磁悬浮球的自适应径向基函数控制方法研究

Research on adaptive radial basis function control method of magnetic levitation ball

磁悬浮是集众多学科为一体的高新技术,具有无摩擦、清洁环保和安全可靠等优点。而悬浮控制作为磁悬浮技术的核心引起了人们的关注。以单点磁悬浮球作为研究对象,由于磁悬浮球系统具有高度非线性、随机不确定性和时滞性等特点,采用其他传统控制算法往往会引起系统超调量过大和响应速度过慢等问题。针对此类问题,提出一种不依赖于精确数学模型的自适应径向基函数(A-RBF)控制算法,以此实现磁悬浮球的稳定悬浮和获取系统满意的动态性能。首先建立磁悬浮球的非线性数学模型;其次通过非线性坐标变换得到磁悬浮球的线性数学映射模型;然后设计出A-RBF算法中相应的控制律和自适应律,并利用Lyapunov函数验证该算法的稳定性;最后通过不同的评判指标进行SMC和A-RBF算法的比较验证。仿真结果表明:由于A-RBF算法未忽略磁悬浮球系统中的高阶项,因此它不仅具有较快的响应速度和较小的超调量等优点,而且还具有适应系统参数变化范围大的能力。当依次输入正弦和方波信号作为输入时,A-RBF算法的跟踪效果最佳,其次为SMC。实验结果表明:当外部扰动存在时,A-RBF算法不仅实现了磁悬浮球的稳定悬浮,而且其误差仅在0.2 mm之内,并且在正弦跟随下的误差仅在0.15 mm之内,再次证明了A-RBF算法具有良好的适用性。

Magnetic levitation is an advanced technology that integrates many disciplines and offers advantages such as frictionless movement,cleanliness,environmental friendliness,safety,and reliability.Levitation control is the core of magnetic levitation technology and has attracted significant attention.Due to the high nonlinearity,random uncertainty,and time delay of the magnetic levitation ball system,traditional control algorithms often result in problems such as excessive overshoot and slow response speed.To address these issues,an adaptive radial basis function(A-RBF)control algorithm that is independent of accurate mathematical models was proposed to achieve stable suspension of a single-point magnetic levitation ball and obtain satisfactory dynamic performance of the system.First,the nonlinear mathematical model of the magnetic levitation ball was established.Second,the linear mathematical mapping model was obtained through nonlinear coordinate transformation.Then,the corresponding control law and adaptive law in the A-RBF algorithm were designed,and the stability of the algorithm was verified by using the Lyapunov function.Finally,the comparison and verification of the SMC algorithm and A-RBF algorithm were conducted by using different evaluation indicators.The simulation results demonstrates that the A-RBF algorithm has the advantages of fast response speed,small overshooting,and the ability to adapt to a wide range of changes in system parameters,as it takes the high-order terms in the magnetic levitation ball system into account.The tracking effect of the A-RBF algorithm is superior to that of the SMC algorithm when the sine and square wave signals are input sequentially.The experimental results show that even when external disturbances exist,the A-RBF algorithm can achieve stable suspension of the magnetic levitation ball with an error of only within 0.2 mm.The error under sinusoidal following is only within 0.15 mm,which once again proves the good applicability of the A-RBF algorithm.