基于反双曲正弦函数的转台伺服系统滑模控制

摘要

为了补偿转台伺服系统的非线性扰动以及抑制滑模控制的高频震颤现象，设计了一种新型滑模控制器。首先，利用反双曲正弦函数设计一种三阶扩张状态观测器，通过该扩张状态观测器估计二阶系统的状态变量和未知非线性扰动。然后，采用反双曲正弦函数构造滑模控制律，设计了一种利用扩张状态观测器的滑模控制器，并证明系统渐近稳定。最后，三轴转台伺服系统的仿真实验结果表明扩张状态观测器能获取系统各状态高精度估计值，采用该新型滑模控制器的伺服系统具有较高的位置和速度跟踪精度，有效抑制了滑模控制输入的高频震颤现象。%A new sliding mode controller is designed in order to compensate nonlinear uncertainties of the servo system and reject high frequency chattering phenomena of sliding mode control.At first, a third-order Extended State Observer (ESO) with an inverse hyperbolic sine function is presented. The ESO can estimate state variables and uncertainties of a second-order system. Then, a sliding mode control law is constructed with the inverse hyperbolic sine function, and a sliding mode controller with the ESO is designed. The asymptotic stability of the sliding control mode system is proved. Finally, the simulation experiments of the three-axis turntable servo system demonstrate the ESO could obtain the higher precision estimations of state variables, and the servo system with the new controller has the higher position tracking and velocity tracking precision. Moreover, the sliding mode control input signals reduce high frequency chattering phenomena.