分数阶PIλDμ控制器参数λ和μ分析

Analysis of Parameters of λ andμ for Fractional Order PIλDμ Controller

针对分数阶PIλDμ控制器的积分阶次A和微分阶次μ在0〈λ，μ〈2的范围内变化时，对分数阶控制系统的影响进行了频率特性和阶跃响应分析，给出了阶次取值的合理范围。首先采用分数阶微积分方程的数值解法，对分数阶闭环控制系统进行数值计算，且其中的分数阶微积分算子用近似计算公式来代替。然后分别采用分数阶PIλ控制器和分数阶PDμ控制器当积分阶次A和微分阶次肛变化时，利用Bode图从频率特性和单位阶跃响应两方面分别对其性能进行分析，频率特性分析与实际阶跃响应的结果一致，表明分数阶PIλDμ矿控制器的积分阶次λ和微分阶次μ均有一较佳的取值范围。

The influence of frequency characteristic and step response performance for the fractional order control system while the integral order λand differential orderμ are changed in the range of 0 〈 λ ,μ 〈 2 for the fractional order PIλDμcontroller are analyzed. The reasonable ranges of orders are also obtained. Firstly, the numerical solution of fractional order differential equation is adopted to compute the numerical solution for the fractional order closed control system. The fractional order differential and integral operators are replaced by the approximate recurrent evaluate operator. Secondly, fractional order PIλ and PDμ controller are adopted to analyze the performance of control system which adopt the frequency characteristic and step response for fractional order control system while the integral order Aand differential orderμ change, respectively. The analyses of frequency characteristic are accord with the result of practical step response, which shown the integral order Aand differential orderμ of fractional order PIλDμcontroller have the better range.