Abstract

We propose a solution of the robust stabilization problem for linear dynamic plants with unknown parameters belonging to a known compact set, bounded exogenous disturbances, and bounded high-frequency measurement noise. The control algorithm synthesis is divided into two stages. The filtering algorithm synthesized at the first stage permits one to reduce the influence of the measurement noise on the plant output variable. Constructive conditions for selecting the filtering algorithm parameters are proposed for the case in which the measurement noise can be represented as a sum of sinusoidal signals. At the second stage, we synthesize a control algorithm suppressing the influence of the parametric uncertainty and exogenous disturbances. This algorithm is based on the use of finite differences in continuous time; this allows avoiding the use of dynamic observers increasing the dimension of the closed-loop system. Simulation results illustrating the efficiency of our algorithm in comparison with some existing analogs are presented. A comparative analysis with the results by Astolfi et al. has shown that our control algorithm has lower dynamic order and guarantees higher accuracy in the output signal and its derivatives. Moreover, the algorithm parameter selection in our algorithm is easier owing to the independent adjustment of the filter and control law in contrast to the results by Astolfi et al., where the controller parameters are selected simultaneously for the entire algorithm.

中文翻译：

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存在干扰和高频测量噪声时线性设备的稳健稳定

摘要

我们提出了一种线性动态植物的鲁棒稳定问题的解决方案，其中未知参数属于已知紧凑集、有界外生干扰和有界高频测量噪声。控制算法综合分为两个阶段。在第一阶段合成的滤波算法允许减少测量噪声对工厂输出变量的影响。针对测量噪声可以表示为正弦信号之和的情况，提出了选择滤波算法参数的构造条件。在第二阶段，我们综合了一种控制算法来抑制参数不确定性和外生干扰的影响。该算法基于使用连续时间的有限差分；这允许避免使用动态观察器增加闭环系统的维度。仿真结果说明了我们的算法与一些现有类似物相比的效率。与 Astolfi 等人的结果进行比较分析。已经表明，我们的控制算法具有较低的动态阶数，并保证了输出信号及其导数的较高精度。此外，与 Astolfi 等人的结果相比，我们算法中的算法参数选择更容易，因为滤波器和控制律的独立调整，其中控制器参数是为整个算法同时选择的。仿真结果说明了我们的算法与一些现有类似物相比的效率。与 Astolfi 等人的结果进行比较分析。已经表明，我们的控制算法具有较低的动态阶数，并保证了输出信号及其导数的较高精度。此外，与 Astolfi 等人的结果相比，我们算法中的算法参数选择更容易，因为滤波器和控制律的独立调整，其中控制器参数是为整个算法同时选择的。仿真结果说明了我们的算法与一些现有类似物相比的效率。与 Astolfi 等人的结果进行比较分析。已经表明，我们的控制算法具有较低的动态阶数，并保证了输出信号及其导数的较高精度。此外，与 Astolfi 等人的结果相比，我们算法中的算法参数选择更容易，因为滤波器和控制律的独立调整，其中控制器参数是为整个算法同时选择的。