An adaptive reaching law of chattering-free discrete-time sliding mode control for systems with external disturbance

An adaptive reaching law of chattering-free discrete-time sliding mode control is proposed for the systems with external disturbance. An adaptive function is proposed in the reaching law which can increase reaching speed as sliding variable is far away from zero and avoid undesired chattering when sliding variable is close to origin. Moreover, a third-order backward difference of disturbance is added to obtain a narrower quasi-sliding mode band (QSMB). Both the closed-loop system performance and finite reaching steps to achieve the desired QSMB are theoretically analyzed. The simulation results verify the effectiveness of the proposed control strategy.     

Fixed-time sliding mode observer-based controller for a class of uncertain nonlinear double integrator systems

This paper investigates a fixed-time convergence issue using the sliding mode observer-based controller for a class of uncertain nonlinear double integrator systems. This observer-based controller is designed assuming that only the first state measurement is available and there is no information about external disturbances and modeling uncertainties. A new form of sliding mode observer in combination with a sliding mode controller is designed to estimate unmeasured state and unknown disturbances and uncertainties as well as provide the estimated data in the control law. A novel form of sliding surfaces for the robust observer-based controller is proposed for which fixed-time convergence is guaranteed to achieve trajectory tracking. In the proposed fixed-time scheme, the bound on the settling time is user-defined using design parameters regardless of the system's initial conditions. The control law and observer law are designed such that the chattering issue is alleviated in the control signal. The stability analysis of the closed-loop system using the observer-based controller is established via the Lyapunov theory. The validity of the controller design is tested by applying and simulating an example of a robot manipulator in Simulink/MATLAB. The superiority of the proposed method is demonstrated by comparing it with two other methods from the relevant literature.     

非匹配不确定离散系统的无抖振积分滑模控制

针对一类非匹配不确定离散系统, 设计一种无抖振离散积分滑模控制器. 为了抑制非匹配不确定性对系统的影响, 采用线性矩阵不等式方法设计一种新型的切换函数和对应的滑模控制律, 并证明了闭环系统的Lyapunov 稳定性. 同时, 引入饱和函数设计控制器, 使系统状态在积分滑模面的某个小邻域内做准滑模运动, 并通过合理选择饱和函数的边界层厚度, 使控制信号不含任何抖振. 理论分析和数值仿真验证了所提出方法的有效性.

     

一种新的约束变速趋近律离散滑模控制方法

考虑惯性执行器输出速度有限的实际,引入趋近律变化速率的控制函数,设计了一种新的无抖振离散滑模变速趋近律算法. 首次提出了通过设计趋近律变化速率来构造离散滑模趋近律的思想,使得控制器的物理意义更加明显,设计更加灵活和简单.对于标称系统, 该算法可以使切换函数在有限时间内快速无抖振地收敛至零;对于满足匹配条件的不确定系统,切 换函数能够收敛至与不确定性及控制参数相关的某一数值,通过设置控制参数,可使这一数值任意小.     

一类主从混沌系统的同步控制

针对一般变结构控制方法存在高频抖振和需要事先已知不确定项的上界等不足,提出了自适应无抖振变结构控制方法,以实现一类含有不确定项及外部噪声干扰的主从混沌系统的同步控制.该控制方法不仅对参数变化和噪声干扰具有很强的鲁棒性,而且能消除滑模面附近的抖振现象且不需要不确定项的上界已知的条件.理论分析与仿真结果表明了该控制器的有效性.     

具有控制时滞的离散系统的无抖振滑模控制

研究含时滞的线性离散系统的变结构控制问题. 首先将之简化为不含时滞项的线性离散系统. 然后对简化系统提出一种新的无抖振滑动模态控制算法. 该算法使滑模控制分为两个阶段,当系统轨迹在滑模某邻域以外时, 利用传统的到达控制律使系统状态轨迹单调趋近滑模面; 当系统轨迹进入该邻域内, 无抖振控制律使其轨迹一步到达滑模面. 该控制律有效地削除了由离散系统解轨迹的不连续性产生的抖振现象. 仿真结果表明了这种方法的有效性.     

无抖振离散重复控制器的设计与实现

针对周期参考/干扰信号下的不确定离散时间系统,提出一种基于吸引律的重复控制方法,在吸引律中"嵌入"干扰抑制措施,构造理想误差动态,并基于此设计重复控制器.文中推导出单调减区域、绝对吸引层和稳态误差带边界的表达式,用于整定控制器参数和表征闭环系统的跟踪性能,并给出了跟踪误差在无干扰时收敛于原点及在干扰存在时收敛进入稳态误差带内所需最多步数的表达式.设计的重复控制器不仅能够完全抑制周期干扰信号,而且可以消除系统抖振.在电机实验装置上的应用结果表明了所提出控制方法的有效性.     

无抖振离散滑模趋近律

针对离散滑模趋近律形式多样且容易产生高频抖振的问题,提出了离散滑模趋近律的一般形式,并给出了无抖振的到达条件及其理论证明,从一般意义上为离散滑模趋近律的设计提供了理论依据。针对满足匹配条件的不确定系统,给出了切换函数收敛域的推导方法,推导了无抖振的最小收敛域。以典型的高氏指数趋近律为例,利用无抖振的到达条件,对其一般形式进行了无抖振改进,验证了所提出方法的有效性。     

无抖振全程滑态离散变结构控制算法

针对离散时间系统的变结构控制问题,对常规离散变结构抖动产生原因的分析,结合全程滑态变结构算法,给出了改进的离散趋近律。仿真结构表明,该方法是可行的,减小了系统的抖动,并从一开始就保证了系统的稳定性。