최명수(Myeong-Soo Choi) ; 이정훈(Jung-Hoon Lee)
In this paper, a complete proof of Utkin's theorem is presented for the ITSMC(integral terminal sliding mode control) of second order uncertain linear plants when ??≠. The addition of integral action to the TSMCs so called the ITSMC enhances performance in both transient and steady states. Therefore, proof of Utkin’s theorem is essential for ITSMC systems. There are five approaches to designing ITSMCs; control input transformation, sliding surface full transformation, and three sliding surface part transformations, which is for first time pointed out in this paper. The invariance property of the Utkin’s theorem applies only to the first two transformations. Specifically, the sliding mode equation, i.e., the sliding surface, remains invariant for the first two transformations.
However, the invariance property of Utkin’s theorem can not apply to the three additional sliding surface part transformations, although they serve as design and stabilization approaches. The sliding surface full transformation first appears in the TSMCs, except in , while the three sliding surface part transformations appear for the first time in the TSMCs. This paper includes research on the first three transformations, and further studies will cover the last two sliding surface part transformations. This paper presents three transformation methods that achieve the same performances as those obtained through output prediction, predetermination, and predesign. Through an illustrative example and simulation study, the usefulness of the main results is verified.