An adaptive dynamic sliding mode control via a backstepping approach for a microelectro mechanical system (MEMS) vibratory z-axis gyroscope is presented in this paper. The time derivative of the control input of the dynamic sliding mode controller (DSMC) is treated as a new control variable for the augmented system which is composed of the original system and the integrator. This DSMC can transfer discontinuous terms to the first-order derivative of the control input, and effectively reduce the chattering. An adaptive dynamic sliding mode controller with the method of backstepping is derived to real-time estimate the angular velocity and the damping and stiffness coefficients and asymptotical stability of the designed systems can be guaranteed. Simulation examples are investigated to demonstrate the satisfactory performance of the proposed adaptive backstepping sliding mode control.
Keywords: adaptive control; backstepping control; dynamic sliding mode control.