基于QFT的鲁棒抗饱和设计

Design of anti-windup control systems based on QFT

针对具有执行器饱和以及参数大范围不确定性的LTI(线性时不变)控制系统的鲁棒稳定性问题,在研究QFT(定量反馈理论)传统的二自由度(2DoF)设计方案的基础上,提出一种基于QFT与圆判据绝对稳定理论相结合的三自由度(3DoF)鲁棒抗饱和设计方法。受控对象的不确定性利用对象模板进行描述,通过将抗饱和结构转化为Lur'e系统的稳定性问题,并运用圆判据确定Lur'e系统中线性环节的稳定边界,进而设计系统的抗饱和补偿器,使饱和发生时受控系统能够稳定到任意参数点。最后,通过数值仿真说明此方法设计的控制系统不仅能成功克服饱和非线性,而且对参数不确定性具有很好的鲁棒性。

Concerning the robust stability problem of linear time invariant （LTI） feedback control systems with both actuator saturation and potentially large parametric uncertainty, after the analysis of the traditional two degree of freedom （2DoF） control scheme used in QFT, a 3DoF robust anti-windup design method based on the combination between the QFT and the absolute stability theory Circle Criterion is proposed. In this paper, the uncertainty of the control system＇s plant was represented by plant template, and the anti-windup structure was transformed into Lur＇e equivalent system problem. Then using the circle criterion to obtain the stability boundary for the linear plot in the Lur＇e system, and based on the stability boundary, the anti-windup compensator was designed to guarantee that the controlled system is stable with arbitrary parameter when the saturation occurs. Finally, the simulation shows that the control system designed by this method can not only overcome the nonlinear saturation, but also robust to parameter uncertainties.