分数阶PIλDμ控制器参数设计方法——极点阶数搜索法

A Design Method of the Parameters of Fractional-order PIλDμ Controller -Poles-Orders Searching Method

  • 摘要: 分数阶PIλDμ控制器将传统整数阶PID控制器的微分与积分阶数扩展到分数.利用μ、λ两个参数,可以灵活地设计PID控制器.本文提出了一种整定分数阶PIλDμ控制器参数的有效方法——极点阶数搜索法.其基本原理是,首先估计分数阶PIλDμ控制器的比例参数KP,然后设计一对稳定度较好的极点,再估计参数μ和λ的搜寻范围,最后将KP极点代入分数阶控制系统的特征方程中,并在μ和λ的搜寻范围内搜寻一组能满足分数阶控制系统时域性能指标的分数阶PIλDμ控制器的参数KP、KI、λ、KD、μ.仿真结果证明,用极点阶数搜索法设计出的分数阶PIλDμ控制器能更好地调节分数阶被控系统.

     

    Abstract: Fractional-order PIλDμ controller expands the orders of integrator and differentiator of classical integer-order PID controller into fractional order.A PID controller can be designed flexibly by using the two parameters μ and λ.In this paper,an effective method for tuning the parameters of fractional-order PIλDμ controller-the poles-orders searching method-is proposed.The fundamental principle of the method is as follows: firstly proportional parameter KP of the fractional-order PIλDμ controller is estimated;secondly a pair of poles with better stability measures are designed;thirdly the searching ranges of μ and λ are estimated;finally the known parameter KP and the poles are introduced into the characteristic equation of fractional control system,and a group of parameters of the fractional-order PIλDμ controller in the ranges of μ and λ are found,which can meet performance requirements of the fractional control system in time domain.The simulation verifies that the fractional-order PIλDμ controller designed with poles-orders searching method can adjust the controlled system in a better way.

     

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