带有输出约束的柔性关节机械臂预设性能自适应控制

针对带有输出约束和模型不确定的柔性关节机械臂系统,提出一种基于时变障碍李雅普诺夫函数的预设性能自适应控制方法.通过构造指数衰减的时变约束边界,提出时变正切型障碍李雅普诺夫函数,能够同时适用于约束与非约束情况,进而拓宽传统对数型障碍李雅普诺夫函数的适用范围.此外,通过预先设置时变边界函数的相关参数,使得系统输出在初始阶段具有较小的超调量和较快的跟踪速度,并能够满足系统的稳态性能要求.在此基础上,结合反演法设计反馈控制律,保证系统的输出约束性能和轨迹跟踪精度.最后,基于李雅普诺夫稳定性定理证明所有闭环信号能够达到一致最终有界,并给出数值仿真对比验证所提出方法的有效性.

Prescribed performance adaptive control of flexible-joint manipulators with output constraints

In this paper, an adaptive prescribed performance control scheme is proposed based on time-varying barrier Lyapunov function for flexible-joint manipulator systems with output constraints and model uncertainties. A time-varying tangent barrier Lyapunov function is first presented by constructing a time-varying constrained boundary which attenuates exponentially, and it extends the application scope of the conventional logarithmic barrier Lyapunov functions. In addition, by presetting the parameters of the time-varying boundary function, the system output has the smaller overshoot and faster tracking speed in the initial stage, and the satisfactory steady-state performance can be guaranteed simultaneously. Then, the feedback control law is designed by employing the backstepping technique to ensure the output constraints and the trajectory tracking accuracy. All the closed-loop signals are proved to be uniformly ultimately bounded through using the Lyapunov stability theorem, and numerical simulations are given to show the effectiveness of the proposed scheme.