Research On Modeling,Precise Algorithm And Control Of Flexibl Impact System

In the present paper, modeling, numerical simulation, control of flexible impact system and applications of the precise integration method were studied.To model the flexible impact system, finite element theory and mode method were respectively used to establish the dynamic equation of the rotating flexible beam, then impact models were built using constraint equation and Hertz contact theory, they were differential/algebraic equation and complicated nonlinear equation respectively. At the same time, the model of ball-flexible body impact system was built using Hertz contact theory, its equation was nonlinear integral equation.The precise integration method of differential equation was presented by using 2 algorithm, its numerical precision was also analyzed. Applied the precise integration method to solve stiff equations and nonlinear equations, and improved the method from explicit and implicit aspects. It found that the exact solution of some differential equations may be obtained, and always stable absolutely.To the problems of numerical simulation. According to the different dynamic models, the time precise Baumgarte modify technique and the method to solve state equations were used to simulation the flexible impact system, the satisfactional results were obtained.To the control problem. The dynamic control equation of the problem that a simplified flexible rotating beam impact system was established, and the linear quadratic optimal control strategy was used to study above control problem. Let the impact phenomena to be the disturbance of the system, in the frame of H₈ control theory, the control model of simple fleixble was established. Because the emphasis of two control methods was computing matrix Riccati equation, so based on the simulation relations between computational structural mechanics and optimal control, the minor structure method was applied to solve the matrix riccati equations, and combined with the precise integration method, increased the precision of solution greatly. The numerical solution showed that the control strategy in this paper was effective.