Sliding mode control and experiment study for underactuated manipulator

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.