法，将未知参数在不影响的控制性能的条件下由多减少，再由相关参数取得系统性能稳定的参数域中优化，最后以差分进化算法为导向，以两种方法取得的相关约束条件为指标取得最优控制器参数，在确保所选极点的优势下使所设计的控制器达到理想的控制性能。最终，将所设计的控制器通过应用在整数阶和分数阶被控对象上，使用仿真验证新方法的鲁棒性和快速性，同时也表现了新方法的有效性和实用性。

Abstract:

In this paper, a new parameter tuning method based on D decomposition method and dominant pole placement is proposed for the complex problems such as design parameters of two-degree-of-freedom fractional PID controllers and complicated structure. The basic principle is to first configure the dominant pole based on dynamic response index constraints, and to determine the system overshoot and adjustment time under the condition of ensuring good response characteristics of the closed-loop system, and then obtain the functional relationship between unknown parameters through conversion. Secondly, the D decomposition method is used to reduce the unknown parameters by more than one without affecting the control performance, and then optimize the related parameters to obtain stable system performance in the parameter domain. Finally, guided by the differential evolution algorithm, the two methods are used. The relevant constraint condition for the index is to obtain the optimal controller parameters, and the designed controller can achieve the desired control performance under the advantage of ensuring the selected pole. Finally, the designed controller is applied to the integer and fractional order controlled objects, and the simulation is used to verify the robustness and rapidity of the new method. At the same time, it also shows the effectiveness and practicability of the new method.