基于ESO与线性化反馈的磁悬浮球系统自适应全局积分滑模控制

Adaptive Global Integral Sliding Mode Control of Magnetic SuspensionBall System Based on ESO and Linearized Feedback

【目的】本文针对磁悬浮球系统的非线性特性、不确定性以及其易受外部扰动影响的特性,将线性化反馈控制与自适应全局积分滑模控制(AGISMC)相结合,优化系统控制效果、提高控制精度。【方法】首先,通过线性化反馈建立数学模型,使用自适应控制实现对系统参数的实时估计,降低系统的不确定性;其次,引入全局函数以改善系统的瞬态响应,将滑模函数中的符号函数替换为饱和函数以减小系统抖振;再次,在不确定干扰方面,利用扩张状态观测器(ESO)对系统未知干扰信号做出实时估计;最后,基于Matlab/Simulink进行仿真分析,并搭建试验平台进行试验验证。【结果】仿真和试验结果表明:AGISMC-ESO控制器与比例积分微分(PID)控制器在阶梯响应时均没有超调,且本文设计的AGISMC-ESO控制器到达稳态的时间更短;AGISMC-ESO控制器能在扰动出现后更快进行补偿,使系统快速到达稳态;施加正弦信号下,磁悬浮系统的实际运动轨迹与ESO所观测的位移曲线基本吻合。【结论】与PID控制器相比,本文设计的AGISMC-ESO控制器具有更快的响应速度、更高的控制精度、更好的动态跟踪性能和更优的抗干扰性能。

[Objective]This paper combined linearized feedback control with adaptive global integral sliding mode control(AGISMC)to optimize the control performance and the control accuracy of the system based on the nonlinear characteristics,uncertainty and susceptibility to external perturbations of the magnetic suspension ball system.[Methods]First,a mathematical model was established using linearized feedback,and adaptive control was employed to achieve real-time estimation of the system parameters to reduce the uncertainty.Second,a global function was introduced to improve the transient response of the system,and the sign function in the sliding mode function was replaced with a saturation function to reduce system chattering.Third,for uncertain disturbances,an extended state observer(ESO)was utilized to estimate unknown disturbance signals in real time.Finally,simulations were conducted in Matlab/Simulink,and an experimental platform was built for validation.[Results]Simulation and experimental results showed that neither the AGISMC-ESO controller nor the proportional integral derivative(PID)controller exhibited overshoot in step response,with the AGISMC-ESO controller achieving a shorter time to reach steady state.The AGISMC-ESO controller compensated more quickly when disturbances occur,allowing the system to reach a steady state rapidly.Under the application of a sinusoidal signal,the actual trajectory of the magnetic suspension system closely matched the displacement curve observed by the ESO.[Conclusion]Compared to the PID controller,the AGISMC-ESO controller designed in this paper offers faster response speed,higher control accuracy,better dynamic tracking performance,and superior disturbance rejection.