Finite time tracking of unilaterally constrained planar systems with pre-specified settling time: Second order sliding mode synthesis and chattering-free digital implementation

In this paper, tuning rules are established when a second order sliding mode controller is utilized to achieve finite time tracking for a class of unilaterally constrained planar systems in the presence of external disturbances in continuous and discrete-event phases. Rigid body inelastic impacts are incorporated at the unstable equilibrium. A numerical chattering-free digital implementation is also presented. This implementation, while being based on strong theoretical foundations, appears to bring the present advances in the area closer to industrial application.