球杆系统的建模、仿真与控制器设计

Modeling,simulation and controller design of ball-beam system

球杆系统是一个非线性不稳定系统,其中小球在导轨上滚动过程的动态描述十分复杂.通过建立球杆系统机械部分模型、角度模型和电机模型,简化后得到了整个球杆系统的传递函数.同时通过设计最优鲁棒控制器、最优瞬态控制器和二自由度控制器对其进行控制,证明了系统是可控的和稳定的.在Matlab的Simulink环境下的仿真试验也印证了上述结论.充分说明了球杆系统对学习控制理论来说是一个很好的实验装置.

Ball-beam system is a nonlinear and unstable system. The dynamic description of the ball roiling on the beam is quite complex. By modeling the mechanical part, angle and motor of the ball-beam system, the simplified transfer function of the ball-beam system is obtained. By applying optimal robust controller, optimal transient controller and two freedoms controller to the system, it is proved that the system is controllable and stable. Simulations under Simulink of the Matlab also show that the system has the same behavior. It is demonstrated that the ball-beam system is a good test device for learning control theory.