| Microresonator is a typical nonlinear dynamics device in micro-electro-mechanical systems（MEMS）.It has the many advantages,such as low power consumption,high sensitivity,fast dynamic response and high driving efficiency.So the studies of microresonator has attracted extensive attention from scholars at home and abroad.In this paper,the theory of fractional differential dynamic analysis is applied to establish a general fractional-order dynamics model of microresonator,which effectively describes the viscoelastic properties and internal thermal damping of materials.Based on this model,the influence of system parameters of the system on the motion characteristics of the system is analyzed.And,the problem of controlling chaos of the system is dealt with.The main research work and conclusions of this thesis are as follows:1.According to the structural principle of the microresonator system,the electrostatic driving force and the damping coefficient of the film are derived.A general fractional dynamics model of the microresonator is established by Rayleigh-Ritz method,Lagrangian equation and fractional Caputo differential theory.2.Through the mathematical derivation of the Hamilton equation of the system,the equilibrium points and their characteristics of the system under the different system parameters are studied.The global dynamic behavior of the microresonator system is analyzed by simulation.The results show that the number and stability of the equilibrium point of the microresonator system are related to the two internal parameters of the system,nonlinear stiffness?and DC bias voltage?.Further more,by mathematical derivation,the value ranges of internal parameters for both working properly and chaotic motion are determined.3.Using the predictive-corrected numerical algorithm,the dynamic characteristics of the microresonator under different fractional orders,external excitation voltage amplitude and frequency are systematically studied.The results show that the fractional orders have an obvious influence on the dynamics of the system.The influence of fractional orderp1 is more significant than the fractional orderp2.That indicate that chaos can be suppressed by changing the viscoelastic and internal damping of the material of the system.The amplitude and frequency of excitation voltage also have certain influence on the dynamic characteristics of the system.With the variation of excitation amplitude and frequency,the system shows complex dynamics behavior.4.Aiming at the controlling of chaotic motion arising from the fractional-order microresonator system,both the delay feedback control method and the fuzzy sliding mode control method are applied.The results show that the delay feedback control method can effectively control the chaotic motion of the system into a large periodic orbit motion by introducing the velocity feedback term with a simpler controller structure;And the fuzzy sliding mode control method not only can effectively suppress the chaotic motion of the system,but also can control the system into a desired orbit with faster response speed and the high stability.But the controller structure is more complicated. |
