Modeling And Active Vibration Isolation Of Low Frequency Precision Permanent Magnetic Vibration Isolation System

The low frequency micro-vibration isolation is a key technology problem in the field of ultra precision machining and measurement such as nanotechnology,microelectronics,cold atom interference,precision gravity measurement,gravitational wave detection,etc.With the rapid development of ultra precision machining precision to nanometer or sub-nanometer scale,the supporting structure of the platform,as the core basic equipment of ultra precision machining equipment,is facing the serious influence of low frequency micro-vibration.The reaction force generated by the high speed motion of the motion stage inside the lithography machine has an increasingly significant impact on precision mechanisms such as objective lenses and measurement sensors.Vibration noise will cause fluctuations in the tip-sample spacing in a scanning tunneling microscope,significantly reducing its measurement accuracy.At present,the research on the magnetic isolation system with low frequency vibration isolation performance and considering both ground vibration isolation and payload direct interference suppression is a core frontier of the field of vibration isolation.The solution of this problem must break through the key technologies of structural optimization,accurate modeling of magnetic field,parameter optimization and active vibration isolation control of magnetic isolation system.In view of this,the main contents of this paper are as follows:In order to solve the problem that it is difficult to considering both low stiffness and large load of low-frequency magnetic vibration isolation system,a low-frequency magnetic levitation isolation structure design method based on the objective of minimizing the equivalent stiffness gradient in the working interval is proposed.In this paper,a multi-pole structure with alternating repulsive and suction forces between permanent magnets is designed using this method.The stator in this structure uses three layers of alternating magnetic poles,and the three layers are designed to alternate the magnetic repulsion and magnetic suction forces respectively.The repulsive force between the permanent magnets generates positive stiffness characteristics and the suction force between the permanent magnets generates negative stiffness characteristics.The superimposed enhancement of the magnetic field between alternating poles increases the magnetic flux density of the air gap in the working interval,thus increasing the suspension force,and decreases the gradient of the air gap magnetic field,thus reducing the equivalent stiffness of the system.The single-layer mover is centered and symmetrically distributed with respect to the stator,which further reduces the equivalent stiffness in the working interval.To address the problem that the working points of permanent magnets in the low stiffness permanent magnet array structure composed of magnetic repulsive force and magnetic suction force are easily affected by external magnetic field,which reduces the calculation accuracy of force characteristics of magnetic levitation isolation system,an accurate analytical modeling method of magnetic levitation force based on the variation law of working points of permanent magnets is proposed.First,the working point of the permanent magnet is analytically modeled as a function of the external magnetic field strength using the equivalent magnetic circuit principle.Based on the working point variation law model,the magnetic field strength of the permanent magnet array is solved accurately.On this basis,the analytical calculation model of the magnetic levitation force of the permanent magnet array structure is established based on the principle of virtual work.Then the broadband vibration isolation performance index is introduced as the optimization objective of size parameters.The performance index is obtained by integrating the vibration transmissibility and payload direct disturbance rejection rate in the low frequency band.Finally,dynamic multi swarm particle swarm optimization algorithm is used to optimize the size parameters of the magnetic suspension vibration isolation system.Aiming at the problem that the model parameters of magnetic suspension vibration isolation system are uncertain,and it is difficult to suppress the ground vibration and the direct disturbance of payload at the same time,an H_∞active vibration isolation method based on weighted isolation performance parameters is proposed.This method makes the active vibration isolation controller of this thesis have the function of isolating ground vibration and direct load disturbance suppression by designing a weighting function of ground vibration transmission rate and load direct disturbance suppression rate as the performance constraint target in the design of H_∞active vibration isolation controller.The designed weighting function varies with frequency,and the weighting coefficients are not fixed.Therefore,the weight between the weighting functions of vibration trans-fer rate and load disturbance suppression rate will change dynamically with frequency.The H_∞control theory is used to design the controller,which can solve the uncertainty problem of the control model.The uncertainty of the model is due to the fact that the equivalent stiffness of the system varies nonlinearly in the operating interval.A force characteristic test system was built to test the force and suspension stiffness of the magnetic levitation vibration isolation system.The results of the force characteristics test show that the relative error between the experimental measured force and the calculated value of the analytical model is as low as 2.10%,which verifies the accuracy of the analytical model of the magnetic levitation force considering the variation of the working point.The vibration isolation performance of the magnetic levitation isolation system was tested in two vibration isolation modes:passive vibration isolation and active vibration isolation,and the inherent frequency and vibration transfer function of the magnetic levitation isolation system were tested respectively.The results of the vibration isolation performance tests show that:the inherent frequency of the vibration isolation system is as low as 0.56 Hz,which verifies the feasibility of the designed low frequency vibration isolation structure;the vibration transmission rate of the active vibration isolation system is less than-23 d B at greater than 1 Hz,which verifies the effectiveness and feasibility of the performance-weighted H_∞active vibration isolation method proposed in this paper to achieve low frequency vibration isolation considering the model uncertainty.