基于变量梯度法的磁悬浮控制系统的状态稳定性

State stability of maglev control system based on variable gradient method

磁悬浮系统是个典型的非线性系统,将非线性系统进行线性化后设计磁悬浮控制器,可以保证系统在平衡点附近稳定,但是当存在较大的干扰时,系统有可能失去稳定.本文分析单支点悬浮系统的稳定性,运用变量梯度法构造李雅普诺夫函数,推导出系统相对于平衡点的状态稳定保守区间,给出了系统的一个抗干扰程度,当磁悬浮系统受到较大干扰而偏离这一区间时,就应采取必要的自适应控制措施.最后用试验验证了这种控制方案的可行性.

Magnetic levitation system is a typical nonlinear system. A controller based on linear magnetic levitation system can guarantee the system＇s stability around the equilibrium point. In fact, under severe disturbance the system＇s stability may be destroyed. The stability of single point magnetic levitation system is analyzed. A Lyapunov function is built by the variable gradient method, and a conservative state stability region is then derived. When the magnetic levitation system moves away from the stability region by severe disturbance, an adaptive control action should be taken. Finally the feasibility of this method is testified by our experiments.