基于ESO−SMC的煤矿井下机械臂控制方法

ESO-SMC-based control method for underground coal mine robotic arms

  • 摘要: 针对煤矿井下机械臂在强非线性、参数不确定性与外部复杂扰动下控制精度不足、鲁棒性较弱的工程问题,提出一种基于扩展状态观测器(ESO)与滑模控制(SMC)的煤矿井下机械臂控制方法。基于拉格朗日法建立包含模型参数不确定性、未建模动态与外部扰动的机械臂动力学方程,并通过扩张状态变量构建扩展状态空间模型;设计三阶扩展状态观测器,将参数摄动、时变摩擦与井下冲击负载统一归为系统总扰动进行实时在线估计与前馈补偿,降低SMC对高切换增益的依赖;结合扰动观测信息设计滑模控制律,采用饱和函数替代符号函数,以抑制滑模抖振,并基于Lyapunov稳定性理论分析证明闭环系统具有稳定性。以PUMA560机械臂第4—第6关节为研究对象开展仿真实验,结果表明:ESO能够快速、有效地估计系统总扰动,估计误差不超过5%;ESO−SMC方法控制下第4—第6关节的稳态跟踪均方根误差(RMSE)分别为0.026 1,0.029 1,0.016 9 °,较传统SMC方法分别降低45.2%,45.4%和26.2%,最大跟踪误差分别为0.046 3,0.055 0,0.032 5 °,分别降低38.4%,33.7%和17.3%,平均RMSE和平均最大跟踪误差分别降低41.7%和32.3%,且滑模面收敛速度更快、稳态波动幅度更小,验证了该方法具有较好的轨迹跟踪精度和抗扰性能。

     

    Abstract: To address insufficient control accuracy and weak robustness of underground coal mine robotic arms subject to strong nonlinearities, parameter uncertainties, and complex external disturbances, a control method based on an Extended State Observer (ESO) and Sliding Mode Control (SMC) was proposed. Robotic arm dynamic equations incorporating model parameter uncertainties, unmodeled dynamics, and external disturbances were established using the Lagrangian method, and an extended state-space model was constructed by augmenting the state variables. A third-order ESO was designed to treat parameter perturbations, time-varying friction, and underground impact loads collectively as the total system disturbance for real-time online estimation and feedforward compensation, thereby reducing the dependence of SMC on high switching gains. A sliding mode control law was designed using the disturbance estimates, with a saturation function replacing the sign function to suppress chattering. The stability of the closed-loop system was established through an analysis based on Lyapunov stability theory. Simulations were conducted on joints 4–6 of a PUMA560 robotic arm. The results showed that the ESO rapidly and effectively estimated the total system disturbance, with an estimation error of no more than 5%. Under ESO-SMC, the steady-state tracking Root Mean Square Error (RMSE) values for joints 4–6 were 0.026 1, 0.029 1, and 0.016 9°, respectively, representing reductions of 45.2%, 45.4%, and 26.2% compared with conventional SMC. The maximum tracking errors were 0.046 3, 0.055 0, and 0.032 5°, respectively, representing reductions of 38.4%, 33.7%, and 17.3%. The average RMSE and average maximum tracking error decreased by 41.7% and 32.3%, respectively. The sliding surface also converged faster and exhibited smaller steady-state fluctuations. These results confirm that the proposed method provides good trajectory tracking accuracy and disturbance rejection performance.

     

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