Hitting time reduction and chattering attenuation in multi-input variable structure systems

In the variable structure control (VSC) design, the hitting time reduction and the chattering attenuation are two essential but contradictory tasks. To remove the contradiction, we first transform a multi-input system into a set of single-input subsystems, and then two kinds of controllers are developed for the transformed system. The first kind of controller is a two-phase VSC, which is a reaching-phase controller used to reduce the hitting time, and the other kind is a sliding-phase controller used to attenuate the chattering. The two-phase VSC can steer each switching variable to hyperplane exponentially, but does not slow down the system response. The second kind of controller is an adaptive VSC derived from the concept of model reference adaptive control, such that both the switching variable tracks the desired trajectory and the above contradiction can be removed.