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滑模控制方法对处理满足匹配不确定的外部扰动或模型不确定具有很好的鲁棒性。然而,很多不确定系统的模型不确定或外部扰动很难满足匹配条件,针对不确定线性系统扰动不满足匹配条件问题设计滑模控制器,为减少扰动影响,将系统不确定扰动通过投影矩阵分成两部分:一部分为匹配扰动,另外一部分为非匹配不确定扰动。经扰动分析知该分解会使不匹配不确定扰动的影响最小并且不会使该部确定的影响放大。根据积分滑模面和滑模趋近律设计滑模控制器,为了进一步减少抖振影响,引入无高频抖振的双极函数代替符号函数。通过Lyapunov稳定定理分析可知,根据积分滑模面和趋近律所设计的控制器的稳定性和鲁棒性能够得到保证。最后,数值仿真算例说明了该方法的有效性。
The sliding mode control method is robust to dealing with uncertain external disturbances or uncertain models. However, it is difficult for many uncertain systems to model uncertainties or external perturbations to meet the matching conditions. The sliding mode controller is designed to solve the problem that the uncertain linear system perturbations do not meet the matching conditions. To reduce the influence of disturbance, the system uncertain perturbations are divided into projection matrix Two parts: one part is matched disturbance, the other part is unmatched and uncertain disturbance. The perturbation analysis shows that this decomposition minimizes the effects of un-matched uncertain disturbances and does not magnify the impact identified by the Department. In order to further reduce the effect of chattering, a sliding mode controller based on integral sliding mode and sliding mode approach is introduced to replace the sign function with dipole function without high frequency chattering. The Lyapunov stability theorem analysis shows that the stability and robustness of the controller based on the integral sliding mode surface and the approach law can be guaranteed. Finally, the numerical simulation shows the effectiveness of the method.