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Theoretical and Experimental Study of Friction Emulation and Compensation

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Theoretical and Experimental Study of Friction Emulation and Compensation Theoretical and experimental study of friction emulation and compensation By Tore Bakka Johannes Bächer Thesis submitted in Partial Fulfillment of the Requirements for the Degree Master of Science in Mechatronics Faculty of Engineering and Science University of Agder Grimstad May 2010 Abstract This project deals with hydraulics, mechanics, electronics, dynamic modeling and control theory. The focus is on constructing a test rigg in order to to emulate desired friction and compensate for this with a control loop. The rigg is modeled in matlab/simulink and at last compared to the physical rigg. The rigg reads sensor values and control the servo valves via a CompactRIO. The controllers that are made and implemented in the matlab/simulink model are PI and LQR tracking with integral action. Preface Special thanks is made to our supervisors Professor Michael Hansen and Morten Ottestad. And also thanks to Eivind Johansen for helping us assembling the test stand. 1 Contents Contents 2 List of Figures 5 List of Tables 9 1 Introduction 10 1.1 Motivation . 10 1.2 Goal . 11 1.3 Project description . 11 1.4 Contributions . 11 1.5 Report outline / Thesis Organization . 11 1.6 Project overview . 12 2 Test stand 14 2.1 Overview . 14 2.2 Hydraulics . 14 2.2.1 Accumulator . 15 2.2.2 Valves . 16 2.3 Sensors . 17 2.3.1 Position . 17 2 CONTENTS 2.3.2 Force . 19 2.4 National Instruments components . 21 2.5 Range of Operation . 22 3 Dynamic model 24 3.1 Dynamic equations . 25 3.2 Simulation parameters . 29 3.2.1 Bypass valves . 29 3.2.2 Servo control valve . 31 3.3 Nonlinear model . 36 3.4 Linear model . 36 3.5 Matlab model . 39 3.5.1 Velocity side . 39 3.5.2 Force side . 47 3.6 State space model . 53 3.6.1 Velocity side . 53 4 Verification of Model 56 4.1 Velocity Side . 58 4.2 Force Side . 66 5 Friction Models 68 5.1 Coulomb Friction . 69 5.2 Viscous Friction . 69 5.3 Stiction . 70 5.3.1 Stick-Slip Effect . 70 5.4 Stribeck Effect . 71 5.5 Summary the Models . 72 6 Control strategies/design 73 6.1 Frequency domain technique . 74 6.1.1 Velocity side . 74 3 CONTENTS 6.1.2 Force Side . 80 6.2 Tracking optimal control with integral action . 80 7 Experiments and Results 88 8 Conclusion and further work 89 8.1 Summary of Results . 89 8.2 Problems . 90 8.3 Further Work . 91 Bibliography 93 A SimulationX 95 B Optimal Control with Step Input 97 C Measurements 99 D Test stand 104 4 List of Figures 1.1 Project concept . 13 2.1 Hydraulic scheme for double flow . 15 2.2 Electrical scheme . 16 2.3 Cross-sectional view of a HYDAC standard bladder accumulator, www.hydac.de . 17 2.4 Cross-sectional view of a HYDAC standard bladder accumulator at different volume and pressure levels, www.hydac.de . 18 2.5 Celesco PT1MA-50-UP-420E-M6 . 18 2.6 Electrical coupling . 19 2.7 Calibration curve for position sensor, extension vs. voltage drop . 20 2.8 Load cell, cross-sectional view . 21 2.9 Load cell, installation . 22 2.10 Load cell, Fmeasured vs. Fapplied ................... 23 3.1 Hydraulic cylinder . 26 3.2 Accumulator . 28 3.3 Servo valve sketch . 32 3.4 Bode plot for the servo control valve (from datasheet) . 33 3.5 Bode plot for the servo control valve (from Simulink) . 33 5 LIST OF FIGURES 3.6 Step response for the servo control valve (from datasheet) . 33 3.7 Step response for the servo control valve (from Simulink) . 33 3.8 Mass-spring-damper system for servo valve . 35 3.9 SimulationX model . 37 3.10 Bode plot of velocity side model . 41 3.11 Bode plot of velocity side model . 42 3.12 Block diagram of velocity side model . 43 3.13 Nyquist plot of velocity side model, with disturbance . 45 3.14 Root locus plot of velocity side model, with no disturbance . 46 3.15 Bode plot of force side model . 48 3.16 Block diagram of force side model . 49 3.17 Nyquist plot of force side model, with disturbance . 51 3.18 Root locus plot of force side model, with no disturbance . 52 3.19 Modified block diagram for velocity side . 54 4.1 Definition of system variables . 58 4.2 Results A for 0[V ] and −10[V ] valve signal, velocity side . 61 4.3 Results B for 0[V ] and −10[V ] valve signal, velocity side . 62 4.4 Results A for sine signal to valve, velocity side . 63 4.5 Results B for sine signal to valve, velocity side . 64 4.6 Simulink plots of position and velocity . 65 4.7 Simulink plot of piston side pressure . 65 4.8 Corresponding Simulink plot for results A . 65 4.9 Results A for 0[V ] and −5[V ] valve signal, force side . 66 4.10 Results B for 0[V ] and −5[V ] valve signal, force side . 67 5.1 Coulomb friction model . 70 5.2 approximation with arcus tangent . 70 5.3 Coulomb+viscous+stiction . 71 5.4 Stic-Slipp Effect . 71 6.1 Scheme for feedback control . 74 6 LIST OF FIGURES 6.2 Phase angle as K and Ti vary . 75 6.3 Reference Velocity . 76 6.4 Velocity output . 76 6.5 Servo valve position . 77 6.6 Piston side pressure . 77 6.7 Cylinder position . 77 6.8 Error signal . 77 6.9 Reference Velocity . 78 6.10 Velocity output . 78 6.11 Servo valve position . 79 6.12 Piston side pressure . 79 6.13 Cylinder position . 79 6.14 Disturbance force . 79 6.15 Error signal . 79 6.16 Phase angle as K and Ti vary . 80 6.17 Typical transient response . 81 6.18 Linear quadratic tracking controller with integral action . 84 6.19 Reference Velocity . 86 6.20 Velocity output . 86 6.21 Error signal . 86 6.22 Cylinder position . 87 6.23 Servo valve position . 87 6.24 Piston side pressure . 87 6.25 Disturbance force . 87 A.1 Reference and output velocity . 95 A.2 Reference and output force . 95 A.3 Piston side pressure, force side . 96 A.4 Piston side pressure, velocity side . 96 A.5 Servo valve opening, velocity side . 96 A.6 Servo valve opening, force side . 96 7 LIST OF FIGURES A.7 System pressure . 96 B.1 Reference and output signal . 98 B.2 Error signal . 98 C.1 Servo valve constant, velocity side . 100 C.2 Serve valve constant, force side . 101 C.3 Voltage-current characteristics for self made amplifier . 102 C.4 Oil temperature change during operation . 103 8 List of Tables 2.1 Key data for HYDAC accumulator SB330 - 20 A 1 / 112 U - 330 A050 ................................ 15 2.2 Celesco displacement transducer - data . 19 2.3 Calibration data for position sensor . ..
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