为解决二阶非线性系统的输入饱和约束和收敛时间区间预设问题,设计了一种系统信号有界的迭代学习控制算法。使用不等式变换,分离出系统中的未知参数函数,建立限幅迭代学习算法估计未知参数函数;借助预设时间收敛转换函数,将任意初值滑模面转换为初值为零的新变量,构建变增益限幅迭代学习控制器,严格的理论分析证明了滑模面的迭代收敛性和闭环系统所有信号一致有界,保证系统轨迹跟踪误差在预设时间内收敛。任意初值机器人轨迹跟踪控制的仿真分析,验证了方法的有效性和收敛时间区间可根据工程需求设置的优良特性。
A signal bounded iterative learning control algorithm is designed to address the input saturation constraint and convergence time interval setting problem of second-order nonlinear systems. Using inequality transformation to separate unknown parameter functions in the system, establish a limited amplitude iterative learning algorithm to estimate unknown parameter functions; By means of the predefined time convergence conversion function, the arbitrary initial value sliding mode surface is converted into a new variable with zero initial value, and a variable gain limiting iterative learning controller is constructed. Strict theoretical analysis proves that the sliding mode surface converges to zero after finite iterative learning and all signals of the closed-loop system are uniformly bounded,ensuring the trajectory tracking error converges within the preset time. The numerical simulation of arbitrary initial value robot trajectory tracking control verifies the effectiveness of the proposed method and the excellent characteristics of the convergence time interval that can be set according to engineering requirements.
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