基于奇异摄动的柔性关节机械臂鲁棒控制

Robust control of flexible joint manipulator based on singular perturbation

针对柔性关节机械臂在扰动过大情况下难以实现高精确度轨迹跟踪的问题,提出一种基于奇异摄动的鲁棒控制方案。该方法不需要对连杆角加速度及其高阶导数进行计算,因此该方法不受高阶导数估计不准确的影响。首先,用奇异摄动法对原系统进行解耦,得到快慢两个异时间尺度的二阶子系统。然后,对慢子系统设计二次补偿控制律,用扰动观测器对扰动进行观测后,进行首次补偿;设计基于Hamilton-Jacobi-Issacs不等式理论的鲁棒控制器进行二次补偿,并证明当扰动有界时,系统跟踪误差将很快收敛于零。最后,对快子系统添加阻尼项,并通过Lyapunov稳定性定理与Lasalle不变性定理证明系统的稳定性。将所提控制方案与反馈线性化方案及奇异摄动PD控制方案相对比,结果表明,所提控制方案设计的系统具有较强的抗干扰能力及更好的动态、稳态性能。

Aiming at the problem that in the flexible joint manipulator it is difficult to achieve high-precision trajectory tracking under the condition of large disturbance,a robust control scheme based on singular perturbation was proposed.This method does not need to calculate the angular acceleration of the connecting rod and its higher-order derivative,so it is not affected by the inaccurate estimation of the higherorder derivative.First,the singular perturbation method was used to decouple the original system,and two second-order subsystems with different time scales were obtained.Then,a multiple compensation control law was designed for the slow subsystem.After the disturbance was observed by the disturbance observer,the first compensation was performed;A robust controller based on Hamilton-Jacobi-Issacs inequality theory was designed for secondary compensation.And it is proved that when the disturbance is bounded,the system tracking error will quickly converge to zero.Finally,the damping term was added to the fast subsystem,and the stability of the system was proved by Lyapunov stability theorem and Lasalle invariance theorem.Comparing the proposed control scheme with the feedback linearization scheme and the singular perturbation PD control scheme,the results show that the system designed by the proposed control scheme has strong anti-interference ability and better dynamic and steady-state performance.