Stabilization of Ball-On-Sphere System with Super Twisting (ST) Sliding Mode Control (SMC) as a Method of Chattering Reduction

A SMC for the ball-on-sphere system was designed in this work. The mathematical system’s model was first derived and a SMC was designed. Then, Lyapunov’s method was used to test for the convergence on the sliding surface, and convergence of the system's states to the sliding surface was guarant...

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Bibliographic Details
Published inInternational Journal of Engineering and Manufacturing Vol. 10; no. 5; pp. 1 - 17
Main Authors Mohammed, Usman, U. Hussein, Suleiman, Koyunlu, Gokhan
Format Journal Article
LanguageEnglish
Published Hong Kong Modern Education and Computer Science Press 08.10.2020
Subjects
Asymptotic properties
Control systems design
Convergence
Nonlinear equations
Sliding mode control
Stability
Twisting
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Summary:A SMC for the ball-on-sphere system was designed in this work. The mathematical system’s model was first derived and a SMC was designed. Then, Lyapunov’s method was used to test for the convergence on the sliding surface, and convergence of the system's states to the sliding surface was guaranteed. To reduce chattering, a super twisting SMC was designed. A controller that is linear was first given to the system and the simulation results showed that, while there is disturbance, achieving origin’s asymptotic stability is not viable. A SMC was then applied next, while there is disturbance, origin’s asymptotic stability was attained in finite-time. Then a 2nd order SMC was applied and the results showed faster origin’s asymptotic stability in finite time. Therefore, the real effect of applying a 2nd order SMC is faster asymptotic stability of the origin1. To reduce chattering, a ST SMC was applied and the chattering was observed to be reduced efficiently.
ISSN:2305-3631
2306-5982
DOI:10.5815/ijem.2020.05.01