Direct reaching sliding mode control

Sliding mode control(SMC) system synthesized by traditional reaching condition can not grantee all phase trajectories from the neighborhood of the sliding mode to direct reach the nearby sliding mode branch. It will cause the state transition to be slow and overshooting which are not allowed in some engineering. In order to make the dynamic procedure of a SMC system unidirectional convergent, the direct-reaching SMC(DRSMC) was presented. By analyzing the shortcomings in the expression of traditional reaching condition, the definition of direct-reaching function and the establishment of direct-reaching condition were introduced. Direct-reaching condition(DRC) is the basis of using DRSMC to synthesize a SMC system. A DRSMC system is composed of a command mode model and an on-off type DRSMC model. Different from the traditional reaching condition, the control which satisfies the DRC can guarantee all phase trajectories from the neighborhood of sliding mode to direct reach the nearby branch of the sliding mode and then go to zero state. Therefore the state transition process will be fast and monotonous. The DRSMC was applied to an example system and was simulated. The simulation result accords with the performance expectation of DRSMC.