Accelerated Adaptive Backstepping Control of the Chaotic MEMS Gyroscope by Using the Type-2 Sequential FNN

In this paper, we propose an accelerated adaptive backstepping control algorithm based on the type-2 sequential fuzzy neural network (T2SFNN) for the micro-electromechanical system (MEMS) gyroscope with dead-zone and constraints. Firstly, the mathematical model of the MEMS gyroscope is established to perform dynamical analyses and controller design. Then, the phase diagrams and Lyapunov exponents are presented to reveal its chaotic oscillation, which is harmful to system stability. In order to suppress oscillations derived from chaos and dead-zone, an accelerated adaptive backstepping controller is proposed wherein an adaptive auxiliary is established to compensate the influence of nonsymmetric dead-zone on stability performance, along with the T2SFNN designed to approximate unknown functions of dynamic systems. Furthermore, the speed function is introduced to accelerate convergence speed of the control system, and the problem of complex term explosion in traditional backstepping is successfully solved by a second-order tracking differentiator. Finally, simulation results show that the proposed control scheme can guarantee asymptotic convergence of all signals in the closed-loop system, as well as satisfying states constraints and fulfilling the purposes of chaos suppression and accelerated convergence.