Research On Dynamic Modeling And Controlling Of Hydraulically Driven Flexible Arms

Theory of dynamics of flexible multibody system is now paid more attention to than before with the development of large,light-weight and high speed mechanics.Flexible arms are taken as an object in this paper.Theories about construction of dynamics model of the flexible arms,natural frequencies of the flexible arm vibrating about the nominal rigid rotation and control of the flexible arms are studied in this paper.There are four main topics:(1)The first topic is the research on the dynamic model of the arms. Approximation of the structure of the flexible arms is taken into consideration/which is one of the key points in modeling of the flexible system. Main tasks are as following (a)establishing mass matrix of the arm by three dimensional finite element method; (b) Infinite method is used to simulate the structure of the two-flexible links. Displacements and angles of the nodes are defined to be the elastic coordinates.This method can obtain a more accurate simulation of the flexible structure.Density of the beam with loads on the tip is expressed in density function,which is defined as the following:The expression of the function is simple and it cannot cause complex calculations when deducing the dynamic model of the beam; One of the steps to build models of flexible systems is expression of the generalized force, and always virtual energy theory is used to work it out,studies are also done on the method to calculate generalized force.(2) The second topic is developing dynamic models for the hydraulic flexible arms. A CC2500 crane is set as an object in this paper,model of this crane is developed and a whole model of the flexible two-links' system which includes mechanical part,electric part and hydraulic part is also developed,simulation of the dynamics of the flexible two-links is done.(3)The third topic is the analysis of the natural frequencies of the arm's elastic vibration in a nonlinear inertial frame.Flexible arm undergoes elastic vibration during it's rigid rotation, and the two movements are coupled with each other, which makes the natural frequencies more complex, and it is no longer a constant, but a variable varying with the rotary speed of the arm. Based on nonlinear displacement frame and dynamic stiffening, vibrating model is established around the nominal movement. Complex modal analysis method is used in uncoupling the dynamic equation. The results turn out that the natural frequencies of the arm will increase when rotary speed of the arm increases, and it gets prominent if the rotary speed get higher. When rotary speed slows down especially when it is lower than the basic natural frequency of the arm which is obtained by means of structural mechanics, the frequencies turned to be a constant, and rigid flexible coupling can be ignored.(4)The forth topic is designing the controller for tracing the displacement of the tip of a flexible arm.This paper takes the hydraulic crane as an example. Linguistic variables of a Fuzzy controller has the decoupling function,so control of the angles and the control of the elastic vibration can be independent with each other.The angle subsystem is called slow subsystem and the elastic vibration system is called quick subsystem.In the slow subsystem, a fuzzy PD controller is designed for controlling the trajectory of the angle's displacement.The expected angle of the arm joint is decided through the rigid geometry between the arm and angle of the joint.My work done in this aspects are as the followings,(a)Initial parameters of the Fuzzy PD controller are set according to Bode steady analysis;(b)the increments of the parameters are obtained through online fuzzy control.(c)In the quick subsystem,a fuzzy controller is designed to eliminate the elastic vibration of the arm.My work about controlling on the flexible two-links is:(a)fuzzy PD and basic Fuzzy method are used to control the angles of the arms' moving trace.(b)Point error method are presented to be the error of the system, the tip's trace of the upper arm is controlled by the above two independent controller. (c)Displacement of the tip is controlled through the control of the angles and the control on the elastic vibration.