参数不确定时滞系统分数阶PI~λD~μ控制器稳定域算法

Algorithm for stability region of parameter uncertain system with time delay using fractional-order PI~λD~μ controller

对分数阶PIλDμ控制器提出了求解参数不确定时滞系统稳定域的方法。通过Kharitonov理论将参数不确定时滞系统分解为若干参数确定的子系统,根据D分解方法分别求出使各个子系统获得最大稳定域时的PIλD和PIDμ控制器的参数λ和μ,获得了PIλDμ控制器的参数。以这个PIλDμ控制器去计算各个子系统的稳定域,各子系统稳定域的交集即为参数不确定时滞系统的稳定域。采用参数不确定时滞系统对此算法进行了验证,表明本算法在计算分数阶PIλDμ控制器的稳定域上是可行有效的。

This paper presents a new algorithm for solving the stability region of a parameter uncertain system with time delay using PIλDμ controller.Firstly,Kharitonov theorem is used to decompose the parameter uncertain system into several subsystems.Secondly,D-decomposition method is applied to solve the biggest stability region of each subsystem.The values of λ and μ of PIλD and PIDμ controllers corresponding to the biggest stability regions are obtained.A new PIλDμ controller is constructed using the obtained values of λ and μ.Thirdly,the stability regions of the subsystems are calculated using the new PIλDμ controller.Finally,the intersection of the stability regions of the subsystems is the stability region of the parameter uncertain system with time delay.The algorithm was verified by a parameter uncertain integer order plant with time delay and result indicates that the algorithm is feasible and effective in calculating the stability region of fractional order PIλDμ controller for parameter uncertain system.