变分数阶振子振动控制方法研究

Active vibration control method for variable order oscillator

针对含变分数阶的无量纲振子振动方程,考虑变分数阶微分算子表达式的复杂性,直接进行控制器设计不现实。通过分析位移时程曲线,采用截断变分数阶微分算子方式获得较好拟合效果。提出变遗忘因子概念,使变分数阶算子变为有限阶次,用其进行控制器设计成为可能,并仿真实例验证该方法的有效性。

The dimensionless version of a model oscillator was studied, whose equation of motion is given. Due to the complication of the approximate expression of variable order（VO） differential operator, it is difficult to design directly the controller. Based on the analysis of the curve of displacement versus time, a truncation mode of VO differential operator was proposed. The concept of variable oblivion factor was introduced, meanwhile, an optimal controller was developed for the VO differential equation under study in order to reduce the dynamic responses.