Dynamic sliding mode control design

Dynamic sliding mode control and higher order sliding mode are studied. Dynamic sliding mode control adds additional dynamics, which can be considered as compensators. The sliding system with compensators is an augmented system. These compensators (extra dynamics) are designed for achieving and/or improving the system stability, hence obtaining desired system behaviour and performance. Higher order sliding mode control and dynamic sliding mode control yield more accuracy and also reduce and/or remove the chattering resulting from the high frequency switching of the control. It is proved that certain J-trajectories reach a sliding mode in a finite time. A sliding mode differentiator is also considered.