Comparison of Time-Variant Sliding Modes for Second Order Systems with ITAE Optimization

This paper presents a comparison of the most commonly found in the nowadays literature time-variant sliding line concepts for continuous time sliding mode control. Considered sliding lines are designed so that they cross the initial position of the representative point of the system at the initial time and then they start moving in the state space until they reach the desired steady state. Consequently, the reaching phase is eliminated and the system's representative point becomes bounded to the sliding plane through the whole regulation process. This guarantees insensitivity of the system's trajectories to matched external disturbances or modelling uncertainties. In the literature we may find various time-variant sliding mode designs for second and third order systems. This study takes into account a constant-velocity sliding line and a constant-acceleration sliding line for a second order continuous time system. The proposed control schemes are designed in an ITAE optimal way and they comply with system's constraints.