| Micro-electromechanical systems(MEMS)gyroscopes are high-performance inertial sensor systems with the advantages of high precision,low cost,micro size and great integration with IC circuitry,which have greatly revolutionized the inertial navigation industry.However,due to the complexity of its working environment,MEMS gyroscopes are affected by the temperature variation,the mechanical shock and other internal and external interferences.These interferences will lead to the instabilities such as drifts and harmful oscillations,especially for high-frequency chaotic oscillations which will directly lead to performance deterioration or even cause system crash.Meanwhile,there exist problems such as imprecise mathematical modeling,vague dynamic cognition and lack of core control algorithm,all of which make the gyroscope gradually fail to meet the highprecision and high-reliability requirements of current intelligent navigations.Therefore,taking the MEMS gyroscope as the research object,this paper establishes its dynamic model;reveals its dynamic evolution mechanism;and fuse nonlinear dynamics,fuzzy neural network,adaptive backstepping control and other multidisciplinary theories and methods to explore the adaptive control mechanism of the MEMS gyroscope thus eliminating the adverse effects caused by high-frequency chaotic oscillations and unknown nonlinearities,and improving the system accuracy and response speed.This research enriches the adaptive control theory for the MEMS gyroscope,and provides a theoretical basis and a technical guidance for the research and development of advanced equipment such as the inertial navigation,the intelligent vehicle and un-manned orbiting satellite,all of which are integrated with MEMS gyroscope.Specific work contents are as follows:(1)Modeling and dynamical analysis of the MEMS gyroscope: Based on Newton’s law and Kirchhoff’s law,the mathematical model of the MEMS triaxial gyroscope is established.In order to further improve the sensitivity and anti-interference performance of the gyroscope,the mentioned single isolated MEMS triaxial gyroscope is extended to a dualmass MEMS gyroscope with coupling structure based on a mutual mechanical coupling of the mass blocks and considering high-order nonlinearities and asymmetric terms,and then establish its dynamical model.Through dynamical analysis tools such as time histories,phase diagrams and Lyapunov exponents,the inherent nonlinear vibrational characteristics(especially for chaotic oscillations)of the MEMS gyroscope are revealed under different scenarios and system conditions,and the significant influence of the revealed characteristics on the system sensitivity is also demonstrated.This research result provides important theoretical basis and technical support for the subsequent control scheme design.(2)Accelerated adaptive backstepping control for MEMS triaxial gyroscope: For the MEMS triaxial gyroscope with high-frequency chaotic oscillations and state constraints,an accelerated adaptive backstepping control scheme is designed.In controller design,utilize a type-2 fuzzy wavelet neural network(T2FWNN)to estimate the nonlinearities of the system;fuse a speed function to realize the accelerated convergence of state variables;construct a time-varying barrier Lyapunov function(BLF)to restrict the state variables into the prescribed ranges;and design a hyperbolic tangent tracking differentiator(HTTD)to approximate the virtual control inputs with high precision thus reducing the computational complexity in the traditional backstepping.Stability analysis proves that all signals in the closed-loop system are ultimately bounded.The majority of the simulated results demonstrate that the proposed scheme not only suppresses the chaotic oscillations but also achieves good tracking performance(stable in 0.02 seconds and the tracking errors are limited within [-0.005,0.005]).This study provides a useful theoretical basis for the subsequent adaptive backstepping control design for the dual mass MEMS gyroscope with a coupled structure.(3)Event-triggered fuzzy PID control for the dual-mass MEMS gyroscope:Aiming at the dual-mass MEMS gyroscope with a coupled structure,an event-triggered fuzzy PID control scheme is proposed to realize its stability control.In controller design,the fuzzy logic is used to adjust three parameters of PID online thus improving its control effect;the event triggering strategy is introduced to reduce the update rate of control signals and realize the communication resources saving.Simulation results verify the effectiveness of the control scheme.This research provides a meaningful research idea for the subsequent adaptive backstepping control scheme design of the dual mass MEMS gyroscope.(4)Adaptive backstepping funnel control for dual-mass MEMS gyroscope: To break through the limitations of PID control and further improve the stability and robustness of the dual-mass MEMS gyroscope,an adaptive backstepping funnel control scheme with an event-triggered mechanism is researched based on the research contents of(2)and(3).In order to comprehensively address the control problem involving the uncertainty,the slow convergence,the state constraint,the “item explosion” and the communication resource waste,an accelerated adaptive backstepping funnel control mechanism is revealed by fusing a type-2 sequential fuzzy neural network(T2SFNN),a speed function,asymmetric funnel boundaries,an accelerated exponential integral tracking differentiator(AEITD)and an event-triggered strategy.Lyapunov stability analysis proves that all signals in closed-loop system are bounded,the state constraints are not violated and Zeno behavior is excluded.Simulation results demonstrate that the recommended control scheme achieves highprecision target trajectories tracking(stable within 0.05 seconds;steady-state error is limited in [-0.1,0.08]),along with saving the computational resources for about 95%.Meanwhile,the superiority of the proposed scheme is verified,compared to the research content in(3). |
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