Second order sliding mode control with adaptation

The paper proposes a new control scheme for nonlinear robotic systems. The basis of the scheme is an existing second order sliding mode controller augmented with an adaptive component. A computed torque-like adaptive controller with a second order system type of measure of tracking accuracy is the source of the adaptation law. Extensive simulations of a nonlinear robotic system with one rotational and one translational degree-of-freedom unmodeled actuator dynamics and parameter mismatch, confirm the suitability of the proposed scheme. The adaptation law allows smaller feedback gains to be used, and thus improves the robustness without degrading the performance. Adaptation may also improve the performance when unmodeled actuator dynamics is present, although to a lesser degree and not uniformly. The stability robustness in this case is slightly worse