一种具有时滞的离散系统的控制设计

Control design of a kind of time-delay discrete system

研究含时滞的线性离散系统的变结构控制问题。首先将离散系统简化为不含时滞的线性离散系统,然后对简化的系统提出一种新的变结构控制设计算法。该算法分为2个阶段:当系统轨迹在滑模某邻域外时,控制律使系统轨迹单调趋近于滑模面;当系统轨迹渐近进入到该邻域内,控制律使其轨迹一步到达滑模面。抖振现象是离散系统滑模控制算法的主要缺陷,一些学者针对离散系统在消弱抖动方面做了广泛而深入的研究。离散系统在消弱抖振方面的研究提出的算法可以有效地消弱系统解轨迹的不连续性产生抖振的现象,使系统稳定。理论证明该方法可消除离散滑模控制系统的抖振且能够保证控制系统具有强鲁棒性。

This paper considers the variable structure control for linear discrete systems with time-delay. First, discrete system is simplified to a linear discrete system without time-delay and a new variable structure strategy is designed for this simplified discrete system. The control algorithm is divided into two phases： when the system trajectory is outside of the given neighborhood, the control law is used to drive the trajectory toward the switching surface monotonically, while when the trajectory is inside the neighborhood, the control law drives the trajectory to the switching surface precisely in one step. Chattering phenomena is the main defect of the sliding mode control algorithm for discrete system. Some scholars have done abroad and in-depth study in the aspect of weakening chattering for discrete system. The algorithm focused on the research for discrete system chattering can effectively eliminate the chattering phenomena caused by the discontinuity of system solution trajectory, and then making the system stability. It＇s proved that the method can eliminate the chattering for the discrete-time sliding mode control systems and guarantee strongly the robust performance of the system.