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针对分数阶系统,提出了一种基于伯德理想传递函数的分数阶比例-积分-微分(PID)控制器设计方法.首先分析了伯德理想传递函数的增益和分数阶微积分阶次分别与系统动态性能和鲁棒性之间的关系,然后将伯德理想传递函数作为参考系统,选择分数阶被控对象的阶次作为控制器中微积分阶次,并根据系统动态响应性能和鲁棒性调节增益K,简化了控制器参数的整定.仿真结果表明:所提方法不但设计简单,整定方便,而且具有较好的动态性能、干扰抑制特性,以及克服系统参数变化的鲁棒性.
Aiming at the fractional order system, a fractional-order proportional-integral-derivative (PID) controller design method based on the Byrd ideal transfer function is proposed.Firstly, the relationship between the gain and fractional order calculus of Byrd’s ideal transfer function Then, the ideal transfer function of Byrd is taken as the reference system, the order of fractional order controlled objects is chosen as the order of the calculus in the controller, and according to the system dynamic response performance and robustness Adjust the gain K, which simplifies the tuning of the controller parameters.The simulation results show that the proposed method not only has the advantages of simple design, convenient setting, but also has better dynamic performance, interference suppression characteristics and robustness to overcome the system parameter changes.