基于LuGre模型的有摩擦结构自适应主动振动控制

Adaptive active vibration control for frictional structures based on LuGre model

针对参数不确定的有摩擦结构振动控制问题,设计一种基于LuGre动态摩擦模型的模型参考自适应控制器(MRAC)。采用LuGre动态模型描述系统摩擦力,建立单自由度有摩擦结构的动力学模型;以理想的Skyhook结构为参考模型,使用双观测器估计摩擦状态,设计了一种模型参考自适应主动振动控制器,并通过Iyapunov方法证明整个闭环系统具有全局稳定性,位移跟踪误差和速度跟踪误差渐进收敛到零。利用Simulink进行仿真研究,仿真结果表明,该控制器可以显著地减小有摩擦结构在共振频率附近的响应,并改善系统在较高频率的隔振性能。

Based on LuGre dynamic friction model, a model reference adaptive controller （MRAC） was proposed to solve vibration isolation problems of frictional structures with undetermined parameters. The dynamic model of a single-degree-of-freedom （SDOF） frictional structure was established using LuGre dynamic friction model to describe the friction force. Choosing an ideal Skyhook structure as a reference model, a dual-observer was used to estimate the friction state, and a MRAC active controller was designed. It was shown with Lyapunov method that the closed-loop system is asymptotically stable, and both the displacement tracking error and the velocity tracking one converge to zero. The simulation results showed that this kind of controller not only greatly decreases the response of frictional structures near the resonance frequency, but also improves the system＇s vibration isolation performance at higher frequency.