Compound Fractional Integral Terminal Sliding Mode Control and Fractional PD Control of a MEMS Gyroscope

Abstract

This paper proposes a compound fractional order integral terminal sliding mode control (FOITSMC) and fractional order proportional-derivative control (FOPD-FOITSMC) for the control of a MEMS gyroscope. In order to improve the robustness of the conventional integral terminal sliding mode control (ITSMC), a fractional integral terminal sliding mode surface is applied. The chattering problem in FOITSMC, which is usually generated by the excitation of fast un-modelled dynamic is the main drawback. A fractional order proportional-derivative controller (FOPD) is employed in order to eliminate chattering phenomenon. The stability of the FOPD-FOITSMC is proved by Lyapunov theory. The performance of the proposed control method is compared with FOITSMC. Numerical simulations clearly verified the effectiveness of the proposed control approach.