SPEED CONTROL OF PERMANENT MAGNET …

1 I SPEED CONTROL OF PERMANENT MAGNET SYNCHRONOUS MOTOR USING EXTENDED HIGH GAIN OBSERVER By Abdullah Ahmad Alfehaid A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Electrical Engineering Master of Science 2015 ii ABSTRACT SPEED CONTROL OF PERMANENT MAGNET SYNCHRONOUS MOTOR USING EXTENDED HIGH GAIN OBSERVER By Abdullah Ahmad Alfehaid Feedback linearization is used to regulate and shape the SPEED of a surface mount PERMANENT MAGNET Synchronous Motor (PMSM). An extended high gain observer, which is driven by the measured position of the PMSM s rotor, is also used to estimate both the SPEED of the motor and the disturbance present in the system to recover the performance of feedback linearization.

2 Two methods are presented to design the extended high gain observer. The first method is based on the full model of the PMSM and the second method is based on a reduced model of the PMSM. The reduction of the model is made possible by creating fast current loops that allowed the use of singular perturbation theory to replace the current variables by their quasi steady state equivalent. The design of the SPEED controller and the extended high gain observer is based on the nominal parameters of the PMSM. The disturbance is assumed to be unknown, and time varying but bounded. Stability of the output feedback system is shown. Finally, simulation and experimental results confirm stability, robustness, and performance of the system. iii Copyright by ABDULLAH AHMAD ALFEHAID 2015 iv To my family v ACKNOWLEDGMENTS I would like to express my sincere appreciation to the following people: To my advisor Dr.

3 Hassan K. Khalil who patiently and excellently guided me through my research. He is truly an honest, patient and a humble person. His knowledge and passion for the subject is inspiring. Indeed, his advice and suggestions have been and will be of great help to me. I am honored to have been his student. To Dr. Elias G. Strangas who offered his laboratory for conducting the experiment and for his excellent insights and assistance throughout the experiment. To my parents (Ahmad Alfehaid and Moody Alhomaidy) who supported me, encouraged me, and believed in me. I sincerely thank them for teaching me the love of seeking knowledge. And to my wife (Yara Almani) who stood by me during my studies and created a comfortable atmosphere. I could not have done it without you. vi TABLE OF CONTENTS LIST OF TABLES.

4 Viii LIST OF FIGURES .. ix CHAPTER 1 .. 1 Introduction .. 1 Mathematical Model of 4 7 CHAPTER 2 .. 11 CONTROL Algorithm .. 11 Full Model Approach .. 11 Extended High Gain Observer .. 13 Reduced Model Approach .. 15 Current Loops .. 16 Extended High gain Observer .. 18 Feedback Linearization .. 20 Closed Loop analysis .. 21 CHAPTER 3 .. 27 Simulation .. 27 Simulation Setup .. 27 Simulation 28 Simulation I .. 28 Simulation II .. 30 Simulation III .. 31 Simulation IV .. 32 CHAPTER 4 .. 33 Experiment .. 33 Experiment Setup .. 33 Current Measurement .. 35 Incremental Encoder Interface .. 37 Incremental Encoder s Digital Filter .. 44 PWM controller Circuit .. 44 CONTROL Algorithm Loop .. 49 Three Phase to Transformation.

5 50 to d q Transformation .. 51 vii Extended High Gain Observer .. 52 Feedback Linearization .. 54 PI controller .. 55 d q to Transformation .. 56 to Three Phase Transformation .. 57 Experimental 58 Experiment I .. 60 Experiment II .. 60 Experiment III .. 61 CHAPTER 5 .. 63 Conclusion and Future Work .. 63 Conclusion .. 63 Future Work .. 64 Field Weakening .. 64 Sensorless CONTROL .. 65 APPENDIX .. 66 BIBLIOGRAPHY .. 68 viii LIST OF TABLES Table Routh s array for the characteristic equation ( ).. 25 Table Nominal parameters of the used PMSM.. 28 Table Truth table for the driving clock clk of the edges counter.. 40 Table State transition table for the state diagram of channel A and B and the direction of rotation.

6 42 Table State transition table for the high side switching signal.. 48 Table State transition table for the Low side switching signal.. 49 ix LIST OF FIGURES Figure Cross sectional view of a surface mounted PMSM [2].. 2 Figure Relationship between the stator and the rotor frame of references.. 6 Figure Block diagram of the proposed CONTROL algorithm.. 16 Figure (a) SPEED of PMSM using nominal parameters, (b) SPEED deviation of PMSM from target SPEED .. 29 Figure (a) SPEED of PMSM using a 20% increase in the nominal parameters, (b) SPEED deviation of PMSM from target SPEED .. 30 Figure (a) SPEED of PMSM before and after the external load was applied, (b) Applied external load and its estimate.. 31 Figure Error between target SPEED and motor SPEED as 0 & 0.

7 32 Figure Block diagram of the experimental setup.. 34 Figure First order RC low pass filter.. 37 Figure Incremental encoder output signals.. 38 Figure State diagram for channel A and B and the direction of rotation.. 41 Figure Incremental encoder interface circuit.. 43 Figure High frequency corruption of Channel A and B.. 43 Figure Implementation of the digital filter circuit in LabView.. 45 Figure Signals generation by the PWM controller circuit.. 47 Figure Implementation of the PWM controller circuit for one phase pole.. 50 Figure Implementation of the three phase to transformation in LabView.. 51 Figure Implementation of to d q transformation in LabView.. 52 Figure implementation of the discrete extended high gain observer in LabView.. 53 Figure Implementation of the SPEED controller ( ) with saturation in LabView.

8 54 Figure Block diagram of the PI controller .. 55 x Figure Implementation of the discrete PI controller with anti winding in LabView.. 56 Figure Implementation of d q to transformation in LabView.. 57 Figure Implementation of to three phase transformation in LabView.. 58 Figure (a) Simulation and experimental SPEED of PMSM using nominal parameters, (b) simulation and experimental SPEED deviation from target SPEED .. 59 Figure (a) Simulation and experimental SPEED of PMSM when the nominal parameters are increased by 20%, (b) simulation and experimental SPEED deviation from target SPEED when the nominal parameters are increased by 20%.. 61 Figure SPEED of PMSM before and after the external load was applied.. 62 1 CHAPTER 1 Introduction PERMANENT MAGNET Synchronous Motors (PMSM) are increasingly used in the industries and rapidly replacing induction and DC motors particularly in servo application such as CNC machines and robotic systems.

9 PMSM are popular due to their efficiency, high power density, light weight, maintenance free, and small size comparing to DC and induction machines [1]. There are two types of three phase AC PMSMs: the surface mounted PMSMs and the interior MAGNET PMSM. The surface mounted PMSMs are built with magnets mounted on the surface of the rotor while the interior MAGNET PMSMs are built with magnets embedded in the rotor. This structural difference leads to different mathematical models and hence leads to different CONTROL approaches. Throughout this document, only the surface mounted PMSM will be considered. Figure shows a cross sectional view of a four pole surface mounted PMSM [2]. PMSMs are not easy to CONTROL because they exhibit time varying nonlinear dynamic behavior.

10 The parameters of PMSMs are prone to temperature changes and variation in operating points, the stator winding resistance can vary by as much as 200% of its nominal value and the rotor flux linkage can vary by as much as 20% of its nominal value [3]. PMSM popularity in the recent years has triggered the interest in the CONTROL community which led to many CONTROL approaches. 2 In the industry, linear Proportional and Integral (PI) controllers have been largely used in PMSM drives. It is considered to be one of the simplest CONTROL techniques that offer an adequate performance. However, PI controllers are not a great choice in applications where high performance and high precision are required. Figure Cross sectional view of a surface mounted PMSM [2]. Sliding mode CONTROL (SMC) is becoming popular in PMSM drives due to its robustness to parameter variations.