Simulation and Control of a Ball Screw System Actuated by a Stepper Motor with Feedback

109 Pages·2014·7.97 MB·English

Simulation and Control of a Ball Screw System Actuated by a
Stepper Motor with Feedback

by

John Cloutier

A Thesis
presented to
The University of Guelph

In partial fulfilment of requirements
for the degree of
Master of Applied Science
in
Engineering

Guelph, Ontario, Canada

© John Cloutier, December, 2014
ABSTRACT

Simulation and Control of a Ball Screw System
Actuated by a Stepper Motor with Feedback

John Charles Cloutier Advisor:
University of Guelph, 2014 Professor M. Biglarbeigan
Professor M. Hassan

This thesis presents an investigation on motion control of a ball screw
system actuated by a permanent magnet stepper motor (PMSM). Using a PMSM
for high speed application to operate in feedforward mode is difficult; therefore, a
servo system needs to be developed to allow operations at those velocities.

To convert a PMSM into a servo system, a linearizing program called a
preprocessing filter (PPF) is used to convert the controller signal into a velocity
signal the stepper driver can use. The filter was developed along with the methods
for extraction of the PPF parameters. Vibrations information, obtained from the
rotational velocities, was gathered in order to ensure optimal design and
performance of the PPF. The system velocity causing the critical vibrations was
excluded.

Using the PPF, two types of controllers, Proportional (P) and Proportional
Derivative (PD), were designed and implemented for precise displacement of the
PSMS. It was found that the PD controller is superior to the P controller in terms of
settling time to peak for the PMSM system. As well, the P controller for the FDS
outperformed the PD controller in terms of settling time.
DEDICATION
I would like to dedicate this thesis to all the women in my life: my grand
mother, mother, god mother, and girlfriend. Thank you for everything.
iii
ACKNOWLEDGEMENTS
I would like thank both my supervisors: Dr Mohammad Biglarbegian
and Dr Marwan Hassan; for all of there advise, mentoring, patents, and effort
in helping me complete my Master’s degree. I would also like to thank Dr
Howard Li for his believe in me and all of his effort for my acceptance into the
University of Guelph. These three professor have been fundamental for my
education and development.
There are several technical personnel I would like to give a special thanks
to: Nathaniel Groendyk and Hong Ma for all of his technical assistance with
electrical systems; Dave and Ken for all of the assistance, provided in the
machine shop; Izabella Onik and Laurie Gallinger for always making time for
me; and finally Lenore Latta for the hours and hours spent teaching me to
write.
The final acknowledgement goes out to my friends and family. I would
like to give a special thank you to best friend Gurvinder Mundi for helping me
get through the last two years and always listening, my mother, god mother,
and grand mother: Joanna, Patrica, and Nana Bernard for whom without I
know I would not have made it. My girlfriend Shirley Lam for her continuous
support and belief in me.
Finally I would like to thank the School of Engineering for all the skills
and memories you have provided me with. I would finally like to thank my
first nation:the Madawaska Maliseet First Nation, I owe them so much and
will not forget all the assistance and support you have provided me with.
iv
TABLE OF CONTENTS
DEDICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . iv
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Preamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.1 Ball Screw System (BSS) . . . . . . . . . . . . . . . 1
1.2.2 Permanent Magnet Stepper Motor (PMSM) . . . . . 3
1.3 Thesis Contributions . . . . . . . . . . . . . . . . . . . . . 4
1.4 Thesis Layout . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 LITERATURE SURVEY . . . . . . . . . . . . . . . . . . . . . . 6
2.1 Ball Screw Systems . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Modeling BSS . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 Vibrations . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.3 Control . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Permanent Magnet Stepper Motor . . . . . . . . . . . . . . 9
2.2.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . 10
3 MODELING and SIMULATIONS . . . . . . . . . . . . . . . . . . 12
3.1 Adapted Models . . . . . . . . . . . . . . . . . . . . . . . . 12
3.1.1 Adapted Ball Screw System Models . . . . . . . . . 13
3.1.2 Adapted Permanent Magnetic Stepper Motor Modeling 19
3.2 Simulations Results . . . . . . . . . . . . . . . . . . . . . . 23
3.2.1 PMSM Simulation Results . . . . . . . . . . . . . . 23
3.3 Pre-processing Filter . . . . . . . . . . . . . . . . . . . . . 38
4 EXPERIMENTAL SETUP and METHODOLOGY . . . . . . . . 42
4.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . 42
4.1.1 Mechanical . . . . . . . . . . . . . . . . . . . . . . . 42
4.1.2 Electrical . . . . . . . . . . . . . . . . . . . . . . . . 48
4.1.3 Control . . . . . . . . . . . . . . . . . . . . . . . . . 49
v
4.1.4 Data Acquisition . . . . . . . . . . . . . . . . . . . . 50
4.2 Methodology and Experimental Procedures . . . . . . . . . 51
4.2.1 Experimental Validation of the Apparatus . . . . . . 52
4.2.2 Feedforward Parameter Identification . . . . . . . . 54
4.2.3 Controller Design . . . . . . . . . . . . . . . . . . . 55
5 RESULTS and DISCUSSION . . . . . . . . . . . . . . . . . . . . 60
5.1 Apparatus Validation . . . . . . . . . . . . . . . . . . . . . 60
5.1.1 Data Acquisition Validation . . . . . . . . . . . . . 60
5.1.2 Displacement Validation . . . . . . . . . . . . . . . 60
5.1.3 Velocity Validation . . . . . . . . . . . . . . . . . . 62
5.2 Feedforward Parameter Identification . . . . . . . . . . . . 64
5.2.1 The Maximum Velocity . . . . . . . . . . . . . . . . 65
5.2.2 Maximum Acceleration . . . . . . . . . . . . . . . . 67
5.3 Feedback Controller Results . . . . . . . . . . . . . . . . . 70
5.3.1 PPF Tuning . . . . . . . . . . . . . . . . . . . . . . 71
5.3.2 Proportional Controller . . . . . . . . . . . . . . . . 73
5.3.3 Proportional Derivative Controller . . . . . . . . . . 75
6 CONCLUSION and FUTURE WORK . . . . . . . . . . . . . . . 79
6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 80
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
A Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
B Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
C Data Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
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LIST OF TABLES
Table page
3–1 Parameters and values required for simulation of PMSM. . . . 26
4–1 Specification of the ball screw used in the experimental setup. . 45
4–2 Specification of the nut screw used in the experimental setup. . 46
4–3 Specification for the PMSM used in this thesis. . . . . . . . . . 47
4–4 Specification of the accelerometers used in the following disser-
tation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4–5 Specification for Optical Encoder . . . . . . . . . . . . . . . . . 51
5–1 Result of velocity error for different target velocities. . . . . . . 63
5–2 Results for dynamic velocity of PMSM . . . . . . . . . . . . . . 70
5–3 Results for dynamic velocity of PMSM . . . . . . . . . . . . . . 70
5–4 PPF parameters used for PMSM FBC. . . . . . . . . . . . . . 72
5–5 PPF parameter used FDS FBC. . . . . . . . . . . . . . . . . . 73
5–6 PMSM P Controller results. . . . . . . . . . . . . . . . . . . . . 75
5–7 FDS Proportional controller results. . . . . . . . . . . . . . . . 75
5–8 PMSM Proportional Derivative controller results. . . . . . . . . 77
5–9 FDS Proportional Derivative controller results. . . . . . . . . . 78
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LIST OF FIGURES
Figure page
2–1 Schematic of general FDS [1]. . . . . . . . . . . . . . . . . . . 6
3–1 Block Diagram of FDS . . . . . . . . . . . . . . . . . . . . . . 13
3–2 Block Diagram of BSS . . . . . . . . . . . . . . . . . . . . . . 13
3–3 How a coupling connects the BSS to the PMSM. . . . . . . . . 13
3–4 FDB of ball screw . . . . . . . . . . . . . . . . . . . . . . . . . 15
3–5 FDB of the carriage used to obtain the dynamic model. . . . . 17
3–6 Example of interface between nut and screw through ball
bearings [24]. . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3–7 Block diagram of a PMSM. . . . . . . . . . . . . . . . . . . . . 19
3–8 General Schemcatic for 2 phase PMSM [1]. . . . . . . . . . . . 20
3–9 Diagram of the teeth of the PMSM rotor and how they lock
with the stator. . . . . . . . . . . . . . . . . . . . . . . . . . 20
3–10 Circuit for single phase of PMSM. . . . . . . . . . . . . . . . . 21
3–11 Demonstrates the required sequence for operation of a two
phase PMSM. . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3–12 Pulse frequency voltage delivered to the both phases. . . . . . 25
3–13 Response of phase coil to increasing pulse frequency. . . . . . . 27
3–14 Response of phase coil to increasing pulse frequency with a
chopping circuit. . . . . . . . . . . . . . . . . . . . . . . . . 28
3–15 Sample data for the torque applied to the shaft of the PMSM 29
3–16 Zoomed result of developed torque in order to identy the nature
frequency of the system. . . . . . . . . . . . . . . . . . . . . 30
3–17 Rotors displacement for varying frequency from 1 - 0.5. . . . . 32
3–18 PMSM results for varying frequency from 0.1 - 0.01. . . . . . . 33
3–19 PMSM results for varying frequency from 0.01 - 0.001. . . . . 34
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3–20 PMSM results when failure occurs. . . . . . . . . . . . . . . . 36
3–21 Displacement simulation to observe the transience that happens
from a single step. . . . . . . . . . . . . . . . . . . . . . . . 37
3–22 Block diagram used help visualize the functionality of the PPF. 38
3–23 Process Flow Diagram for the PPF. . . . . . . . . . . . . . . . 39
3–24 The velocity profile with both the dead-zone and velocity
mapping function concatenated. . . . . . . . . . . . . . . . . 40
4–1 The experimental setup showing the particular components. . 43
4–2 Mechanical subsystem of the experimental apparatus . . . . . 44
4–3 Flowchart demonstrating the reliance of each experiment for
this thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5–1 Angular displacement profile for different sampling frequencies. 61
5–2 Rotational displacement results versus simulations for sampling
frequency of 333 Hz. . . . . . . . . . . . . . . . . . . . . . . 62
5–3 FFC displacement response at a velocity of 1 rad/s. . . . . . . 63
5–4 Illustration of the operating capabilities of the PMSM with
respect to operating velocity. . . . . . . . . . . . . . . . . . 64
5–5 Differentiated displacement signal before being filtered. . . . . 65
5–6 Response of velocity profile for PMSM after applying a Butter-
worth filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5–7 Difference between actual velocity versus FFC velocity. . . . . 67
5–8 Ramping at an acceleration rate of 2000 and increasing from
30 to 100 rad/s. . . . . . . . . . . . . . . . . . . . . . . . . . 68
5–9 Example of filtered signal superimposed on a non-filtered signal. 69
5–10 Results of stepping PMSM to demonstrate the effects of oper-
ating at a low velocity. . . . . . . . . . . . . . . . . . . . . . 71
5–11 Data collected for acceleration experiments with an initial
velocity of the 4 rad/s. . . . . . . . . . . . . . . . . . . . . . 72
5–12 Example of the believed trajectory of the PMSM’s rotor in
order to achieve greater acceleration. . . . . . . . . . . . . . 73
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5–13 Results of FDS’s relationship between initial velocity and the
acceleration. . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5–14 Results for PMSM displacement with proportional gain equal
to 0.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
x