Chattering-free sliding mode control-based disturbance observer for MEMS gyroscope system

This paper proposes a novel disturbance observer (DOB) based on the free-chattering sliding-mode control (SMC) to compensate the changing of the disturbance and uncertain values of a micro-electromechanical system (MEMS) gyroscope. First, the mathematical model of the MEMS system is briefly described. Second, the SMC without the sign function was designed to deal with the problem of tracking references of the MEMS system. Due to the chattering occurs from switching control value, this paper used the sliding phase control without the sign function. Third, a DOB was proposed without the information of control inputs. To delete the conjunction of the first derivative disturbance value, a low-pass-filter was applied to drive the feedback disturbance value for compensating the perturbations of the MEMS system. Fourth, the stability of proposed control method was fulfilled the Lyapunov condition. The simulation results are used to verify the correction of the proposed theory. The effectiveness of the novel disturbance observer based on free-chattering control is a good result of tracking control performances for MEMS system. The tested disturbances and uncertainties on x- and y-axis were mostly rejected. The settling time and overshoot values are very small, the maximum settling-time value is 0.3 s. The steady-state are \(e_{x} \in ( - 10.09, \, 10.03) \times 10^{ - 4}\) and \(e_{x} \in ( - 13.29, \, 14.88) \times 10^{ - 4} ,\) for x- and y-axes, respectively.