An algorithm for third order sliding mode control by keeping a 2-sliding constraint

The paper presents a new control law for higher order sliding mode control. The control law keeps a constraint in 2-sliding mode such that the finite time stabilization of triple integrator is achieved. The switching function from non-singular terminal sliding mode is used to achieve the goal. The switching function is designed to have relative degree two with respect the input and thus the twisting controller can be exploited for finite time convergence. The fractional powers are carefully designed to prevent the unboundedness or singularity arising because of some constraint being kept at zero. The disturbance rejection is a natural consequence of use of twisting controller.