Adaptive super-twist control with minimal chattering effect

The, so-called, adaptive super-twist controller is considered here. It contains the adaptive gain-parameter which adjusts the level of a scalar control action on-line based on direct measurements the “equivalent control” obtained by a first-order low-pass filter. It is shown that the problems of the finite time convergence and keeping a small chattering amplitude can be handled simultaneously if the gain magnitude is reduced to a minimal admissible level defined by the conditions for sliding mode to exist. The suggested methodology is compared numerically with another schemes of a gain-adaptation (including σ-adaptation) showing a high effectiveness under a significant level of uncertainties and external disturbances.