不匹配不确定线性系统滑模控制设计

Design Sliding Mode Control for Mismatched Uncertain Linear Systems

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。

Sliding-mode control(SMC)is a robust technique,well known for its ability to withstand external disturbances and model uncertainties satisfying the matching condition,but the matching condition is difficult to satisfy.This correspondence proposes a sliding mode controller design for the robust control of mismatched uncertain linear systems.In order to make that the perturbation is minimal, the perturbation is provided into two parts by projection matrix-the matched and unmatched perturbation.It is also shown that when the minimum is attained and the resulting perturbation is not amplified.In order to reduce chattering,a bipolar sigmoid function without high frequency switching is induced to take the place of sign function.The controller based on integral sliding mode and rate reaching law stability is ensured using the Lyapunov method.Simulation results support the analysis developed.