改进双幂次指数趋近律的滑模控制设计

针对目前系统抖振仍影响滑模趋近律在实际中应用，并导致系统收敛速度缓慢、滑模平面趋近至原点时间长等缺陷，提出一种改进的双幂次指数趋近律。改进趋近律中指数项采用分段设计，指数项分段参数将系统分为两部分进行。当状态绝对值小于1时，系统沿滑模面平滑进入，抖振影响可忽略不计；当状态绝对值大于等于1时，系统的动态响应显著提高，收敛时间缩短，且总时间小于初始状态运动至临界值时间和系统运动至滑模面平衡点的时间之和。在理论上验证了改进后的双幂次指数趋近律能够快速收敛到平衡点且消除了抖振影响，并通过实验验证了该趋近律的有效性。对比多种趋近律，改进的双幂次指数趋近律具有最佳性能且收敛速度最快，并通过实验验证在外界干扰下该趋近律仍可快速收敛于平衡点。

Design of Sliding Mode Control with Improved Double Power Exponential Reaching Law

For the existing double power reaching law,the chattering problem of exponential approach law affects the use of sliding mode control in practice,and results in the defects of too slow global convergence speed and long time.To overcome the problems,an improved double power exponential approach law was proposed.In the proposed double power exponential approach law,the design of variable exponential term was adopted.That was,the sliding mode control process was divided into two parts when reaching the sliding surface.When the absolute value of the state was less than 1,the system entered smoothly along the sliding surface,and the buffeting effect was negligible;when the absolute value of the state was greater than or equal to 1,the dynamic response of the system was significantly improved,the convergence time was shortened,and the total time was less than the sum of the time when the initial state moved to the critical value and the time when the system moved to the sliding surface equilibrium point.It is theoretically verified that the improved double power exponential approach law can quickly converge to the equilibrium point and eliminate the buffeting effect,and the effectiveness of the approach law is verified through experimental simulation comparison.Comparing multiple reaching laws，the improved double power exponential reaching law has the best performance and the fastest convergence speed.The experimental results show that the reaching law can still converge to the equilibrium point rapidly under external interference.