时滞分数阶系统PD^μ控制器参数整定的图解法

Graphical Tuning of PD^μ Controllers for Fractional-Order Time-Delay Systems

针对时滞分数阶系统,讨论分数阶PDμ控制器的参数整定问题。首先,利用一个可应用于时滞分数阶系统的图解稳定性准则,固定μ值,在比例-微分平面上绘制PDμ控制器参数稳定域,并讨论不同μ值对参数稳定域形状和大小的影响。该图解稳定性准则给出的是时滞分数阶系统稳定的一个充分必要条件,所得结果没有任何保守性。然后,将该种图解法思想扩展应用于系统性能设计,给出PDμ控制器最优参数整定的图解设计方法。在稳定域内分别考虑幅值裕度、相角裕度和相对稳定度性能设计问题。最后,提出了PDμ控制器参数整定的具体算法。仿真设计算法说明该图解法简洁有效,设计灵活,为一种实用的工程设计方法。

The graphical tuning problem of PD^μcontrollers for fractional-order time-delay systems is discussed.By using a graphical stability criterion applicable to fractional-order time-delay systems,the stability parameter region of PD^μcontroller in proportional-derivative plane for a fixed value of μ is ploted,and the shapes and sites of stability parameter regions for different values of μ is analyzed.The graphical stability criterion gives a necessary and sufficient stability condition for fractional-order time-delay systems,and the result obtained does not have any conservation.The graphical stability approach is generalized to the performance design,and the optimal graphical parameter tuning is given for PD^μcontrollers.In the stability region,the performance design of the gain margin,phase margin and the relative stability degree,is considered respectively.An algorithm of tuning the parameters of PD^μcontrollers is proposed.Simulation studies show that this kind of graphical method is simple,effective and flexible in design,and can be served as a practical engineering design method.