控制系统的分数阶建模及分数阶PI^λD^μ控制器设计

Fractional order model for control system and design of fractional order PI^λD^μ controller

在系统分析与设计过程中,针对高阶动态系统所具有的时滞性,常常利用具有延迟环节的一阶(first order plus time delay,FOPTD)或者二阶系统(second order plus time delay,SOPTD)模型对其进行近似处理,由于建模误差过大影响所描述系统的准确性和控制性能。本文给出了具有延迟环节的新型非整数阶类一阶系统模型(non-integer order plus time delay,NIOPTD),并分别设计了某高阶系统降阶得到的传统模型与新型类一阶系统近似模型,对比分析新型类一阶系统模型的优点与可行性。针对上述3种系统模型(FOPTD、SOPTD、NIOPTD)在频域内给出分数阶PIλDμ控制器新的参数整定方法,通过仿真对比分析得出方法的有效性,并证实分数阶PIλDμ控制器作用于NIOPTD模型具有最好的控制性能和鲁棒稳定性。

For the delay performance of the higher order dynamic system model in the process of system analysis and design, first or second order plus time delay system model are used to make approximations for it, but the described system accuracy and control performance are reduced because of oversize error of the model. A new non-integer order plus time delay （NIOPTD） system model was designed, then the tra- ditional model and the NIOPTD model were received to take the place of a higher order system, and the advantages of the NIOPTD system model were given via comparisons. A new method of fractional order controller parameter tuning in frequency domain was given for the three system models （first order, sec- ond order system and NIOPTD）. Simulations results illustrate that the best control performance and robust stability can be performed as desire by utilizing NIOPTD system model.