PARAMETERES ESTIMATION FOR MOTION CONTROL AND

FRICTION COMPENSATION

Branesh Madhavan Pillai

(128018U)

Degree of Master of Science

Department of Electrical Engineering

University of Moratuwa

Sri Lanka

August 2013

PARAMETERS ESTIMATION FOR MOTION CONTROL AND

FRICTION COMPENSATION

Branesh Madhavan Pillai

(128018U)

Thesis submitted in partial fulfillment of the requirements for the degree

Master of Science

Department of Electrical Engineering

University of Moratuwa

Sri Lanka

August 2013

i

DECLARATION

I declare that this is my own work and this thesis does not incorporate without acknowledgement

any material previously submitted for a Degree or Diploma in any other University or institute of

higher learning and to the best of my knowledge and belief it does not contain any material

previously published or written by another person except where the acknowledgement is made in

the text.

Also, I hereby grant to University of Moratuwa the non-exclusive right to reproduce and

distribute my thesis, in whole or in part in print, electronic or other medium. I retain the right to

use this content in whole or part in future works.

Signature: Date:

Branesh Madhavan Pillai

I endorse the declaration by the candidate

Dr. A.M.Harsha S.Abeykoon

ii

ABSTRACT

Physical systems used for control applications require proper control methodologies to obtain the

desired response. Controller parameters used in such applications have to be tuned properly for

obtaining the desired response from the systems. Tuning controller parameters depends on the

physical parameters of the systems. Therefore, the physical parameters of the systems have to be

known. Number of techniques has been developed for finding the mechanical parameters of DC

motors. But, no straight forward method has been established for estimating the parameters of

the load so far. This research presents a method of determining mechanical parameters viz.

moment of inertia and friction coefficient of motor by introducing the Disturbance Observer

(DOB). This research also stresses that load parameters have appreciable effect on the response

of the systems and have to be determined. A DC servo motor velocity control system is

considered for applying the method. For this research, Sensorless torque detection technique is

used to find the external torque. Disturbance observer is used as a disturbance rejection tool and

also to improve the system’s robustness. Moment of inertia and friction coefficient of the DC

servo motor are determined using the method. It is evident that moment of inertia and friction

coefficient can be determined for any type of DC servo motor using the proposed method. Effect

of parameters on the system is emphasized by considering the PID controller tuning. It is found

that PID controller when tuned based on estimated parameters could yield optimum response.

The effectiveness of estimated parameters is verified by applying it towards the conventional

bilateral control system in the different situations including the contact motion and non contact

motion. Validity of the proposed method is verified by the experimental results.

Friction, especially its nonlinear component, may degrade the tracking performance of robots.

Uncertainties in the parameters but also in the structure of the friction model may lead to inexact

friction compensation in Servo-Mechanism. This will lead to a difference between the predicted

friction and the real friction torques, in certain cases creates instability. This research presents a

method of compensating friction of DC motor by introducing the Reaction torque observer

(RTOB). Friction compensation requires correct measurement of the reaction torque. But a

torque sensor has its own frequency response and measuring the torque accurately has become

difficult. For this reason torque sensing has become often erroneous with sensors. For this study

sensorless torque detection method named Reaction Torque Observer is used. When

compensated, the DC Servo system should behave as if there is no friction. This could be clearly

visible when there is no applied load. When the external load is applied to the system the

proposed method should compensated for the friction. Validity of the proposed method is

verified by the experimental results.

Keywords: Moment of Inertia, Friction Coefficients, Parameters Estimation, Disturbance

Observer, Reaction Torque Observer, Velocity Controller, Bilateral control, Friction

compensation.

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ACKNOWLADGEMENT

This thesis is a partial requirement for the completion of Master of Science degree in University

of Moratuwa. This text is a compilation of research work that has been carried out at the Control

and Robotics Laboratory, Electrical Engineering Department, Faculty of Engineering, University

of Moratuwa, SriLanka.

This research was accomplished under the supervision of Dr. A.M.Harsha S. Abeykoon, towards

who I am particularly grateful for his encouragement, guidance and support to realize this task.

His contribution for my research and technical support for the entire problem I encountered

during my research deserves my deepest thanks. He has been assisting me in many ways during

my stay in SriLanka not only as an academic Supervisor.

Many thanks and gratitude to Professor Dr. N. Wickramarachchi, Dr. W. D. Asanka S. Rodrigo

and Dr. A. G. Buddhika P. Jayasekara, Electrical Engineering Department, Faculty of

Engineering, University of Moratuwa. Their valuable comments, encouragements and

informative discussions in the progress review meetings helped me to realize this research.

I deeply thank Mr.Hasala R. Senevirathne, Mr. M.N.S.Ariyanshinge, Postgraduate students,

Electrical Engineering Department, Faculty of Engineering, University of Moratuwa. Their

valuable guidance helped me to overcome panic situations when I entered the laboratory as a

newcomer. They guided me throughout my Masters studies.

All members of Electrical Engineering Department, University of Moratuwa are also gratefully

acknowledged. They constantly helped me during my research activity.

I would like to sincerely thank my colleagues Hasitha Talawatura, W.A.P.S.Madusanka for their

kind assistance throughout my stay in SriLanka.

I would like to express my sincere gratitude to all those who have assisted me in my life

specially my parents and my sister M. Bradha Rajendran. Last but not least, I should thank

Dr.A.M.Harsha S.Abeykoon for his guidance not only in research activities but also in my

personal matters.

Finally, I would like to thank everybody who was important to the successful realization of

thesis, as well as expressing my apology that I could not mention personally one by one.

Branesh Madhavan Pillai,

University of Moratuwa

July 2013

iv

TABLE OF CONTENTS

1 Introduction ...................................................................................................................................... 1

1.1 Advance Motion Control ................................................................................................................ 1

1.2 Current Controller .......................................................................................................................... 2

1.3 Velocity Controller ......................................................................................................................... 2

1.4 Importance of estimation of Parameters ......................................................................................... 2

1.5 Bilateral tele-Operation .................................................................................................................. 2

1.6 Friction Compensation ................................................................................................................... 3

1.7 Overview of the Research .............................................................................................................. 4

1.8 Composition of the paper ............................................................................................................... 5

2 Motion Control ................................................................................................................................ 7

2.1 Introduction .................................................................................................................................... 7

2.2 DC Motor Modeling ....................................................................................................................... 8

2.3 Disturbance Observer ................................................................................................................... 10

2.4 Torque Control ............................................................................................................................. 13

2.4.1 Disturbance Observer as a Torque Sensor .......................................................................... 13

2.5 Summary ...................................................................................................................................... 14

3 Hardware and Software .................................................................................................................. 15

3.1 Hardware Experimental System ................................................................................................... 15

3.1.1 Components ........................................................................................................................ 15

3.1.2 Simulator Hardware Setup Circuits .................................................................................... 21

3.2 Software Experimental System .................................................................................................... 35

3.2.1 The mbed Developer Website ............................................................................................. 35

3.2.2 The mbed Compiler ............................................................................................................ 35

3.2.3 Operating cycle time ........................................................................................................... 37

3.2.4 Ethernet ............................................................................................................................... 37

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3.2.5 Data storage ........................................................................................................................ 38

3.2.6 Real-time operating system (RTOS) ................................................................................... 39

3.2.7 Ticker interface ................................................................................................................... 40

4 Current Controller .......................................................................................................................... 41

4.1 Introduction .................................................................................................................................. 41

4.2 Modeling and Analysis of Current Controller .............................................................................. 41

4.3 Experimental Results.................................................................................................................... 43

4.4 Conclusion .................................................................................................................................... 47

5 Velocity Controller ........................................................................................................................ 48

5.1 Introduction .................................................................................................................................. 48

5.2 PID based Velocity Controller ..................................................................................................... 48

5.3 PID based velocity controller with DOB ..................................................................................... 50

5.4 Results .......................................................................................................................................... 53

5.4.1 Stability Analysis ................................................................................................................ 53

5.4.2 Simulation Results .............................................................................................................. 55

5.4.3 Experimental Results .......................................................................................................... 57

5.5 Conclusion .................................................................................................................................... 59

6 Parameters Estimation ................................................................................................................... 60

6.1 Introduction .................................................................................................................................. 60

6.2 Experiments and Simulations ....................................................................................................... 61

6.2.1 Estimation of Torque Constant ( tk ) ................................................................................... 61

6.2.2 Estimation of Friction ......................................................................................................... 62

6.3 Estimation of Motor Inertia .......................................................................................................... 65

6.3.1 Deacceleration Motion Test ................................................................................................ 66

6.3.2 Angular Acceleration Motion Test...................................................................................... 67

6.3.3 Acceleration Motion Test .................................................................................................... 70

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6.4 Conclusion .................................................................................................................................... 72

7 Friction Compensation ................................................................................................................... 74

7.1 Introduction .................................................................................................................................. 74

7.2 Friction ......................................................................................................................................... 75

7.2.1 Static Friction ...................................................................................................................... 75

7.2.2 Coulomb Friction ................................................................................................................ 75

7.2.3 Viscous Friction .................................................................................................................. 75

7.3 System Modelling ........................................................................................................................ 76

7.4 Results .......................................................................................................................................... 77

7.5 Conclusion .................................................................................................................................... 80

8 Bilateral Control ............................................................................................................................ 81

8.1 Introduction .................................................................................................................................. 81

8.2 Bilateral Control ........................................................................................................................... 83

8.3 Results .......................................................................................................................................... 86

8.4 Conclusion .................................................................................................................................... 89

9 Conclusion ..................................................................................................................................... 90

10 References ...................................................................................................................................... 93

11 Appendix ...................................................................................................................................... 100

vii

List of Figures

List of Figures

Figure 1.1: Broader view of Bilateral Tele-Operation .................................................................................. 3

Figure 1.2: Overview of research .................................................................................................................. 4

Figure 1.3: Outline of the text ....................................................................................................................... 5

Figure 2.1: Electrical model of a DC Motor ................................................................................................. 8

Figure 2.2: Simplified model of servo motor .............................................................................................. 10

Figure 2.3: Calculation of disturbance torque ............................................................................................. 11

Figure 2.4: Estimation of Disturbance ........................................................................................................ 12

Figure 2.5: Reaction torque observer .......................................................................................................... 14

Figure 3.1: Electrocraft E240 DC motor ..................................................................................................... 15

Figure 3.2: Dimensions of the motors ......................................................................................................... 16

Figure 3.3: Master encoder ......................................................................................................................... 16

Figure 3.4: Dimensions of master encoder ................................................................................................. 17

Figure 3.5: Slave encoder ........................................................................................................................... 17

Figure 3.6: Dimensions of slave encoder .................................................................................................... 18

Figure 3.7: Hardware modification of QEI Module.................................................................................... 19

Figure 3.8: Connection of encoder and motor ............................................................................................ 20

Figure 3.9: New manipulator ...................................................................................................................... 20

Figure 3.10: Hardware Functional block diagram ...................................................................................... 21

Figure 3.11: Power circuit configuration .................................................................................................... 22

Figure 3.12: Power flow ............................................................................................................................. 23

Figure 3.13: Microcontroller Circuit ........................................................................................................... 23

Figure 3.14: SD Card module ..................................................................................................................... 24

Figure 3.15: One section of the current sensor ........................................................................................... 25

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List of Figures

Figure 3.16: Current Sensor module ........................................................................................................... 26

Figure 3.17: Current Sensors arrangement ................................................................................................ 26

Figure 3.18: Current vs. Voltage of the current sensor ............................................................................... 27

Figure 3.19: Differential amplifier circuit ................................................................................................... 28

Figure 3.20: Actual current vs. differential amplifier output for master anti-clockwise direction ............. 28

Figure 3.21: Actual current vs. differential amplifier output for master clockwise direction ..................... 29

Figure 3.22: Actual current vs. differential amplifier output for slave anti-clockwise direction ................ 29

Figure 3.23: Actual current vs. differential amplifier output for slave clockwise direction ....................... 30

Figure 3.24: DC motor driver ..................................................................................................................... 31

Figure 3.25: DRV 8432 Motor Driver IC ................................................................................................... 31

Figure 3.26: Frequency vs. Efficiency of the DRV8432 ............................................................................ 32

Figure 3.27: Functional block diagram of hardware ................................................................................... 34

Figure 3.28: Hardware setup ....................................................................................................................... 34

Figure 3.29: Mbed compiler ....................................................................................................................... 36

Figure 3.30: Two microcontrollers connected using Ethernet .................................................................... 38

Figure 3.31: Functions of the Thread Class ................................................................................................ 39

Figure 3.32: Structure of real time operating system .................................................................................. 40

Figure 4.1: Basic velocity controllers ......................................................................................................... 41

Figure 4.2: Voltage to velocity in block form ............................................................................................. 42

Figure 4.3: DC motor with Current controller ............................................................................................ 42

Figure 4.4: Current input current output representation of a DC motor. .................................................... 42

Figure 4.5: A DC motor with DOB............................................................................................................. 43

Figure 4.6: Current response without DOB ................................................................................................ 44

Figure 4.7: Current response DOB ............................................................................................................ 44

Figure 4.8: Disturbance current .................................................................................................................. 45

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List of Figures

Figure 4.9: Periodic disturbance without DOB ........................................................................................... 46

Figure 4.10: Periodic disturbance with DOB .............................................................................................. 46

Figure 5.1: Block diagram model of the PID based velocity controller ..................................................... 49

Figure 5.2: System equivalents with superposition..................................................................................... 49

Figure 5.3: PID based velocity controller with DOB .................................................................................. 51

Figure 5.4: System equivalent with DOB ................................................................................................... 52

Figure 5.5: Reduced block diagram with DOB ........................................................................................... 53

Figure 5.6: Root locus for 0disT without DOB ...................................................................................... 55

Figure 5.7: Root locus for 0disT with DOB ........................................................................................... 55

Figure 5.8: Root locus for 0ref without DOB .................................................................................... 55

Figure 5.9: Root locus for 0ref with DOB. ........................................................................................ 55

Figure 5.10: Opposing disturbance without DOB ..................................................................................... 56

Figure 5.11: Opposing disturbance with DOB ............................................................................................ 56

Figure 5.12: Supporting disturbance without DOB ................................................................................... 56

Figure 5.13: Supporting disturbance with DOB ........................................................................................ 56

Figure 5.14: Periodic disturbance without DOB ......................................................................................... 57

Figure 5.15: Periodic disturbance with DOB .............................................................................................. 57

Figure 5.16: Experimental platform ............................................................................................................ 57

Figure 5.17: Supporting Disturbance .......................................................................................................... 58

Figure 5.18: Opposing Disturbance ............................................................................................................ 58

Figure 5.19: Periodic Disturbance .............................................................................................................. 58

Figure 5.20: Opposing disturbance without DOB ..................................................................................... 58

Figure 5.21: Opposing disturbance with DOB ............................................................................................ 58

Figure 5.22: Supporting disturbance without DOB ................................................................................... 59

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List of Figures

Figure 5.23: Supporting disturbance with DOB ........................................................................................ 59

Figure 5.24: Periodic disturbance without DOB ......................................................................................... 59

Figure 5.25: Periodic disturbance with DOB .............................................................................................. 59

Figure 6.1: Measurement of Torque constant ............................................................................................. 62

Figure 6.2: Velocity response of constant angular velocity test ................................................................. 63

Figure 6.3: Disturbance Torque .................................................................................................................. 64

Figure 6.4: Measured friction torque .......................................................................................................... 64

Figure 6.5: Velocity response of De-acceleration test ................................................................................ 66

Figure 6.6: Position Response ..................................................................................................................... 67

Figure 6.7: Velocity response of Self Inertia variation test ........................................................................ 68

Figure 6.8: Self inertia variation torque ...................................................................................................... 69

Figure 6.9: Velocity Response of DC Motor .............................................................................................. 71

Figure 6.10: Acceleration Response of DC motor ...................................................................................... 71

Figure 6.11: Average Acceleration Torque ................................................................................................. 72

Figure 7.1: A Simple DC motor .................................................................................................................. 76

Figure 7.2: Disturbance Observer as a Torque sensor ................................................................................ 76

Figure 7.3: Friction compensation model ................................................................................................... 77

Figure 7.4: RTOB Response ....................................................................................................................... 78

Figure 7.5: Response of error and duty ....................................................................................................... 78

Figure 7.6: RTOB responses when external torque applied ....................................................................... 79

Figure 7.7: Error, Position response when external torque applied ............................................................ 79

Figure 7.8: Current, duty response when external torque applied .............................................................. 80

Figure 8.1: Transmission of sense of touch. ................................................................................................ 81

Figure 8.3: Transmission of real world haptic information. ....................................................................... 82

Figure 8.2: Law of action and reaction. ...................................................................................................... 82

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List of Figures

Figure 8.4: Block diagram of bilateral control. ........................................................................................... 83

Figure 8.5: Basics of bilateral control. ........................................................................................................ 84

Figure 8.6: Block diagram of conventional bilateral control ...................................................................... 86

Figure 8.7: Torque response in free motion ................................................................................................ 88

Figure 8.8: Position response free motion .................................................................................................. 88

Figure 8.9: Torque response in contact motion ........................................................................................... 89

Figure 8.10: Position response contact motion ........................................................................................... 89

Figure 11.1: Current sensor module .......................................................................................................... 100

Figure 11.2: Motor controller.................................................................................................................... 101

xii

List of Tables

List of Tables

Table 3.1: Output termination of slave encoder .......................................................................................... 18

Table 5.1: Experimental Parameters. .......................................................................................................... 54

Table 8.1: Parameters of Direct-Drive motors ............................................................................................ 87

Table 8.2: Experimental Parameters ........................................................................................................... 87