| China is an earthquake prone country,shaking table as the equipment of testing building seismic resistance,plays the vital role in disaster prevention and mitigation.In order to avoid the problems brought by the reduced scale experiment,redundant multi-axis shaking table is a development trend.For multi input multi output system,inevitably there are coupling between each degrees of freedom(DOF),not only make the actual vibration generated unnecessary output coupling,but also affect the regulation of performance each DOF.Decoupling is a basic work,the performance of the system can be improved greatly only if the coupling is reduced,this article focuses on study of modal decoupling control.Aiming at the multi-axis redundant shaking table,the kinematics and dynamics equations are established,and the vibration coupling between each DOF are analyzed,the results show that the coupling between each DOF are severe,and the dynamic characteristics of each DOF exist multiple resonant peaks,therefore it is difficult to control to improve the performance.In this paper,the analysis of modal theory is carried out,and the mapping relation between physical space and modal space is established.The basic reason for introducing the modal control is that there is no coupling between each DOF in the modal space,the vibration modes of each stage are independent.Therefore,this paper focuses on the analysis of impact of modeling error for the modal control,the results show that without considering the quality of hydraulic legs,in modal space the coupling of each DOF is still very severe,thus it can't ignore the quality of hydraulic legs.In this paper,the inherent modal space frequency,damping ratio and resonance peak are analyzed,the results showed that with the increase of 6 order modal frequencies,the corresponding damping is getting smaller,and the resonant peak is higher.At the same time,in modal space,the dominant coupling resonant peaks is at two times of the modal natural frequency,but in the physical space,the dominant coupling resonant peaks between each DOF is at the modal natural frequency,meanwhile the coupling resonance peak between each DOF depends on the natural frequency and damping of the coupling output modal DOF.In this paper,modal feedforward and DOF feedforward are analyzed.The results show that the modal feedforward after mapping uncoupled moda l space to the physical space,can make each DOF uncoupled as before.DOF feedforward has slightest impact on the coupling between each DOF in physical space,but the DOF feedforward can improve the coupling between each DOF in modal space,greatly reduce the impact of flexible foundation in modal space.Given that the uncertainty of the mass and stiffness matrices of the actual system,this paper proposes a method based on experimental modal matrix calculation,and the number of parameter influence of modal matrix 6×6 is simplified to two.The results show that the modal matrix is relatively accurate,so the method is feasible.Given that the uncertainty of the mass and stiffness matrices of the actual system,this paper proposes a method based on experimental modal matrix calculation,and the number of parameter influence of modal matrix 6 × 6 is simplified to two.Given that after mapping uncoupled modal space to physical space,physical space coupling is still serious,this paper proposes modal control combination with DOF control,feedforward control,three state feed Back control,force control strategy.This method fully decouples the coupling between each DOF in physical space in theory,the simulation results show that the decoupling effect is very obvious,approximate to full decoupling,while decoupling effect is 3-8d B in experiment,it shows that this algorithm is feasible.Meanwhile the results show that the modal feedforward can adjust the amplitude frequency characteristics uniformly,after mapping to the physical space,there is still no coupling between each DOF.But the DOF feedforward has no influence on the coupling of each DOF in physical space. |
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