Abstract
We propose a VSC(Variable Structure Controller) with a PI-type reaching law. In General, conventional VSCs with a reaching law including a discontinuous term have the chattering problem, and thus the system may be unstable due to the disregarded high frequency dynamics in the modeling process. To resolve this problem, the PI-type reaching law is proposed in this paper. The proposed reaching law makes it easy to determine the reaching dynamics as well as the reaching time by utilizing the 2nd-order system analysis. Furthermore, since the discontinous term is not involved in the reaching law, the chattering is considerably reduced. To show the effectiveness of the proposed scheme, the stability of the proposed system is proved by Lyapunov method and the computer simulations are performed for the Ball Balance System.
