一类非匹配不确定纯反馈非线性系统新型变幂次趋近律滑模控制

针对以熔化极气体保护焊（gas metal arc welding，GMAW）为代表的一类非匹配不确定纯反馈非线性系统的输出问题，提出一种基于变幂次趋近律的滑模控制方法。首先，采用滑模微分器得到含系统非匹配不确定性干扰的输出一阶导数。得益于终端滑模有限时间稳定的性能，该方法具有估计精度高、估计误差收敛速度快的优点。然后，提出一种新型的变幂次趋近律，并证明在相同增益下，其趋近速度均快于现有各种趋近律，且具有自适应调节趋近速度的能力，既保证了在全局范围内系统轨迹有限时间趋近滑模面，又避免了在滑模面附近出现抖振。最后，采用变幂次趋近律滑模变结构控制方法和传统趋近律滑模变结构控制方法分别对带有非匹配干扰的GMAW中的弧长进行控制仿真，并对比弧长跟踪效果，分析稳态误差。结果表明，变幂次趋近律滑模变结构方法能够有效的提高系统收敛的快速性，滑模控制方法对于非匹配不确定非线性系具有强鲁棒性。

New Exponential Reaching Law Sliding Mode Control for the Pure Feedback Nonlinear Systems with Mismatched Uncertainties

In order to solve the output problem of a class of non-matching uncertain nonlinear systems represented by gas metal arc welding (GMAW),a sliding mode control method based on variable power law was proposed.Firstly,the first derivative of the output of system with non-matching uncertainty was obtained by using the sliding mode differentiator.Since the terminal sliding mode is stable in a finite time interval,the method has high estimation precision and the advantage that the speed the estimation error convergence is fast.Then,the paper put forward a new kind of exponential reaching law,and proved that under the same gain,the approach speed was faster than the existing various kinds of reaching laws.Furthermore,the approach speed of the proposed reaching law can be adaptively controlled,which not only ensured the system trajectory in the global scope to reach the sliding surface in a limited time,but also avoided the chattering around the sliding surface.Finally,the simulation results of sliding mode control method with the variable power reaching law and ones with traditional reaching laws are compared in controlling the arc length of non-interfered GMAW.Then,the tracking effect of arc length were compared and the steady-state errors were analyzed.The results showed that the sliding mode method with the variable power reaching law and variable structure can effectively improve the fastness of the system convergence.In conclusion,the sliding mode control method had strong robustness to the non-matching uncertain nonlinear system.