Abstract

An autonomous mechanical system with two rotational degrees of freedom, undergoing the action of conservative and nonconservative forces, is considered. The corresponding dynamical system contains changeable parameters that can be treated as amplifying coefficients for control actions. It is required to select the values of these parameters in order to form an autorotation mode in the system that possesses the prescribed properties. We propose an iterative search method for the corresponding values of the parameters. This approach is a modification of the Andronov–Pontryagin method and, unlike the latter, it does not assume that there is a small parameter in the system. We provide an example of the application of the proposed method to a model of a wind turbine: the value of the parameter, ensuring the existence of a mode with a high value of the mechanical power trapped from the flow, is selected. In the dynamical system, an attractor that is a trajectory close to a periodic one corresponds to this mode.

中文翻译：

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具有两个自由度的可控机械系统中自动旋转的形成方法

摘要

考虑具有两个旋转自由度的自主机械系统，该机械系统受到保守和非保守力的作用。相应的动力学系统包含可变参数，这些可变参数可以视为控制动作的放大系数。需要选择这些参数的值，以便在具有规定属性的系统中形成自动旋转模式。我们为参数的相应值提出了一种迭代搜索方法。该方法是对Andronov–Pontryagin方法的修改，并且与后者不同，它不假定系统中的参数很小。我们提供了将建议的方法应用于风力涡轮机模型的示例：参数的值，选择确保存在从流中捕获的具有较高机械动力值的模式。在动力系统中，接近周期的轨迹的吸引子对应于该模式。