采用改进快速变幂次趋近律的滑模控制方法

A Sliding Mode Control Method with Improved Rapid Power Approximation Law

针对基于传统幂次趋近律的滑模控制方法在使用中抖振现象突出、趋近速度慢、时间长等问题,提出一种改进快速变幂次趋近律的滑模控制方法。首先,采用快速双幂次趋近律并加以改进,在原快速双幂次趋近律的基础上加入变指数项,使系统状态在不同趋近阶段中针对性地调节速度,大大地提高了系统动态响应过程的趋近速度,限制了抖振现象的产生,同时具有有限时间收敛性。对改进后的快速变幂次趋近律的数值分析结果表明:当系统状态的绝对值小于1时,系统相当于快速幂次趋近律,系统可平滑进入滑模段,消除抖振;当系统状态的绝对值大于等于1时,又相当于快速双幂次趋近律,系统的动态响应速度有所提高,趋近时间缩短。然后,将改进的快速变幂次趋近律用于滑模控制中,构成改进快速变幂次趋近律的滑模控制方法。采用所提滑模控制方法对履带机器人轨迹进行跟踪控制,实验结果表明:与几种基于传统的幂次趋近律控制方法相比,所提控制系统在趋近平衡零点时几乎无抖振现象的产生,具备更优的性能,且收敛时间最短,最短时间仅为其他方法的69.4%。

As sliding mode control methods based on the traditional power approximation law have many problems such as prominent jitter,slow speed and long time,a sliding mode control method with improved rapid power approximation law is proposed.First,the rapid double power approximation law is adopted and improved,and the variable exponential term is added on the basis of the original rapid double power approximation law,so that the system state adjusts the speed in different approximation stages,which greatly improves the approximation speed of the dynamic response process of the system,limits the generation of jitter phenomenon,and has finite time convergence.The numerical analysis of the improved rapid power approximation law shows that when the absolute value of the system state is less than 1,the system is equivalent to the rapid power approximation law,and the system can smoothly enter the sliding mode segment and eliminate jitter.When the absolute value of the system state is not less than 1,it is equivalent to the rapid double power approximation law,and the dynamic response speed of the system is improved,and the approximation time is shortened.Then,the improved rapid power approximation law is used in sliding mode control to constitute the proposed method.The experimental results show that compared with several control methods based on traditional power approximation law,the proposed control system has almost no jitter phenomenon when approaching the zero point of equilibrium,and has better performance and the shortest convergence time-only 69.4%of other methods.