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    针对非线性不确定运动系统自抗扰控制的定量调参分析

    Quantitative Parameter Tuning Analysis of Active Disturbance Rejection Control Under Nonlinear Uncertain Motion Systems

    • 摘要: 高速高精运动系统通常含有多种不确定性,而克服不确定性使得闭环系统同时满足时域稳定性及频域相对稳定性,是一个具有挑战性的问题。针对含有非线性不确定动态的运动控制系统,给出了使得闭环系统稳定的自抗扰控制定量调参公式。由控制器参数,非线性不确定性大小和系统初值范围可定量得到扩张状态观测器带宽调节公式。针对所设计自抗扰控制的闭环系统,分别给出了控制系统幅值裕度、相位裕度和时延裕度与扩张状态观测器带宽的定量关系,并说明了相应控制系统的稳定裕度能够满足常用运动控制系统的要求。基于典型的含有非线性不确定动态的运动控制系统进行了多组数值仿真,考虑了系统模型多种不确定性下的仿真结果,说明了所提出参数调节方法的有效性。

       

      Abstract: loop systems meet the time-domain stability and the relative stability of frequency-domain becomes a challenging problem. Firstly, the quantity parameter tuning formula for disturbance rejection control(ADRC)of stable closed-loop systems is given for the dy⁃namic motion control system including nonlinear uncertainties. In detail, the bandwidth tuning formula of extended state observer can be quantitatively obtained by the controller parameters, the size of the nonlinear uncertainties, and the range of the initial values. Moreover, the quantity relationships among the amplitude margin, phrase margin, delay margin and bandwidth of extended state observer are pro⁃ vided, and the results indicate that the requirements of these stability margins of the relevant control system can be met by the commonly used motion control system. Finally, multiple groups of numerical simulations are performed based on a typical uncertain motion control system. The simulation results are considered under multiple types of uncertainties of a system model, and the effectiveness of the pro⁃posed methods is illustrated.

       

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