| The flexible manipulator is widely used in aerospace operation manipulator and longspan engineering manipulator because of its outstanding advantages such as light weight,large working radius,high mobility,high load ratio and low energy consumption.However,the flexible manipulator will have obvious elastic vibration in the process of movement,which seriously affects the positioning accuracy of its end.The strong vibration coupling between the multi joint flexible arms greatly increases the difficulty of modeling the rigid flexible coupling dynamics of the flexible arms.It is also very difficult to clarify the nonlinear mapping relationship between the multi-point vibration signal and the vibration state of the flexible arms and to design the active vibration reduction control algorithm of the multi joint flexible arms.Therefore,in-depth study of the rigid flexible coupling dynamics modeling,the vibration state measurement method of the flexible arm and the vibration reduction control algorithm of the flexible arm end have important theoretical significance and engineering application value for the vibration suppression and precise positioning control of the flexible arm end.In this paper,the low-frequency,small amplitude and multi degree of freedom flexible manipulator with rigid rotating joints is studied.The dynamic modeling,real-time measurement of the vibration state and the vibration and precise positioning of the end of the flexible manipulator are studied.The main contents of this paper are as follows:(1)The rigid flexible coupling dynamic model of the flexible arm with small amplitude vibration is established.In view of the complexity of the rigid flexible coupling dynamics modeling and the large amount of calculation work of the multi joint flexible arm,a method for the rigid flexible coupling dynamics modeling of the multi degree of freedom flexible arm is proposed,its mathematical model is established,and the corresponding symbolic expression calculation program is developed by using the software of Mathematica.Finally,the correctness of the modeling method is verified by simulation.It effectively reduces the difficulty of dynamic modeling and simplifies the process of modeling and calculation.(2)The experimental system of two degrees of freedom low frequency small amplitude rigid flexible coupling manipulator is developed.In order to facilitate the theoretical and experimental research of rigid flexible coupling manipulator,an experimental system with two degrees of freedom is developed.Through theoretical calculation and ADAMS simulation,the mechanical structure and size parameters of the flexible arm are determined,a multisensor system is developed to measure the multi-point vibration signal of the flexible arm,an embedded real-time data acquisition and control system based on c RIO 9035 is constructed,a switch drive system of the BLDCM is designed,and the interface program between the systems is developed.The experimental performance test shows that the experimental system is reliable and effective,and can meet the expected performance requirements.(3)A low-cost real-time measurement method of vibration state and end position of flexible arm is proposed.To solve the problem of measuring the vibration state and end position of the flexible arm,a low-cost and high-precision multi-sensor data fusion algorithm based on Kalman filter is proposed,which can measure the vibration state and end position of each arm in real time.The multi-point vibration signal of the flexible arm is measured by strain gauge and accelerometer,and the dynamic bending moment at the joint of the flexible arm is calculated by the theory of elasticity.Data fusion is carried out according to the Kalman filtering principle,and the vibration state and end position of the flexible arm are measured in real time.The error between the real-time vibration state and the end position measurement results and the theoretical results is 5.5 %,which shows that the measurement method is correct and effective.(4)A double optimal control algorithm is proposed,which is suitable for small amplitude and low frequency vibration.In view of the problems of the multi joint flexible arm which is difficult to suppress vibration and the end position is difficult to control accurately,a method of transforming the vibration reduction and precise positioning control of the end of the flexible arm into the virtual angle tracking control of the rigid arm joint is proposed.The optimal controller based on LQR is designed,which can quickly suppress the vibration of flexible arm,and make the end of flexible arm accurately locate in the desired position.Considering the modeling error,a robust optimal guaranteed cost controller based on LMI is designed.The experimental results verify the effectiveness of the control algorithm. |
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