论文标题
Pfaffian微分方程的IDA-PBC方程的匹配方程解决方案
Solution of matching equations of IDA-PBC by Pfaffian differential equations
论文作者
论文摘要
在新开发的方法中，找到部分微分方程（PDE）的一般解决方案对于控制器设计至关重要。基于互连和阻尼分配的基于消极的控制（IDA-PBC）是这样的方法之一，在这种方法中，需要在实践中应用称为匹配方程的相应PDE的解决方案。在本文中，这些匹配方程转换为相应的PFAFFIAN微分方程。此外，结果表明，在满足整合性条件后，可以很容易地获得相应的三阶Pfaffian微分方程的解决方案。该方法应用于某些基准系统（例如磁性悬浮系统，Pendubot和电缆驱动的机器人）中的IDA-PBC的PDE，以验证其适用性。
Finding the general solution of partial differential equations (PDEs) is essential for controller design in newly developed methods. Interconnection and damping assignment passivity based control (IDA-PBC) is one of such methods in which the solution to corresponding PDEs which are called matching equations, is needed to apply it in practice. In this paper, these matching equations are transformed to corresponding Pfaffian differential equations. Furthermore, it is shown that upon satisfaction of the integrability condition, the solution to the corresponding third-order Pfaffian differential equation may be obtained quite easily. The method is applied to the PDEs of IDA-PBC in some benchmark systems such as Magnetic levitation system, Pendubot, and underactuated cable driven robot to verify its applicability.
