Luận án tiến sĩ khảo sát động lực học và điểu khiển vị trí của tay máy hai khâu

MINISTRY OF EDUCATION MINISTRY OF NATIONAL AND TRAINING DEFENCE MILITARY TECHNICAL ACADEMY DUONG XUAN BIEN DYNAMIC MODELLING AND CONTROL OF TWO-LINK FLEXIBLE ROBOTS BY USING FINITE ELEMENT METHOD DOCTOR OF PHILOSOPHY HA NOI, 2019 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com MINISTRY OF EDUCATION MINISTRY OF NATIONAL AND TRAINING DEFENCE MILITARY TECHNICAL ACADEMY DUONG XUAN BIEN DYNAMIC MODELLING AND CONTROL OF TWO-LINK FLEXIBLE ROBOTS BY USING FINITE ELEMENT METHOD Major: Technical mechanic Code: 9.03 DOCTOR OF PHILOSOPHY SCIENCE SUPERVISORS: 1. Associate Prof, Dr Chu Anh My 2. Associate Prof, Dr Phan Bui Khoi HA NOI, 2019 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ACKNOWLEDGMENTS I would like to express my deepest gratitude to Professor Chu Anh My and Professor Phan Bui Khoi for their support, dedicated guide and research orientation on this work. I wish to thank all my colleagues from Advanced Technology Center, Faculty of Mechanical Engineering, Faculty of Aerospace in Military Technical Academy and School of Mechanical Engineering in Hanoi University of Science and Technology for the help they gave me in the many different occasions.

The greatly appreciation is to my family for their love and support. Last but not least, I would like to thank all the others that are not mentioned and helped me on this thesis. LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com CONFIRMATION BY AUTHOR I pled that this thesis is my own research work. The results presented in this work are honest and has not been published by anyone in any other works.

The information cited in this thesis is clearly stated origins. August, 2019 Duong Xuan Bien LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com LIST OF SYMBOLS AND ABBREVIATIONS Li , lie Length of link i , length of each element of link i i Angle between link i − 1 and link i Number of links of robot, number of elements of link i n, ni ,i (t ) and joint variable of link i x Arbitrary point on the element j of link i m (x ), m = 1  4 Shape functions of element j Elastic displacement at arbitrary point on element j of wij (t, x ) link i ui (2 j −1), ui(2 j ), Flexural displacement, slope displacement of node j ui (2 j +1), ui (2 j +2) and node j + 1 of element j of link i , respectively ui (2n +1), ui (2n + 2) Flexural and slope displacement at end point of link i i i u(i −1)(2k −1), u(i −1)(2k ), Flexural and slope displacement at node k and node u(i −1)(2k +1), u(i −1)(2k +2) k + 1 of element k of link i − 1 Flexural and slope displacement at the end point of link u(i −1)f , u(i −1)s i −1 General homogeneous transformation matrix which Hif(i −1) transforms from the coordinate system Oi XY i i to the coordinate system Oi −1Xi −1Yi −1 Position vector of arbitrary point on the element j of rij , r0ij link i in the coordinate systems Oi XY i i and O0X 0Y0 Position vector of the end point of link 2 in cases of rigid r02r , r02 f and flexible models in the coordinate system O0X 0Y0 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com di (t ), i (t ) Translational and rotational joint variable of link i Elastic displacement vector of the element j of link i qijcv (t ), qicv (t ) and elastic displacement vector of link i Generalized elastic displacement vectors of the element qij (t ), qi (t ), q(t ) j , of the link i and of the system Mass per length unit of link i , mass of motor i , mass of mi , mdci , mt the tip load Kinetic energy of element j of link i , kinetic energy of Tij ,Ti ,T link i and kinetic energy of system Elastic deforming kinetic energy of link i , kinetic Tie ,Tid ,Tp energy of motor driving link i and the tip load Elastic deforming potential and gravitational potential Pije , Pijg , Pi , P energy of element j of link i , potential energy of link i and the system Mj , Mi , M Mass matrix of element j , link i and system. Mdc , Mtt Mass matrices of the motor and the tip load Kj , Ki , K Stiffness matrix of element j , link i and system. C(q, q) Coriolis matrix Qex (t ) Generalized force/torque vector of the system Fi (t), i (t ) Driving force, torque at the joint i Joint variable error vector, error vector in objective e*(t ), e(t ),V function and Lyapunov function KP , KI , KD Cross matrix of control parameters in PID controller LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com TABLE OF CONTENTS Pages PREFACE.

LITERATURE REVIEW OF FLEXIBLE ROBOT DYNAMIC AND CONTROL. Applications of flexible robots. Classifying joint types of flexible robots. Classifying flexible robots.

Differential motion equations. Recent works on flexible robots. Position accuracy of motion of flexible robots. Comments and problems.

20 Conclusion of chapter 1. DYNAMIC MODELING OF THE PLANAR FLEXIBLE ROBOTS. Kinematic of the planar flexible robots. Dynamics of the planar flexible robots.

38 Conclusion of chapter 2. DYNAMIC ANALYSIS AND POSITION CONTROL OF THE PLANAR TWO-LINK FLEXIBLE ROBOTS. Position control system of the planar serial multi-link flexible robots. 86 Conclusion of chapter 3.

Objective and experimental model. Parameters, equipment and method of measuring. System connection diagram. 105 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.

Method of handling the measurement data. 110 Conclusion of chapter 4. 115 CONCLUSION AND SUGGESION. 116 LIST OF THE RESEARCH PAPERS OF THE AUTHOR.

139 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com LIST OF TABLES Table 2. The parameters  i , u(i 1)s , u(i 1) f , i , a i depending on types of joints. The dynamic parameters of flexible robot type I (continuous). The mass ratios between the flexible links and tip load.

The maximum elastic displacements at the ending points of the links. The parameters of the flexible robot type IV. The length of the links in two cases. The maximum values in two cases.

The parameters of flexible robot type III. The parameters of the flexible robot type IV. The parameters of the GA and the position PID controller. The comparative results the control quality between two cases 94 Table 3.

The parameters of the GA and the position PID controller. The comparative results the control quality between two cases 97 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com LIST OF FIGURES Figure 0. The structure of the thesis. The order executing the thesis.

The flexible robot in space. Flexible robot in medicine. Translational joint type Pa. Translational joint type Pb.

The single-link flexible robot with rotational joint. The single-link flexible robot with translational joint. The two-link flexible robots with only rotational joints. The two-link flexible robots consist translational joints.

The planar serial multi-link flexible robots. The parallel-link flexible robots. The mobile fiexlible robots. Flexible planar closed mechanism [8].

Spring-mass system [45]. The single-link flexible robot with joint Pa [133]. The two-link flexible robot Quanser. The two-link flexible robot with rotational joints.

The flexible robot with rotational and translational joints. A generalized schematic of an arbitrary pair of flexible links. 35 LUAN VAN CHAT LUONG download : add luanvanchat@agmail. The two-link flexible robot with rotational joints [64].

Parts of matrix M2j. The position of the element k and the robot type VII. The solving algorithm without the joint Pb. The solving algorithm with the joint Pb.

The schematic of the solving forward dynamic on SIMULINK. The torque at joint 1. The torque at joint 2. The value of joint 1 variable.

The value of joint 2 variable. The value of flexural displacement at the end of link 1. The value of slope displacement at the end of link 1. The value of flexural displacement at the end of link 2.

The value of slope displacement at the end of link 2. The position of the end-effector in OX. The position of the end-effector in OY. The flexible robot type IV.

Schematic of solving forward dynamic in SIMULINK. The driving force rule. The driving torque rule. The value of translational joint.

The value of rotational joint. The value of flexural displacement. The value of slope displacement. Position deviation in OX.

Position deviation in OY. The value of translational joint. The value of rotational joint. The value of flexural displacement.

The value of slope displacement. The position deviation in OX. 73 LUAN VAN CHAT LUONG download : add luanvanchat@agmail. The position deviation in OY.

The flexible robot type III. Schematic to solve the forward dynamic of the system in the SIMULINK. The rules of driving torque and force .The rotational joint variable displacement. The translational joint variable displacement.

The value of the flexural displacement. The value of the slope displacement. The position of end-effector in OX. The position of end-effector in OY.

The solving inverse dynamic schematic in SIMULINK. The translational joint variable. The rotational joint variable. The value of driving force.

The value of driving torque. The deviation of force between rigid and flexible models. The deviation of torque between rigid and flexible models. The flexural displacement value.

The slope displacement value. The rotational joint variable value. The translational joint variable value. The driving torque value.

The driving force value. The torque deviation value. The force deviation value. The flexural displacement value.

The slope displacement value. Schematic of the GA. The control schematic PID with the GA. The translational joint variable.

The rotational joint variable. The flexural displacement. The slope displacement. The driving force.

95 LUAN VAN CHAT LUONG download : add luanvanchat@agmail. The driving torque. The position of end-effector in OX. The position of end-effector in OY.

The rotational joint variable. The translational joint variable. The flexural displacement. The slope displacement.

The position end-effector point in OX. The position end-effector point in OY. The driving torque. The driving force.

Lead screw system. Step motor at the rotational joint. DC motor GB37-3530. Step motor NEMA 17.

Flex sensor FSL0095-103-ST. System connection diagram. Principle diagram inside Arduino 2560. Flex sensor circuit.

The value of translational joint variable. The value of rotational joint variable. The value of flexural displacement. The value of translational joint variable.

The value of rotational joint variable. The value of flexural displacement. 149 LUAN VAN CHAT LUONG download : add luanvanchat@agmail. Rotational joint variable (1 element).

Rotational joint variable (7 elements). Rotational joint variable (1, 3, 5, 7 elements). Rotational joint variable (1 element). Rotational joint variable (7 element).

Rotational joint variable (1, 3, 5, 7 element). PID control law in SIMULINK. 158 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com 1 PREFACE In the past several years, lots of robots have been designed and produced all over the world because of their important applications. Nowadays, using robots is more and more popular in various fields.

In the literature, most of the designed robots are considered with an assumption that all the links of the robots are rigid bodies.