线性自抗扰控制系统的鲁棒稳定性

On robust stability of linear active disturbance rejection control system

针对线性自抗扰控制系统,研究了模型参数不确定情况下的鲁棒稳定性问题.首先给出对象为非自治模型时该系统的H∞判据.然后针对线性误差模型的状态矩阵只在某一行存在不确定参数的情况,基于奇异值理论,得到H∞判据的一种新的等价描述,把H∞范数约束转化为对奈奎斯特图的约束.之后为了降低新判据在实际应用中的保守性,对不确定性矩阵的分解方式进行优化.在此基础之上提出了一种新的方法,用于计算时变参数不确定性的最大边界,为线性自抗扰控制器设计提供理论依据.数值实例表明该方法不仅保守性小,而且计算简单.

In this paper, the robust stability problem is studied for the linear active disturbance rejection control（LADRC） system in the presence of parameter uncertainties. Firstly, the H-infinity criterion is presented for the LADRC system with a non-autonomous plant. Secondly, for the case that the uncertain parameters are in the same line of the state matrix of the linear error model, a novel equivalent description of the H-infinity criterion is derived from the singular value theory.With the equivalent description, the H-infinity norm constraint is transformed to the constraint on the Nyquist diagram.Thirdly, the uncertainty matrix decomposition is carried out with optimization to reduce the conservatism of the new criterion in practical application. Based on the above work, a new approach is proposed to compute the maximal bound of time-varying parameter uncertainties and supply some theoretical basis for the design of the linear active disturbance rejection controller. Numerical examples show that the proposed approach is not only less conservative, but also simpler to calculate.