Research On Dynamic Modeling And Vibration Control Of Six-degree-of-freedom Platform

The vibration source generated by the periodic motion of the crank-connecting rod mechanism of the diesel engine inevitably leads to the vibration of the diesel engine and the propulsion shaft system,and then causes the vibration of ship hull.This kind of vibration can be transmitted to other power machinery through the hull,and reduce the reliability and working life of the structure,destroy the stable environment required by the precision instruments,reduce the sensitivity,affect the normal operation.Therefore,studying effective vibration control measures,exploring high-precision,large-capacity vibration isolation and stabilization platforms have practical application value.Since the six-degree-of-freedom(6-DOF)platform can be simultaneously driven by multi-axis coupling,it has incomparable advantages in the fields of vibration isolation and absorption compared with other variable stiffness tuning structures,and can realize vibration control in multiple degree of freedom.Although there are many studies on the dynamics modeling of 6-DOF platform,some assumptions in the modeling don’t conform to the reality,which will reduce the accuracy of the model and affect the selection of control strategies.In this paper,a precise dynamic model of 6-DOF platform is established,and the control algorithm is designed.Furthermore,the mathematical model of 6-DOF platform with moving base is intensively investigated.The main research contents of this paper are described as follows:(1)Establish dynamic model of a 6-DOF platform with a fixed base.Firstly,the original classic closed-loop dynamic model of the Stewart platform based on the Newton-Euler method is improved.The correction factors include: considering the rotational degree of freedom of the pods around the axial direction,correcting the direction of constraint moment at the universal joint,applying the parallel axis theorem when calculating the moment of inertia of each part,distinguishing the momentum theorem based on moving point and fixed point in the dynamic equations of pods and platform.Two improved models expressed by centroid moment of inertia and non-centroid moment of inertia are obtained.By comparing the calculation results of the classic model and the improved model,the influence of the correction factors on the system is quantitatively explained.Finally,the improved model is sorted into a compact form of generalized coordinate expression to facilitate the design of the control algorithm.(2)Analysis of valve-controlled hydraulic servo system.Firstly,the transfer function of the four-way valve controlled asymmetric cylinder electro-hydraulic servo system of this paper is established,and the stability of the system is analyzed through open and closed loop frequency domain analysis.Then the natural frequency equation of the Stewart platform is derived based on the dynamic model,and its correctness is verified.The natural frequency of the system changes with the platform’s pose,since both the mass matrix and the stiffness matrix are functions of the pose.Solve the natural frequencies of the platform at each operating point at different heights,so as to discuss the influence of the correction factors considered by the improved model on the natural frequency characteristics.The calculation results show that in the initial height plane,with the change of the operating point,the changes of the natural frequencies of each order are basically symmetrical about the x-axis and the y-axis.In other planes,the situations are more complicated.For platforms with large load inertia and a small proportion of mass and inertia of the pods,the correction factors mainly affect the non-diagonal elements of the mass matrix,thereby changing the natural frequency of the relative coupling order,while the single degree of freedom natural frequency changes less.On the contrary,for platforms whose load mass and inertia is close to the mass of the pods,the correction factor makes all order frequencies change obviously.(3)Design of control algorithm for 6-DOF platform.Firstly,the correctness of the dynamics model of the platform is verified by comparing the calculated results with the experimental results in other literature.Then,each leg is regarded as an independent system,and the PID control strategy based on the joint space is designed.The algorithm shows good performance for both fixed point control and time-varying trajectory tracking targets,and the steady state error can be eliminated in joint space.In order to improve the transient response characteristics of the system and increase the frequency bandwidth of the control system,dynamic pressure feedback correction is adopted to increase the damping ratio.The PID algorithm with dynamic pressure feedback in joint space has better stability and the dynamic characteristics when tracking the time-varying desired trajectory.Finally,PD control based on gravity compensation,sliding mode variable structure control based on calculated torque method are designed,with the dynamic characteristic of the system is taken into account.These two dynamic control schemes decouple the system by introducing dynamic compensation internal control loop.The simulation results show that compared with the motion control scheme,the dynamic and static characteristics of the system are significantly improved,and the steady-state error is eliminated.(4)Establish dynamic model of a 6-DOF platform with moving base.Based on the Newton-Euler method,the characteristics of the 6-DOF platform on the moving base are studied.In the modeling process,the rotational freedom of the pod around its own axis and the moments of inertia of each part are taken into account to obtain a complete dynamic model represented by generalized coordinates.The model is concise and efficient.Each part of the system equation is more complicated than the case of fixed base,with higher coupling and nonlinearity.The results show that the 6-DOF platform can achieve the vibration control target in multiple directions under various excitation.The improved model can more accurately predict the dynamic response of the system,solve the inherent characteristics,and provide guidance for the design of optimal vibration control scheme.The establishment of the model of the moving base provides a theoretical basis for studying the application of 6-DOF platform in the field of isolating of foundation vibration and vibration absorption.