欠驱动机械臂滑模控制与实验研究

Sliding mode control and experiment study for underactuated manipulator

针对非线性、强耦合的欠驱动两杆机械臂Pendubot,提出了一种在倒立不稳定平衡点邻域内局部线性化的基于Hurwitz稳定判据的滑模控制方法。首先定义一个分别由主动臂和欠驱动臂的角位置、角速度跟踪误差的线性组合滑模面。通过Lyapunov稳定性分析保证了系统的所有状态能够到达滑模面并保持在滑模面上,根据滑模面条件,降低原系统的阶数,再令降阶系统满足Hurwitz稳定判据,从而原系统渐进稳定,其所有状态变量最终收敛于平衡点,同时得到滑模面参数。仿真和实验结果表明,所设计的控制方法易于实现,能够抵抗一定的外界干扰,对模型的参数摄动不敏感、鲁棒性强。

Aiming at the two- link underactuated manipulator- Pendubot with strong coupling and nonlinear characteristics,a sliding mode control approach based on Hurwitz stability criterion is proposed to stabilize the underactuated manipulator Pendubot system linearized locally around the unstable inverted equilibrium points. First,a sliding surface is defined,which is constructed with the linear combination of angle position and angle velocity tracking errors of the actuated and unactuated manipulators. Lyapunov stability analysis guarantees that all the trajectories of the Pendubot system states reach and remain on the sliding surface. According to the sliding surface condition,the order of the original system is reduced,and the order- reduced system is made to meet the Hurwitz stability criterion,so the original system is asymptotically stable and all the trajectories of the system tracking errors converge to this surface and slide along the surface to the original equilibrium. Then,the parameters of the sliding surface can be calculated. The simulation and experiment results demonstrate that the proposed control method is easily implemented,can resist certain external disturbance,is insensitive to the model parametric perturbation,and has strong robustness.