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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。
Aiming at the problem of robust stability of LTI (linear time-invariant) control system with actuator saturation and large-scale uncertainties of parameters, based on the study of QFT (Quantitative Feedback Theory) traditional 2 DOF design , A three degree of freedom (3DoF) robust anti-saturation design method based on QFT and circular stability theory is proposed. The uncertainty of the controlled object is described by using the object template. By transforming the anti-saturated structure into the Lur’e system stability problem and using the circular criterion to determine the stable boundary of the linear link in the Lur’e system, Anti-saturation compensator, so that the controlled system can stabilize to any parameter point when saturation occurs. Finally, the numerical simulation shows that the control system designed by this method can not only successfully overcome the saturation nonlinearity, but also has good robustness to parameter uncertainty.