Abstract
This study focused on a control system of the nonlinear micro-electro-mechanical systems (MEMS) gyroscope. First, sector nonlinearity was used to model a MEMS gyroscope in the Takagi-Sugeno (T-S) fuzzy system. Second, a state observer was designed based on linear matrix inequality (LMI) to identify the optimal eigenvalues of the state tracking error function. Then, full-state fixed-time sliding mode control (FTSMC) was constructed to control the system. Third, a case study of a harmonic disturbance observer was used to address the unknown disturbance of the system. A disturbance observer (DOB) was simply designed based on the error signals of the system outputs and observer outputs. The output signals precisely converged to the predefined trajectories in a very short time, with no overshoots and small of steady-state errors. Moreover, the estimated output states were precisely tracked by the system outputs. These important factors were used to confirm that the control of the T-S fuzzy MEMS was effective and easy to achieve. The study used MATLAB simulation to archive the verification. The maximum of tracking error was ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> ∈ [-4.657:5.565]×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-11</sup> , and the maximum settling time was T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e3</sub> ~ 0.144 for the error of the ẏ- axis and the settling time of the ẋ- axis, respectively.
Highlights
In recent years, the development of robotics, artificial intelligence, and automobile devices have resulted in a need for micro-electro-mechanical systems (MEMS) gyroscope need to be used with high-precision requirements
This paper modeled a nonlinear MEMS in the T-S fuzzy model, and this is an important step for the design of the robust control techniques for MEMS gyroscope systems
A new exogenous disturbance observer based on the fixed-time sliding mode control (FTSMC) for a MEMS gyroscope system was investigated with exponentially convergent speed
Summary
The development of robotics, artificial intelligence, and automobile devices have resulted in a need for micro-electro-mechanical systems (MEMS) gyroscope need to be used with high-precision requirements. The support of a low-pass filter was presented These introduced control technique, such as the LMI, the fixed-time sliding mode control, and the disturbance observer, will be introduced to control the MEMS gyroscope system with the motivation of the following published papers. The mathematical modeling of a MEMS gyroscope into the T-S fuzzy system, the preliminary mathematical operation of the fixed-time sliding mode control, linear matrix inequality and the proposed disturbance observer are shown. Designing the disturbance observer or applying the full-states feedback control is complicated work To meet these difficult requests, the mathematical model of the MEMS gyroscope should be changed into combinations of the sub-linear systems. To control the MEMS gyroscope in (9), this paper proposed the fixed-time sliding mode control based on the state feedback.
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