| Title |
Proof of Utkin’s Theorem for TSMC of Second Order Uncertain Plants |
| Authors |
최명수(Myeong-Soo Choi) ; 이정훈(Jung-Hoon Lee) ; 김정규(Jeong-Gyoo Kim) |
| DOI |
https://doi.org/10.5573/ieie.2023.60.4.83 |
| Keywords |
Variable structure system; Sliding mode control; Proof of Utkin’s theorem; Transformation method; Terminal sliding mode control(TSMC) |
| Abstract |
In this note, a complete proof of Utkin's theorem is presented for the TSMC(terminal sliding mode control) of second order uncertain linear plants when . In the previous works of the TSMCs, the proof is rare and done when . The Utkin’s invariance theorem with respect to the two transformation methods so called the two diagonalization methods is proved clearly and comparatively for second order uncertain linear systems when . With respect to the two transformations i.e. the sliding surface transformation and control input transformation, the equation of the sliding mode i.e., the sliding surface is invariant. Among the two transformations, the sliding surface transformation for the first time appears in the TSMC. By means of the two transformation methods the same performance results can be obtained. Through an illustrative example and simulation study, the usefulness of the main results is verified. |