基于时变终端滑模的任意迭代初态抑制控制

Arbitrary iterative initial value suppression control based on time-varying terminal sliding mode

中文关键词  迭代学习控制  滑模控制  有限时间控制  初值问题  机器人

英文关键词  iterative learning control  sliding model control  finite time control  initial value problem  robot

中文摘要

      为解决迭代学习过程中的任意迭代初值和迭代收敛理论证明难的问题, 本文构造了一种轨迹跟踪误差初 值恒位于滑模面内的时变终端滑模面, 将轨迹跟踪误差初值不为零的轨迹跟踪控制问题转换为滑模面初值恒为零 的滑模面跟踪控制问题, 建立了任意迭代初值与相同迭代初值的迭代学习控制理论连接桥梁. 本文提出一种基于 时变滑模面的比例–积分–微分(PID)型闭环迭代学习控制策略, 基于压缩映射原理证明了迭代学习的收敛性, 给出 了迭代收敛条件. 时变终端滑模面经有限次迭代学习收敛到零, 达到轨迹跟踪误差最终稳定在时变滑模面内的目 的; Lyapunov稳定理论证明了位于滑模面内的轨迹跟踪误差在有限时间内收敛到原点, 达到轨迹局部精确跟踪目 的. 随机初态下的工业机器人轨迹跟踪控制数值仿真验证了本文方法的有效性和系统对外部强干扰的鲁棒性.

英文摘要

      To solve the problem of the theoretical proof of iterative convergence and the arbitrary initial value in the iterative learning process, a time-varying terminal sliding-mode surface with the initial value of trajectory tracking error always located in the sliding-mode surface is constructed. The trajectory tracking control problem with non-zero initial value of trajectory tracking error is transformed into the sliding-mode surface tracking control problem with constant initial value of sliding-mode surface. The bridge between iterative learning control theory with arbitrary iterative initial value and the same iterative initial value is established. A proportional-integral-derivative (PID) closed-loop iterative learning control strategy based on time-varying sliding-mode surface is proposed. The convergence of iterative learning is proved based on the principle of compression mapping, and the iterative convergence conditions are given. The time-varying terminal sliding-mode surface converges to zero after finite iterative learning, and the trajectory tracking error is finally stabilized in the time-varying sliding-mode surface. Based on the Lyapunov stability theory, it is proved that the trajectory tracking error in the sliding-mode surface converges to the origin in finite time to track local trajectory accurately. The numerical simulation of industrial robot trajectory tracking control under random initial state verifies the effectiveness of the proposed method and the robustness of the system to external strong disturbances.