论文标题
在IDA-PBC中的动能形状的匹配方程式上
On the Matching Equations of Kinetic Energy Shaping in IDA-PBC
论文作者
论文摘要
通过总能量塑料，基于互连和阻尼分配的基于被动控制方案已用于稳定许多物理系统，例如机械系统不足的机械系统。在这种方法中，应通过分析求解通过动力学和势能塑造产生的某些部分微分方程（PDE）。找到合适的所需惯性基质作为与动能塑造相关的非线性PDE的解决方案是一个具有挑战性的问题。 在本文中，提出了一种系统的系统方法来解决该匹配方程，以确定一个程度不足的系统。提出了所需的惯性基质的特殊结构，以简化相应的PDE的溶液。结果表明，所提出的方法比文献中一些报告的方法更笼统。为了得出合适的所需惯性矩阵，还会得出必要的条件。提出的方法适用于三个示例，包括VTOL飞机，Pendubot和2D Spidercrane系统。
Interconnection and damping assignment passivity-based control scheme has been used to stabilize many physical systems such as underactuated mechanical systems through total energy shaping. In this method, some partial differential equations (PDEs) arisen by kinetic and potential energy shaping, shall be solved analytically. Finding a suitable desired inertia matrix as the solution of nonlinear PDEs related to kinetic energy shaping is a challenging problem. In this paper, a systematic approach to solve this matching equation for systems with one degree of underactuation is proposed. A special structure for desired inertia matrix is proposed to simplify the solution of the corresponding PDE. It is shown that the proposed method is more general than that of some reported methods in the literature. In order to derive a suitable desired inertia matrix, a necessary condition is also derived. The proposed method is applied to three examples, including VTOL aircraft, pendubot and 2D SpiderCrane system.
