欠驱动球棒系统不动点控制器设计

Design of Fixed Point Controller for Underactuated Ball-and-Beam System

针对欠驱动系统的Benchmark球棒系统,考虑球与棒之间的摩擦系数系统动力学及球质心与棒支点之间垂直于棒方向上的距离,建立其精确的数学模型。基于部分反馈线性化,利用坐标变换将系统动力学转换为便于控制器设计的非三角结构级联规范型,并采用不动点控制方法设计控制器,实现球棒系统的稳定控制。仿真实验表明,在球棒系统的控制过程中考虑系统摩擦系数及球质心与棒支点之间垂直于棒方向上的距离十分必要,并且不动点控制器具有良好的动态性能和强鲁棒性。

To the Ball-and-Beam（BNB）benchmark system of under-actuated mechanism,considering the friction coefficient between the ball and beam and the distance from the centroid of the ball to the fulcrum of beam in vertical direction of the beam,the precise dynamics is established.Based on partial feedback linearization,the system dynamics is transformed into non-triangle cascaded normal form which is easy for controller design by utilizing changes of coordinates.And the fixed point controller is designed to stabilize the BNB system.Simulation result shows that the friction coefficient and distance are quite necessary for the controller design,and the fixed point controller has excellent dynamic performance and strong robustness.