δ-算子描述离散系统的变结构控制

Variable Structure Control of DiscreteTime Systems in Delta Operator Description

利用δ－算子描述的离散时间系统，比移位算子更能反应连续时间系统的动态特性．研究了单输入的δ－算子描述的离散时间系统的变结构控制，给出到达条件（即离散趋近率），得到变结构控制的一般设计方法．对准滑动模态，证明其稳定性并给出切换函数的求解方法．探讨了扰动系统的变结构控制问题，给出其设计方法．对一个简单的确定系统作了仿真．结果表明，本文的方法是可行的且有效地抑制了系统的抖动，优于相应的ｑ－算子的方法．

Discrete time systems described by δoperator is better for approximating continuous time systems than by shift operator. The variable structure control (VSC) of singleinput discrete time systems based on deltaoperator is concerned in this paper. The reaching condition (the discrete reaching law) is given. By use of the deltamodel the selection of reaching condition is similar to that for the continuous case. The VSC is obtained straightforward by the reaching law method. For the definition of quasisliding mode, its stability problem is proved, and a solution to the linear switching function is determined as well. Meanwhile, the VSC of perturbation systems is discussed and its design method is also presented. The simulation results illustrate that the presented method is feasible and it is better than the corresponding method based on shift operator.