CAJ | 학술논문

对区间参数分数阶时滞系统，提出了对分数阶PIλDμ控制器求其鲁棒稳定域的方法。利用边界理论将区间参数分数阶时滞系统分解为若干顶点子系统，求出各顶点子系统特征多项式和与之相对应凸多面体棱边的集合。应用D分解方法分别求出使各子系统获得最大稳定域时的PIλD和PIDμ控制器的参数λ和μ，从而获得了分数阶PIλDμ控制器的参数。由该分数阶PIλDμ控制器计算各个子系统的稳定域，各子系统稳定域的交集即为原区间参数时滞系统的稳定域；并证明了该域为区间参数分数阶时滞系统的鲁棒稳定域。通过实例的验证表明，该算法是可行有效的。
대구간삼수분수계시체계통，제출료대분수계PIλDμ공제기구기로봉은정역적방법。이용변계이론장구간삼수분수계시체계통분해위약간정점자계통，구출각정점자계통특정다항식화여지상대응철다면체릉변적집합。응용D분해방법분별구출사각자계통획득최대은정역시적PIλD화PIDμ공제기적삼수λ화μ，종이획득료분수계PIλDμ공제기적삼수。유해분수계PIλDμ공제기계산각개자계통적은정역，각자계통은정역적교집즉위원구간삼수시체계통적은정역；병증명료해역위구간삼수분수계시체계통적로봉은정역。통과실례적험증표명，해산법시가행유효적。
The paper presents a method to compute the robust stability region of fractional order interval plant with time delay by using fractional order PIλDμ controller. The edge theorem is adopted to decompose interval plant to several vertices sub-plants. The characteristic polynomials of vertices sub-plants and the value set of exposed edge for polytope are given. The D-decomposition technique is applied to solve the stability region of each vertices sub-pant. The values ofλandμof PIλD and PIDμ controllers are obtained in the biggest stability region of all sub-plants. The fraction order PIλDμ controller is constructed by the values of λ and μ. The stability region of each sub-plant is plotted by using fractional order PIλDμ controller. Furthermore, the overlap of stability region of each sub-plant is the stability region of fractional order interval plant with time delay. The paper also proves that the overlap of stability region is the robust stability region of fraction order interval plant.