非匹配不确定时滞系统的自校正滑模控制

Self-tuning sliding mode control for a class of mismatcheduncertain linear systems with state time delay

针对一类不匹配、不确定并具有状态时滞的多输入多输出线性系统,基于线性矩阵不等式理论提出一种新的自校正滑模控制方法。该方法利用线性矩阵不等式给出滑动模态存在的充分条件,使系统在滑动模态运动下对于存在的不匹配不确定性扰动以及状态时滞具有完全不变性。引入双极性Sigmoid函数代替符号函数并根据Lyapunov稳定性理论设计了具有自适应能力的滑模控制器,在自适应律的作用下Sigmoid函数的边界层厚度以及切换增益可根据系统状态进行自适应调节,从而改善了滑模控制器输出量过大以及抖振等现象。基于Lyapunov理论证明了该方法的稳定性,最后通过仿真实验进一步验证了该方法的可行性及有效性。

For a class of mismatched uncertain multiple input multiple output linear systems with state time delay,a new self-tuning sliding mode control method is proposed based on the linear matrix inequality theory.In this method a sufficient condition for the existence of linear sliding surface is given according to the linear matrix inequality theory,while in the sliding phase such that the system is restricted to the switch surface and completely invariant to mismatched uncertainties and state time delay.For controller output chattering case,the Sigmoid function instead of sign function is introduced and a self-tuning sliding mode controller is further designed.Under the self-tuning law,the Sigmoid function＇s boundary layer and switching gain can be adjusted automatically,which can reduce the high frequency chattering of outputs.The Lyapunov theory is applied to prove the stability of this new control method.Finally,the simulation results of an example are investigated to show the feasibility and effectiveness of the proposed approach.