The stability of steady state synchronous and nonsynchronous response of a nonlinear rotor system supported by squeeze-film dampers is investigated. The nonlinear differential equations which govern the motion of rotor bearing system are obtained by using the Generalized Polynomial Expansion Method. The steady state response of system is obtained by using the hybrid numerical method which combines the merits of the harmonic balance and collocation methods. The stability of system response is examined using Floquet-Liapunov theory. Using the theory, the performance may be evaluated with the calculation of derivatives of nonlinear hydrodynamic forces of the squeeze-film damper with respect to displacement and velocity of the journal center. In some cases, these derivatives can be expressed in closed form and the prediction of the dynamic characteristic of the nonlinear rotor system will be more effective. The stability results are compared to those using a direct numerical integration method and both are in good agreement.
The stability of steady-state synchronous and nonsynchronous response of a nonlinear rotor system supported by squeeze-film dampers is investigated. The nonlinear differential equations that govern the motion of rotor bearing systems are obtained by using the Generalized Polynomial Expansion Method. The steady-state response of the system is obtained by using the hybrid numerical method, which combines the merits of the harmonic balance and collocation methods. The stability of system response is examined using the Floquet-Liapunov theory. Using the theory, the performance may be evaluated with the calculation of derivatives of nonlinear hydrodynamic forces of the squeeze-film damper with respect to displacement and velocity of the journal center. In some cases, these derivatives can be expressed in closed form and the prediction of the dynamic characteristic of the nonlinear rotor system will be more effective. The stability results are compared to those using a direct numerical integration method and both are in good agreement.
In the paper, we study the stability of the discretetime networked control systems. If the network link is with a limited communication capacity, the network-induced delay is unavoidable. Considering the network-induced delay, the closed-loop networked control systems are usually subject to the delayed state. The traditional method for the study of the networked control systems is mainly to construct a Lyapunov function and derive the stability criterion. Generally, the derived stability condition is only sufficient. The selection of the Lyapunov function is attracting increasing attention as a better Lyapunov function may lead to less conservative results. In this work, we use an alternate way to get the less conservative results. A time-domain Smith predictor is employed to predict the non-delayed state. Then, the control law is the feedback of the delayed measurements and the non-delayed prediction. Simulation results are given to show that the proposed control law can expand the upper bounds with the existing relative conservative stability criterion.
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