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执行器故障及其非线性机械臂固定时间变参数滑模同步控制

刘树博1,2, 李智1,2, 张志远1,2, 罗先喜1,2

1.东华理工大学 江西省康复辅具产业技术研究院，江西 南昌 330013；2.东华理工大学 机械与电子工程学院；江西 南昌  330013

摘要: 目的 执行器故障及其非线性和有界扰动对不确定机械臂系统影响较大，需要实现机械臂对期望轨迹的快速和高精度跟踪。 方法 基于多项式平方和（sum-of-squares， SOS）理论提出一种固定时间变参数滑模容错同步控制（fixed-time parameter-varying sliding fault tolerant synchronous control， FPS-FTSC）策略。首先，建立具有未知执行器故障及其非线性的统一数学模型；其次，为了使控制器满足机械臂各轴间的协调性，引入同步误差控制项，并结合预设性能函数（prescribed performance function， PPF）完成误差转换，在变参数终端滑模框架下，基于Lyapunov稳定性理论保证位置跟踪误差可以在固定时间收敛到PPF限定的范围内；最后，在求解变参数控制器增益的同时，给出系统具有全局最优H_∞扰动抑制性能存在的条件。 结果 仿真和实验中，在没有执行器故障及其非线性存在的理想情况下，FPS-FTSC策略使位置跟踪误差和同步误差均能快速收敛到0的较小邻域内；在多种执行器故障及执行器非线性存在的情况下，所提策略仍能使系统实现对期望轨迹快速稳定地跟踪，且控制性能优于已有算法。  结论 仿真和实验结果表明，所提控制策略能够使系统在多重约束下具有较好的暂态和稳态性能，表现出良好的鲁棒性和容错性。

关键词:机械臂;执行器故障;变参数滑模同步控制;固定时间容错控制;执行器非线性

doi:10.16186/j.cnki.1673-9787.2023120054

基金项目:国家自然科学基金资助项目（62141102）；江西省自然科学基金资助项目（20202BAB202008）；江西省研究生创新基金资助项目（YC2022-s616）

收稿日期:2023/12/19

修回日期:2024/04/10

出版日期:2025/10/14

Fixed-time parameter-varying sliding synchronous control of manipulators with actuator faults and nonlinearities

Liu Shubo1,2, Li Zhi1,2, Zhang Zhiyuan1,2, Luo Xianxi1,2

1.Jiangxi Industrial Technology Research Institute of Rehabilitation Assistance， East China University of Technology， Nanchang  330013， Jiangxi， China；2.School of Mechanical and Electronic Engineering， East China University of Technology， Nanchang  330013， Jiangxi， China

Abstract: Objectives It is needed to attenuate the adverse effects caused by unknown actuator nonlinearities， actuator faults， and bounded disturbances， and to achieve fast and high-precision tracking of the desired trajectory of manipulator. Methods A fixed-time parameter-varying sliding fault tolerant synchronous control（FPS-FTSC） strategy was proposed based on the sum-of-squares（SOS） theory for a class of uncertain manipulator systems. Firstly， a unified mathematical model of actuators with unknown nonlinearity and faults was established. Secondly， a synchronous error control term was introduced to ensure the coordination between the various axes of manipulators， and it was combined with the prescribed performance function（PPF） to complete error transformation. With the parameter-varying terminal sliding framework， it was demonstrated that synchronous error and position tracking error could converge to the range limited by PPF within a fixed time based on Lyapunov stability theory. Then， while solving for the gain of parameter-varying controller， the conditions for the existence of global optimal H_∞ disturbance suppression performance of the system were given. Results In simulation and experiment， the FPS-FTSC strategy enabled both position tracking error and synchronization error to quickly converge to a small neighborhood of zero under ideal conditions without actuator faults and nonlinearity； In the presence of various actuator faults and nonlinearity， the proposed strategy could still achieve fast and stable tracking of the desired trajectory， and had better control performance than existing algorithms. Conclusions Simulation and experimental results showed that the proposed control strategy could achieve good transient and steady-state performance of the system under multiple constraints， demonstrating good robustness and fault tolerance.

Key words: manipulator; actuator fault; parameter-varying sliding synchronous control; fixed-time fault-tolerant control; actuator nonlinearity