Sliding mode control with decreased chattering-model and simulations

The idea of the system with sliding mode control and adaptation of the switched β⁺ and β^- amplitudes of the relay output is proposed. This is possible owing to the observation that the sliding mode control is equivalent to the two-position relay control of the sliding surface signal on the level zero. The slopes of the increasing and decreasing parts of the sliding surface signal curve are used for independent adaptation of β⁺ and β^- values of the relay output, respectively. The adaptation causes that the difference (β⁺-β^-) is decreased and both the values tend to be placed symmetrically with respect to the needed mean value of the control. Owing to this the chattering effect appearing in the sliding control is decreased significantly and the system remains very robust. Simplified model of the proposed solution is described and simulations are performed