一类非线性系统的滑模控制稳态精度研究

针对一类非线性系统的线性滑模控制和Terminal滑模控制稳态精度问题,分析使用饱和函数代替滑模控制律中符号函数的线性滑模控制和Terminal滑模控制系统的稳态误差与饱和函数宽度的数值关系,得出两者的数学表达式,为协调既削弱滑模控制的颤振又保证稳态精度的滑模控制系统的饱和函数宽度的选择提供了理论依据。定量地比较线性滑模控制和Terminal滑模控制的稳态精度,得出了Terminal滑模控制比线性滑模控制有更好稳态精度的结论,通过数值仿真算例证明理论分析的正确性。

Study on the steady precision of sliding mode control for a class of nonlinear systems

For the steady precision of linear sliding mode control and Terminal sliding mode control for a class of nonlinear systems,the numerical relationship between the steady errors of linear sliding mode control systems and Terminal sliding mode control systems with a saturation function instead of the sign function in the sliding control law and the width of the saturation function is analyzed.Mathematical formulas between the steady errors and the width of the saturation function are deduced,which provides the theoretical basis for the choice of the width of the saturation function used to weaken the chattering of sliding mode control system and guarantee the steady precision simultaneously.Steady precision is quantitatively compared between linear sliding mode control and Terminal sliding mode control,which shows that Terminal sliding mode control performs better than linear sliding mode control in steady precision.A numerical simulation example proves the validity of the theoretical analysis in the end.