小球-滑板系统建模与鲁棒控制器设计

The Modeling and Robust Controller Design of the Ballbeam System

小球-滑板系统是一个非线性不稳定系统,小球在滑板上滚动过程的描述十分复杂。通过建立系统机械模型、角度模型和电机模型,经简化后得到系统的传递函数。系列简化和假设导致实际物理系统和数学模型之间的差异,主要包括有系统参数变动,未建模动态特性,未建模时滞等等。针对数学模型的不足,提出了系统参数变化时的鲁棒PID控制器设计方案,并讨论了在未建模时滞影响下该控制系统的稳定性能。仿真结果表明,该控制器鲁棒性能强,系统可行。

The ball-beam system is a nonlinear and unstable system. The dynamic description of the ball position on the beam is quite complex. By modeling the mechanical part and motor of the system, the transfer function of the system is obtained, based on a set of assumptions that may not reflect reality. The difference between the physical system and the mathematical model arises from many sources, including parameter changes, un-modeled time-delays, and so on. In this paper, the robustness of a PID controller design is researched to changes in important parameters. The robust stability is also discussed in the uncertain time-delay models based on the so-called small gain theorem. The controller is verified via simulation that it＇s feasible for the system enhancing the robustness.