基于扩张状态观测器的液体静压轴承重复控制技术研究  

Research on Repetitive Control Technology of Liquid Hydrostatic Bearing Based on Extended State Observer

作　　者：孙文龙 潘伟[1,2] 向绍通 张艺馨 张聪 路长厚[1,2] SUN Wenlong;PAN Wei;XIANG Shaotong;ZHANG Yixin;ZHANG Cong;LU Changhou(School of Mechanical Engineering,Shandong University,Jinan 250061;Key Laboratory of High-efficiency and Clean Mechanical Manufacture,Ministry of Education,Shandong University,Jinan 250061)

机构地区：[1]山东大学机械工程学院,济南250061 [2]山东大学高效洁净机械制造教育部重点实验室,济南250061

出　　处：《机械工程学报》2025年第5期126-137,共12页Journal of Mechanical Engineering

基　　金：国家自然科学基金(51975337);山东省自然科学基金(ZR2019MEE064)资助项目。

摘　　要：重复控制(Repetitive control,RC)是根据上个周期的误差信号计算新的输入的控制策略,被广泛用于可重复操作的领域。静压轴承的主轴的径向位移可以分解为水平方向和竖直方向的周期运动,因此可以运用重复控制的方法实现振动抑制、轴心轨迹跟踪等。但可控液体静压轴承转子系统是非线性的,存在耦合因素,同时受到加工误差和环境噪声等非周期性干扰,因此提出了一种基于扩张状态观测器(Extended state observer,ESO)的RC策略,前者可以将非周期扰动以及非线性因素观测出来并加入到线性状态反馈控制器中进行补偿,而后者保证了良好的周期轨迹跟踪精度和周期扰动抑制能力。针对可控静压轴承转子系统,推导了ESO的收敛条件和改进后的控制系统的稳定性条件。最后,通过仿真和实验对所提方法进行验证,并与经典的PID控制和传统的RC进行了对比。结果表明,基于ESO和RC的液体静压轴承主动控制比传统RC和PID方法有更好的轴心轨迹跟踪能力和扰动抑制能力。Repetitive control(RC)is a control strategy that calculates a new input based on the error signal of the previous cycle,and is widely used in repeatable operations.The displacement of the spindle of a hydrostatic bearing rotor system can be decomposed into periodic motions in the horizontal and vertical directions,so that vibration suppression,axis trajectory tracking,etc.can be achieved by applying repetitive control methods.However,the hydrostatic bearing rotor system is non-linear and there are coupling factors as well as non-periodic disturbances such as machining errors and environmental noise,so a repetitive control(RC)strategy based on extended state observer(ESO)is proposed,where the former can observe the non-periodic disturbances as well as non-linear factors and add them to the linear state feedback controller for compensation,while the latter ensures good accuracy of periodic trajectory tracking and periodic disturbance suppression.The convergence conditions of the ESO and the stability conditions of the improved control system are derived for the controlled hydrostatic bearing rotor system.Finally,the proposed strategy is validated by simulation and experiment,and compared with classical PID control and conventional RC.The results show that the ESO-based RC has better signal tracking capability and disturbance rejection than the conventional RC and PID.

关 键 词：液体静压轴承 可控轴承 扩张状态观测器 重复控制 轴心轨迹跟踪 

分 类 号：TH137[机械工程—机械制造及自动化]