三维椭圆振动切削系统模糊自适应滑模控制

三维椭圆振动切削被认为是目前最具潜力的机械加工方式,但是加工过程中的控制问题还未被很好的解决,特别是加工过程中对于外界干扰的自适应问题,为了在三维椭圆振动切削过程中实现控制方法的鲁棒性,根据所研制的一种三维椭圆振动切削装置独特的结构方式,首先分析了各个运动之间的串扰情况,并根据装置柔性铰链的特征建立了三维椭圆振动切削装置的动力学模型。提出了三维椭圆振动切削模糊自适应滑模控制的滑模函数与滑模控制律,并通过李雅普诺夫稳定性条件证明了所设计的滑模控制器系统稳定性,采用正弦信号数字实现模糊自适应滑模控制,位置跟踪在3 s内误差控制在0.005范围内,速度跟踪在0.4 s内控制在±0.05之内,能够达到满意的精度,系统模糊自适应滑模控制的模糊逼近也能在0.2 s内收敛,证明了三维椭圆振动切削系统采用模糊自适应滑模控制可以实现较强的鲁棒性。

Fuzzy Adaptive Sliding Mode Control of 3 D Elliptical Vibration Cutting System

3-D elliptical vibration cutting is considered to be the most promising way of cutting difficult to machine materials free -form optics, but the control problem of the processing has not been solution satisfied , especially for adaptive problems for outside inter-ference during processing , in order to achieve robust control in 3-D elliptical vibration cutting process .Based on the unique structural of the developed 3-D elliptical vibration cutting device , firstly the crosstalk between the position of each actuator was analyzed , and then a 3-D elliptical vibration cutting device dynamics model was established according to the characteristics of flexure hinges .The designed sliding mode control function and the sliding mode control law of 3-D elliptical vibration cutting system fuzzy adaptive sliding mode con-trol certified its stability condition by Lyapunov function , the result proved that the design of the system sliding mode controller is sta-bility.Sinusoidal signal was adopt to digital implementation the proposed fuzzy adaptive sliding mode control , position tracking error control within 0.005 range in 3 s, speed tracking control within ±0.05 range in 0.4 s, achieved a satisfactory accuracy .Fuzzy adaptive sliding mode control approximation error can converge in 0.2 s, proved that 3-D elliptical vibration cutting system uses fuzzy adaptive sliding mode control can be achieved over strong robustness .