分数阶参数不确定系统的PIλ控制器

Design of fractional order PIλ controller for fractional order systems with uncertain parameters

利用求解分数阶参数不确定系统稳定域的方法,设计了使分数阶参数不确定系统具有鲁棒性的分数阶PIλ控制器.首先采用Kharitonov理论,将分数阶参数不确定系统分解成若干个参数确定的子系统,然后用D分解方法分别求出在PIλ控制器的控制下,使各个子系统都取得较大稳定域的参数λ值.再采用此λ值构建PIλ控制器并计算各个子系统的稳定域.各个子系统稳定域的交集即为参数不确定系统在PIλ控制器控制下的稳定域.同时证明了所构建的PIλ控制器能稳定整个参数不确定系统组.最后在稳定域内取控制器参数值,便构成了所设计的PIλ控制器.文中采用实例对此设计方法进行验证,并用所构建的PIλ控制器对参数不确定系统组的各个子系统进行阶跃响应分析,结果表明PIλ控制器对参数不确定系统具有较强的鲁棒性.

The paper presents a method for designing the robust fractional order PI^λ controller by computing the stability region of the fractional order system with uncertain parameter. Firstly, the Kharitonov theorem is adopted to decompose the original fractional order system with uncertain parameters into several subsystems with parameter certainties. Secondly, the D-decomposition technique is applied to compute the stability region of each subsystem to determine the parameter ）, value which uniformly ensure a bigger stability region for all subsystem. Thirdly, with the parameter X value, we design a fractional order PI^λ controller for each subsystem and computer its stability region. The intersection of the obtained stability regions is considered the stability region of the original system under the control of the designed PI^λ controller. This paper proves that the designed PI^λ controller stabilizes the original fractional order system with uncertain parameters. Finally, the fractional order PI^λ controller is constructed based on the control parameters in the stability region. The proposed method is illustrated by an example. The step response of each subsystem is analyzed when using this PI^λ controller. The result shows that fractional order PI^λ controller has stronger robustness for the fractional order system with uncertain parameters.