Active Control Method And Experiment On The Stewart Platform For Micro Vibration Isolation

With the development of space industry,the demand for high resolution of imaging,high quality of laser communication and high accuracy of positioning becomes more urgent,but the expected performance is affected by an important factor – the micro-vibration.Micro-vibration is referred to as a kind of vibration that is of unusual small amplitude,e.g.acceleration below 1mg or displacement below 1um.Micro-vibration in spacecrafts is caused mainly by the actuating devices during their on-orbit operation,such as the reaction wheels,the solar-array driving mechanism and the camera swing mechanism.Different from the common vibration,the micro-vibration is inherent,distributed on a wide frequency band and difficult to control.In addition,micro-vibrations induced by different sources in a spacecraft are different,e.g.the solar panel generates low-frequency vibration while the momentum wheel mid-frequency vibration.Due to the complexity of microvibration,control is a challenging task.Active control based on the Stewart platform is proposed to suppress micro-vibration of the payload and two aspects are addressed in this investigation-theoretical analyses and experimental verification.1.The structure of a cubic Stewart platform is analyzed to reveal its advantages in structural symmetry,stiffness and controllability.The cubic configuration simplifies the design of structures,the analysis of dynamics as well as the control methods.The Jacobi matrix that relates the position/ pointing of the payload and the extensions of six struts is derived on the basis of the kinematic analysis of the Stewart platform.This matrix serves as a key factor in the hardware decoupling in active control.To model the Stewart platform,it is simplified into three parts,i.e.the base,the struts and the payload.The substructure synthesis method is applied to derive an FRF model of the platform,which considers the platform as a flexible system and involves inherent modes of the structure.This FRF model is used in the optimization of the platform structure and as a plant in the simulation of active control algorithms.2.Active control methods including the integrated force feedback,the adaptive inverse control reinforced by the Jacobi matrix decoupling and the multi-channel cross-coupling suppression are investigated.The integrated force feedback is deduced on the basis of the constitutive equation of the piezoelectric material.This method uses the force signals of the six-struts to dampen inherent vibration modes.The Jacobi matrix decoupling control incorporating the Jacobi matrix and the superposition principle of linear systems is established to suppress multi-axis micro-vibration in the rigid region(non-resonant region).This method is a hardware decoupling method and it assigns different proportional factors to the six struts and accumulates six pure-direction control to achieve multi-channel decoupling in the rigid region.However,the hardware decoupling control applies only to the rigid region control of the Stewart platform and accordingly is unable to work in the resonant region due to the influence of natural modes.On this account,the multi-channel cross-coupling suppression algorithm is proposed,which takes into account the crosstalk FRFs between different channels to achieve multichannel decoupling control in the resonant region.Through the combination of the above three methods,the multi-channel micro-vibration control of the Stewart platform is realized in a wide frequency range.3.The finite element model of the experimental Stewart platform is established to calculate natural frequencies and mode shapes of each components as well as the whole system.According to the demand of simulation of active control,the impulse responses of the disturbance and control channels of the experimental platform are computed,respectively.Based on the integrated force feedback,the Jacobi matrix decoupling and the multi-channel cross-coupling suppression,active vibration control is simulated to verify the performance of the Stewart platform subjected to periodic,random and hybrid disturbances.The results have demonstrated that the proposed control algorithms are excellent.4.The experimental system mainly consists of a sandbox,a 6-DOF excitation platform,an installation platform and the experimental Stewart platform.Experiments involve measurements of the background vibration,consistency of the six struts,coefficients of the integrated force feedback,calibration of the Jacobi matrix as well as vibration suppression.The effectiveness of the integrated force feedback and the adaptive inverse control in combination with the Jacobi matrix and multi-channel cross-coupling suppression algorithm are verified on the experimental Stewart platform.The results have demonstrated that the Stewart platform is able to suppress tonal,random and hybrid micro-vibration disturbances well,and 35 dB attenuation of tonal vibration and 12 dB attenuation of random vibration can be achieved.