区间参数分数阶时滞系统鲁棒稳定域

摘要

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。%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.