Control Oriented Modeling, Experimentation, and Stability Analysis of an Autorotating Samara
Control Oriented Modeling, Experimentation, and Stability Analysis of an Autorotating Samara
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自转翅片的面向控制的建模、实验和稳定性分析
DOI：
10.1115/1.4062438
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Das, Tuhin
中科院分区：
文献类型：
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作者：
McConnell, Jonathan;Das, Tuhin
本文建立了一个面向控制的模型，用于描述单翼萨马拉种子荚在自转下降过程中的稳态和动态行为。可忽略的横向质心运动和恒定的规定滚转角，以开发简化和紧凑的模型。展向空气动力学相关性被交换为具有两个调谐参数的独立叶素表示，以考虑前缘涡现象的影响。由此产生的模型是一个四阶非线性动力系统。该模型的准确性是通过验证它对我们自己的实验数据，以及对其他研究人员在文献中报道的。验证工作表明，零滚转角是一个可行的假设，显着降低模型的复杂性，同时保持准确性。推导出了萨马拉在自由下降时存在稳定自转的必要条件。此外，进行了稳定性分析表明，四阶系统的特征值，线性化的自转平衡，可以很好地表示为两个解耦的二维系统。分析揭示了决定持续自转稳定性的关键参数。这种稳定性分析为未来模型改进的类似分析探索提供了平台。这个紧凑的模型的有效性表明，设计和控制简单的自转机构的基础上，这些动力学的可扩展性。
This paper presents a control-oriented model for describing the steady-state and dynamic behavior of a single-winged samara seed-pod in autorotative descent. A negligible lateral center of mass motion and constant, prescribed roll-angle to develop a simplified and compact model. Spanwise aerodynamic dependence is exchanged for an independent blade element representation with two tuned parameters to account for the effects of leading-edge vortex phenomena. The resulting model is a fourth-order nonlinear dynamical system. The accuracy of this model is established by validating it against our own experimental data as well as against those reported in the literature by other researchers. The validation exercise reveals that zero roll-angle is a viable assumption that significantly reduces model complexity while retaining accuracy. A necessary condition is derived for the existence of steady autorotation of the samara under free descent. Furthermore, a stability analysis is conducted suggesting that the eigenvalues of the fourth-order system, linearized about the autorotational equilibrium, can be well-represented by those of two decoupled two-dimensional systems. The analysis reveals the critical parameters that determine stability of sustained autorotation. Such stability analysis provides a platform for similar analytical exploration of future model improvements. The validity of this compact model suggests the plausibility of designing and controlling simple autorotative mechanisms based on these dynamics.