李冰林 曾励 张鹏铭 竺志大

摘 要：针对单自由度磁悬浮系统的非线性、不确定性和易受扰动等特点，提出一种基于扩张状态观测器的反步控制方法以提高系统的控制性能。在系统受到不确定性扰动的情况下，运用扩张状态观测器实时估计悬浮球的位置、速度和扰动信息，并将这种估计值与控制器设计相结合，然后采用反步法设计磁悬浮球的悬浮位置跟踪控制律，以Lyapunov方法证明系统的跟踪误差最终有界收敛。仿真结果表明，ESO-BS控制与PID控制相比，前者系统调节时间为0.01 s，后者调节时间为0.08 s，明显偏长，因此，ESO-BS控制的动态特性要优于PID控制。在系统存在不确定性的条件下，所设计的控制律能实现磁悬浮球的稳定悬浮，并能根据要求的悬浮高度位置实现位置跟踪。

关键词：控制系统仿真技术;磁悬浮球;扩张状态观测器;反步控制;位置跟踪

中图分类号：TH117.1 文献标识码：A

doi：10.7535/hbkd.2021yx02007

Back-stepping control based on extended state observer for magnetic levitation ball

LI Binglin1，2，3，ZENG Li2，ZHANG Pengming3，ZHU Zhida2

（1.College of Automobile and Traffic Engineering，Nanjing Forestry University，Nanjing，Jiangsu 210037，China;2.College of Mechanical Engineering，Yangzhou University，Yangzhou，Jiangsu 225009，China; 3.Zhejiang Jinggong Science & Technology Company Limited，Shaoxing，Zhejiang 312030，China）

Abstract：Aiming at the characteristics of non-linearity，uncertainty and susceptibility to disturbance of single-degree-of-freedom magnetic levitation ball system，a back-stepping control method based on extended state observer （ESO-BS） was proposed to improve the control performance of the system.The extended state observer was used to estimate the position，velocity and disturbance information of the levitation ball in real time when the system was disturbed by uncertainty.The estimation was combined with the controller design，then the back-stepping method was used to design the levitation position tracking control law of the magnetic levitation ball，and the Lyapunov method was used to prove the ultimate bounded convergence of the tracking error of the system.The simulation results show that，compared with PID control，the adjusting time of ESO-BS control system is 0.01 s，while that of PID control is 0.08 s，which is obviously longer，so the dynamic characteristic of ESO-BS control is better than that of PID control.When there is uncertainty in the system，the designed control law can realize the stable suspension of the ball，and can realize the position tracking according to the required suspension height position.

Keywords：

control system simulation technology; magnetic levitation ball; extended state observer（ESO）; back-stepping control; position tracking

磁懸浮能使机械实现无摩擦、无需润滑高速运转，在交通、国防、工业等领域有较大的应用前景[1-2]。单自由度的悬浮系统具有非线性、开环不稳定的特性[3]，通常方法都是将系统在平衡点处线性化，然后再设计控制算法，如文献[4—5]采用的PID控制和模糊PID控制，尽管这些控制有一定的鲁棒性能，但容易使系统性能变得超调。考虑模型扰动的鲁棒控制虽然对模型的摄动有一定的容许度，但是该控制方法也需要合理选择灵敏度加权函数[6-7]。滑模控制响应快、对参数变化不敏感，但需要解决变结构时的抖振问题[8]。……