基于模型降阶的最优分数阶PID控制器设计

Design of Optimized Fractional Order PID Controller Based on Model Reduction[JZ)]

摘要:

由于一些受控对象较为复杂或者模型系统阶次较高,使得控制器的设计变得非常困难,这会造成控制系统的鲁棒性和动态特性下降;文章在H₂范数模型降阶的基础上提出一种新的降阶模型结构,它可以使降阶后的模型扩展到分数阶并且更加精确地逼近各种高阶系统,并以降阶后模型的幅频、相频和对象增益变化的鲁棒特性为约束条件进行最优分数阶PID控制器的设计；仿真实验证明,与原有闭环控制系统相比,基于模型降阶的最优分数阶PID控制器控制下的闭环系统具有更好的动态性能,并且鲁棒性较强。

Abstract:

The design of controllers are difficult because of the complex and high order control systems, which reduce the dynamic performance and robustness. First, this paper briefly introduces the common methods of H₂ norm model reduction, then a new model reduction based on that is proposed, which extends to the fractional order after the mode reduction and models a large variety of higher order systems with greater accuracy. And the optimal fractional PID controller is designed with the constraint conditions of the reduced order model of the phase margin and gain crossover frequency and robustness to gain variation. The simulation experiments prove that compared with the original closed-loop control system, the controlled by optimized fractional order PID can get better dynamic performance and have strong robust.