基于一种新型趋近律的自适应滑模控制

首先, 利用特殊幂次函数和反双曲正弦函数构造一种新型滑模变结构控制趋近律; 然后, 采用该趋近律设计一种自适应滑模控制律, 并证明滑模控制系统误差渐近收敛. 仿真实验表明: 在存在时变转动惯量和摩擦力矩扰动的情况下, 该自适应滑模控制系统具有较高的位置和速度跟踪精度, 并有效减弱了控制输入信号的高频震颤现象; 同时, 采用反双曲正弦函数的自适应律能较好地平滑系统转动惯量估计值, 减小控制输入信号的幅值.

Adaptive sliding control based on a new reaching law

Firstly, a new sliding mode control reaching law with a special power function and an inverse hyperbolic sine function is constructed. Then, an adaptive sliding control law is designed with the reaching law, and the error asymptotic convergence of the sliding control system is proved. The simulation experiments demonstrate that the adaptive sliding control system with the changing rotational inertia and friction torque has higher position and speed tracking precision, and reduces high frequency fluctuation phenomenon of the control input signal effectively. The adaptive law with the inverse hyperbolic sine function can well reduce the estimation value of the rotational inertia and control input signal.