| Title |
A Poof of Utkin's Theorem for ISMC of Uncertain Nonlinear Plants |
| DOI |
http://doi.org/10.5370/KIEE.2019.68.3.460 |
| Keywords |
Variable structure system ; Sliding mode control ; Proof of Ukin's Theorem ; Nonlinear system transformation methods |
| Abstract |
Nowadays the integral action has been augmented to the VSS(variable structure system) or SMC(sliding mode control) to improve the control performance. In this note, for the integral sliding mode control(ISMC) of SI(single input) uncertain nonlinear systems, a complete proof of Utkin's theorem is presented. The Utkin's invariance theorem with respect to the two nonlinear transformation methods so called the two diagonalization methods is proved clearly, comparatively, and completely for the ISMC of SI uncertain nonlinear systems. With respect to the sliding surface and control input transformations, the equation of the sliding mode i.e., the integral sliding surface is invariant, which is proved completely. During the proof, the guideline for obtaining the ideal sliding dynamics of the integral sliding surface is provided and by using the solution of the ideal sliding dynamics the controlled output is predictable, which is shown in the design example and simulation study, and the design rule of the nonlinear feedback gains of the ISMC are proposed. Through an illustrative example and simulation study, the usefulness of the main results is verified. By means of the two nonlinear transformation methods, the same results can be obtained. |