Bachelor of Science Thesis in Electrical Engineering
Drive train control of lithium-battery
fed BLDC motor
Motor Control
Bachelor of Science Thesis in Electrical Engineering
Drive train control of lithium-battery
fed BLDC motor
Heshmat Hassani LiTH-ISY-EX-ET–20/0490–SE
Supervisor:
Tomas Uno Jonsson
ISY, Linkoping university
Examiner:
Mark Vesterbacka
ISY, Linkoping university
Department of Electrical Engineering Linkoping university
SE-581 83 Linköping, Sweden Spring, 2020
Abstract
Electrical drive systems are used in various applications and getting more attractive in recent years. When the usage of electric motors increased in different applications then the control model of them has been also demanded. This work is aimed at deeper research to gain a better understanding of three different control models for electric motors, in case of this work a brushless direct current (BLDC) motor. Three different types of control models (6-step, sinusoidal and FOC control) have been investigated and designed using MATLAB/SIMULINK. Then the control models have been implemented in an Arduino Due based BLDC motor and its functionality has been configured. The results show that the FOC control model provided to work better in the simulation while the implementation of the hardware showed that sinusoidal control works a little better and smoother. Making the implementation of the control models to the hardware work better requires more works and this has been left for future work.
Acknowledgement
I would like to thank the following people for their support during this thesis work. Tomas Uno Jonsson, my supervisor for arranging this thesis and for his instructive comments and instructions during the thesis work. Mark Vesterbacka my examiner for his comments and response to my report and presentation. My opponent Fadi Eliasson for his review and comments on the report and his instructive discussion during the presentation.
Contents
1 Introduction 8 1.1 Background . . . 8 1.2 Purpose/Problem Definition . . . 8 1.3 Methodology . . . 8 1.4 Limitation . . . 8 2 Theory 9 2.1 Brushed DC Motor . . . 92.2 Brushless Direct Current/brushless direct current (BLDC) Motor . . . 9
2.3 BLDC and PMSM’s Parameters . . . 10
2.4 Control Models . . . 11
2.4.1 Six-Step Control . . . 11
2.4.2 Sinusoidal Control . . . 13
2.4.3 Field Oriented Control . . . 15
2.4.4 Transformation to Direct and Quadrature Variables . . . 15
2.4.5 PMSM Relation in dq Variables . . . 16
3 Simulation 17 3.1 Simulation Models . . . 17
3.1.1 Six-step Control System . . . 17
3.1.2 Six-step Simulation Result . . . 18
3.2 Sinusoidal Control System . . . 21
3.2.1 Angle and Speed Calculation . . . 22
3.2.2 Sinusoidal Control Simulation Results . . . 24
3.3 Field Oriented Control . . . 26
3.3.1 FOC Control Simulation Results . . . 28
3.4 Comparison of the control systems . . . 30
4 Hardware 32 4.1 Hardware Specifications . . . 32
4.2 Implementation of Control Systems to Hardware . . . 32
5 Discussion 36 5.1 Method . . . 36 5.2 Simulation . . . 36 5.3 Simulation Results . . . 36 5.4 Implementation to Hardware . . . 36 6 Conclusion 37 6.1 Future Work . . . 37 A Detailed specification 39
List of Figures
2.1 A typical brushed DC motor . . . 9
2.2 Typical 3-phase, 8-poles brushless DC motor with hall-effect sensors . . . 10
2.3 Sections on a typical brushless DC motor . . . 12
2.4 Switching currents to phase-A and phase-C . . . 13
2.5 PWM signals with 80 % duty cycles . . . 13
2.6 Generation of sinusoidal signals . . . 14
2.7 abc-reference frame to αβ transformation . . . 15
2.8 Relation between αβ and dq-reference-frame . . . 16
3.1 Six-step control scheme . . . 17
3.2 Mathematical conversion of the hall-effect sensors data to driving stator currents . . . 18
3.3 Mathematical conversion of phase control signals to gate pulses . . . 18
3.4 Six-step: Motor stator currents, Electrical torque and Electrical angular velocity (reference and actual) in respective . . . 19
3.5 Zoomed: Motor stator currents, Electrical torque and Electrical angular velocity (reference and actual) in respective . . . 19
3.6 Six-step maximum angular velocity . . . 20
3.7 Six-step gate pulses . . . 20
3.8 Six-step hall-sensors and back-emf . . . 21
3.9 Control scheme and control signals . . . 21
3.10 Calculation of the motor angle and generation of the sine-wave . . . 22
3.11 Calculation of the motor angle and angular velocity . . . 22
3.12 Motor angle and hall-effect sensor signal . . . 23
3.13 Generation of sine-waves signals . . . 23
3.14 Generation of gates signals . . . 23
3.15 Sinusoidal: Motor phases currents, Electrical torque and Electrical angular velocity (reference and actual) in the respective . . . 24
3.16 Zoomed: Motor stator currents, Electrical torque and Electrical angular velocity (reference and actual) in the respective . . . 24
3.17 Sinusoidal maximum angular velocity . . . 25
3.18 Sinusoidal gate pulses . . . 25
3.19 Angle calculation results . . . 26
3.20 Measured current of phase-A, Reference signal to the inverter and calculated angle . . . 26
3.21 FOC Control scheme . . . 27
3.22 FOC control simulation model . . . 27
3.23 Motor phases currents, Electrical torque and Electrical angular velocity (reference and actual) in respective . . . 28
3.24 FOC control: Motor Phases currents, Electrical torque and Electrical angular velocity (reference and actual) in the respective . . . 28
3.25 FOC control maximal angular velocity . . . 29
3.26 dq currents and voltages controller response . . . 29
3.27 Regulated dq currents and voltages . . . 30
3.28 The phase differences between currents and voltages . . . 30
4.1 Implementation results of six-step control model . . . 33
4.2 Six-step control’s audible noise level . . . 33
4.4 Sinusoidal control’s audible noise level . . . 34 4.5 Implementation result of the FOC control model . . . 35 4.6 FOC control’s audible noise level . . . 35
List of Tables
1 Relationship between hall-effect sensors and phase control signals . . . 12
2 Observed values of all three control models . . . 31
3 Motor parameters values . . . 32
4 12 Volt Battery system specification . . . 32
5 48 Volt Battery system specification . . . 32
Acronyms
AC alternating current BDC brushed direct current BLDC brushless direct current DC direct current
FOC field-oriented control PI proportional and integral
PMSM permanent magnet synchronous motor PWM pulse width modulation
MOSFET metal–oxide–semiconductor field-effect transistor SPWM sinusoidal pulse width modulation
Chapter 1
1
Introduction
Electrical drive systems are widely used everywhere both in home and industrial applications. There are different types of motors that are used in each specific application depends on these expectancy and employment. In recently decades one of the most popular developments in the area of electrical drives machinery are the control characterisations of the BLDC motors contrary to the conventional direct current (DC) motors. There are different types of BLDC motors and usually brushless DC motors have different names, permanent magnet synchronous motor (PMSM) is one of the motors that have the same function and characterisation as brushless DC motor. This thesis will describe some control models of the BLDC motors.
1.1
Background
The thesis was done at Linköping University at the ISY Department of Electrical Engineering on a commitment of the Power Electronics Systems. The hardware which were available in the lab were a hall-sensors based BLDC motor, a 12V battery system, a 48V battery system, two Arduino Due boards and a control board. The control board includes current sensors, voltage sensors, DC converter and an inverter.
1.2
Purpose/Problem Definition
The purpose of this thesis was to investigate how the control of BLDC motors work and how to manage them effectively. The thesis focuses have been on three different types of control models (Six-step, Sinusoidal and Field Oriented Control) for a hall-effect sensors-based BLDC/PMSM motor.
1.3
Methodology
The main part of the thesis is based on litterateur studies. In the theory chapter the theory behind and the studies in the section of electrical drive systems will be described. The thesis will be done on some steps, then on the first step some control models for BLDC motors will be investigated. Then the investigated control models will be simulated by using MATLAB/SIMULINK. To determine the functionality of the control models, the control models will be implemented on an Arduino Due based BLDC motor.
1.4
Limitation
This thesis will cover the implementation of the control models to the control board. Then the full-bridge inverter on control board will be used to generate the desired motor voltages. The thesis will not go into detail of the metal–oxide–semiconductor field-effect transistor (MOSFET) in the inverter. Since the motor in which the control models will be tested on is a BLDC motor with hall-effect sensors, then the thesis focuses will also be on the BLDC motor with hall-effect sensors.
Chapter 2
2
Theory
In this chapter the theory about BLDC motor and its control system will be presented. In the first part the basics about the DC motors will be introduced which would help to understand how these types the motors work. Then the basic theory about BLDC motors will be introduced. Then the introduced theories will be used throughout this thesis.
2.1
Brushed DC Motor
DC motors are commonly used as driving units in the many industrial and home application. DC motor can convert the direct current electrical energy into mechanical energy by relying on magnetic force. Brushed DC machines can be designed in various combinations of shunt-, series-, and separately-excited field winding to display a wide variety of volt-ampere of speed-torque characteristics both in dynamic and steady-state operation. The essentials of typical brushed dc motors are, that they have winding in the rotor (the rotating part) and a permanent magnet on the stator (the stationary part) see figure 2.1 below. The armature of a DC motor contains an electromagnet, when electricity feds into armature via brushes (commutators) it creates a magnetic field in the armature which attracts and repels the magnets in the stator. The rotor spins through 180◦degrees, then the poles of electromagnets should be changed to keep the armature spinning. There are two attached electrodes to the armature which make contact to the brushes (commutators) and these brushes change the polarity of the electromagnetic when the armature spins. [2] [3]
Figure 2.1: A typical brushed DC motor
2.2
Brushless Direct Current/BLDC Motor
The principle of a BLDC motor is almost the same as a regular DC motor. There are some differences between those types of motors, a BLDC has no brush/commutator, that mean there are no mechanical contacts between rotor and stator. In a BLDC motor, there are permanent magnets implemented on the rotor part which creates a constant magnetic flux all the time, as mentioned in the previous part a brushed direct current (BDC) motor had a permanent magnet in the stator part but in a BLDC motor, the rotor part has a permanent magnet, so the rotor and stator have been flipped in the BLDC compared to a BDC motors. [13]
Other differences between BDC and BLDC motors are the control models of these two types of the motors. Brushed DC motors are self-commutated which can be controlled without using any complicated control algorithms. On the BLDC motors the commutations occur electronically, then numerous control algorithms can be used for these types of the motors. To be able to control the BLDC motors the rotor position in such motors must be known. There are different techniques that have been used to indicate the rotor position in the BLDC motors e.g. hall-effect sensors are commonly used for indication of rotor position. Usually the hall-effect sensors are implemented on the stationary part during manufacturing of the motors see figure 2.2. [12]
Hall-effect sensors are solid-state, magnetic field sensors. It means when the current-carrying conductor (hall-element) material is placed into a magnetic field, the electron in the conductor repels and attracts by magnets field polarities. By assuming that when hall-effect sensors are passed by rotor’s north pole a positive voltage will be generated and by rotor’s south pole a negative voltage will be generated, then the generated voltages can be used as analog or digital signal. [11]
Figure 2.2: Typical 3-phase, 8-poles brushless DC motor with hall-effect sensors
2.3
BLDC and PMSM’s Parameters
Permanent Magnet Synchronous motor or brushless DC motor both are synchronous motors. PMSM motors are often referred to as brushless DC motors, but the differences between these two types of motors are in the shape of theirs back-emf, where the BLDC motor has a trapezoidal and the PMSM motor has a sinusoidal back-emf. Back-emf are the voltages that can be induced from the motor when rotor poles pass the stator winding. These types of motors which have permanent magnets rotor are often used in low power application up to several hundred kilowatts. This is because of the limitation of the magnetic flux in the permanent magnets. The mathematical parameters of BLDC/PMSM motors are expressed in this section, these expressions will be used through the sections in the following. [2] [7]
Angular velocity of synchronous motor
ωe= poles
2
wmrad/s (2.1)
The relation between electrical and mechanical frequency can be described as follow. By assuming that in a two-poles or one pole pair single-phase motor, the coil voltages pass through a complete cycle for each revolution. The frequency in cycles per second for a two-poles motor is the same as the rotor revolution per second. When a motor has more than two-poles as it was shown in figure 2.2 then one pole pair in such a multi-poles motor or one cycle of the flux distribution equals 360◦ electrical degrees or 2π electrical radians. Then the number of electrical cycle is poles2 . The relation between pole pairs and revolutions can be expressed as equation 2.2. Then by using equation 2.4 the electrical frequency for such an 8-poles motor which was shown in figure 2.2 can be calculated. [2]
Relation between electrical angle and the actual (rotor) angle in a synchronous motor
θe= poles
2
θrrad/s (2.2)
synchronous angular velocity
ns= 120 poles ferpm (2.3) Electrical frequency fe= poles 2 ns 60[Hz] (2.4)
The following equation 2.5-2.7 represents the flux within a wye-wound stator respective in all three-phases.
λb= Lbaia+ Lbbib+ Lbcic+ φbm (2.6)
λc= Lcaia+ Lcbib+ Lccic+ φcm (2.7)
Where Laa, Lbb and Lcc are the stator windings self-inductance and the Lab, Lac, Lba, Lbc, Lca and Lcb are the mutual inductance of the stator windings. Then the φam, φbm and φcm are the permanent magnet fluxes linking the stator windings. [2] [6]
The terminal voltages of a balanced three-phase motor wye-wound stator can be expressed as
vabc= Rsiabc+ dφsabc
dt (2.8)
Then the total phases voltages can be rewritten by using equation 2.8 as it shows below
vabc= Rsiabc+ jωe(Lsisabc) + jωeφr (2.9) where jωeφris the back-emf induced by rotor and φr is the constant value for permanent magnet in the rotor. [1]
2.4
Control Models
In this section the theory about three different control models as mentioned in section 2.4.4 will be described.
2.4.1 Six-Step Control
As mentioned earlier that the BLDC motors are using electronically switching to realize the current commutation. So that the switching should occur at the right time, a known rotor position is needed. Rotor position is important for starting and keeping the motion of the rotor in a BLDC motor, as can be seen in the figure 2.2 that there are three hall-effect sensors mounted in the stator part which sense the rotor position. Since the rotor in a BLDC motor include Permanent magnets and then the hall-effect sensors will be affected by the rotor’s magnetic flux and the sensors feedback determines when to switch the current through phases. These three hall-effect sensors are placed in a 120◦ interval from each other. For example, the hall-effect sensors change its states for every 60◦, it means that to cover 360◦electrical degree it takes 6-steps to complete a whole electrical cycle. This description refers to a two-poles or one pole pair motor. For simplification sake the sections for a two-poles motor illustrated and can be seen in figure 2.3. [14]
Note that the numbers inside the rotor in figure 2.3 represent the sections for a 2-poles motor. If the motor has 8-poles, then the number of its sections will be 24 sections within the whole circle.
Some other methods that are used to determine the rotor position in a BLDC motor. But in the case of this thesis the hall-effect sensors are used for determination of the rotor position. [15]
Figure 2.3: Sections on a typical brushless DC motor
The principle of six-step control is based on controlling the applied current to the motor by controlling the correct gate pulses to the inverter. The hall-effect sensors in a BLDC motor can be affected by rotor magnetic fields and indicate its position, thereafter the information about the rotor position can be used to apply a proper phase current. As mentioned before there are six sections that the rotor could be located, on these locations, the hall-effect sensors gives a digital number in binary form, these numbers indicate the rotor position. The hall-effect sensors information can be utilized to know that in which phases to drive current through to run the motor in a correct order see table 1. The numbers which represent the hall sensors in table 1 could take any combinations between 1-6. But in table 1 represents one of those combinations. [3] [15]
Table 1: Relationship between hall-effect sensors and phase control signals
Hall Sensors Connected phases
H-A H-B H-C Phase-A Phase-B Phase-C
0 0 1 0 -1 +1 0 1 0 -1 +1 0 0 1 1 -1 0 +1 1 0 0 +1 0 -1 1 0 1 +1 -1 0 1 1 0 0 +1 -1
Furthermore, when the rotor positions are known as it shows in table 1, then the current can be supplied to the right phase by using the combinations from table 1. One of the cases from table 1 have been visualized in the figure 2.4 below, the figure shows that phase-A and phase-C are activated. For simplification sake the motor in figure 2.4 visualized with one pole pair. Here the figure shows that when the switch on the high-side of the inverter is activated then phase-A supplies a positive current and when the switch on the lower side of the inverter is activated then phase-C supplies a negative current. The positive and negative directions of the currents determine that a correct magnetic flux has to be created to drive the motor.
Then to control the angular velocity of the motor, the PWM method must be used. By controlling the duty cycle of the PWM signals to the inverter, then the applied currents can be controlled. Assume that the motor runs with 80 % of its rated currents, then the corresponding switches in the inverter should be on at 80 % of its one period time. In figure 2.5 the duty cycle of the PWM signals have been chosen to 80 %. As can be in the figure 2.5 that both top and bottom switches in one leg of the inverter are switching in parallel. In the figure can also be seen that the currents have been applied to phase-A and phase-C, as it was shown in figure 2.4. As mentioned before, when the switches on the top of the inverter are active the phases will be applied a positive current and vice versa. By exploring the duty of signals in figure 2.5 can be seen that the switches in the corresponding leg of the inverter are switching at 90 %, of the times. On the other hand, the PWM signals are swapped on the opposite switches in the
inverter. That means that the opposite switch contributes to negative currents, in this case 10 %. Then the sum of the duty cycles is equal to 80 %.
Note that here the top and bottom switches of the inverter have been used in the complementary and the dead-time for on and off of the switches have been kept in the account. This type of switching has been used to avoid to short circuit of the inverter. [3] [9]
Figure 2.4: Switching currents to phase-A and phase-C
Figure 2.5: PWM signals with 80 % duty cycles
2.4.2 Sinusoidal Control
The basic principle of sinusoidal control is that to create a sinusoidal phase voltage. The pulse width modulation (PWM) method can be used for voltage source inverter to invert a variable voltage supply. The corresponding input to the inverter is DC voltage which by using PWM transforms into three-phase AC voltages. The idea behind the pulse width modulated three-phase inverter is that to shape and control the three-phase voltages both in magnitudes and frequencies to obtain a sinusoidal three-phase signal by using a full-bridge inverter.
To be able to create a sinusoidal wave-form voltage, two signals are needed, a control signal and a repetitive switching frequency triangular waveform signal. Then the control signal, which is a three-phase sinusoidal signal with a certain frequency is compared with a triangular signal. The triangular signal has a constant frequency and this frequency corresponds to the switching frequency for the inverter as well. To generate a sinuously like signal, the switching frequency of the inverter needs to be much higher than the frequency of the control signals. The motor
feds by the generated sinusoidal formed voltages. Then to be able to control the angular velocity of the motor, the amplitudes of the generated voltages have to be controlled. This can be done by controlling the amplitude of the control signals. [5] [16]
A desired three phase voltage can be represented by using equations 2.10, 2.11 and 2.12. [4]
Va= Vpeakcos(ωt) (2.10)
Vb= Vpeakcos(ωt − 120◦) (2.11)
Vc= Vpeakcos(ωt + 120◦) (2.12)
2.4.3 Field Oriented Control
Field oriented control (FOC) or vector control is another type of control model which is also used for control of the three-phase BLDC motors. With field-oriented control (FOC) the torque and flux of the motor can be controlled independently. Then to be able to control the motor torques and fluxes separately there are some conversion of the stator phases currents/voltages reference frames are needed. A 2-axis reference-frame coordinate system is required while the motor parameters are in a 3-axis reference-frame coordinate system. The motor parameters are separated in two-part, a stationary and a rotational part. The stationary part represents by stator and the rotational part represents by rotor. These conversions can be done by using of some fundamental mathematical equations as they will be shown in some steps in section 2.4.4. [10] [4]
When the system has been converted into a 2-axis coordinate system then the maximum torque can be produced by the motor when the stator magnetic field keeps 90◦degrees ahead of the rotor. Then to be able to produce the maximum torque by the motor, the rotor position is always demanded. Then a faster and higher dynamics response can be provided with FOC when motor running at a higher speed. [8]
2.4.4 Transformation to Direct and Quadrature Variables
In FOC the three-phase stator currents time-domain are converted into 2-axis complex coordinate system. Two of three stator phases currents are measured, since the instantaneous sum of the three-phases currents values will be zero, then the third current can be determined by using Kirchhoff’s current relation as equation 2.13.
Ia+ Ib+ Ic= 0 (2.13)
Transformation of a balanced three phase stator currents 3-axis coordinates system into a 2-axis orthogonal complex coordinate system can be done by using direct Clarke transformation (abc → αβ). This transformation is required for representation of stator three-phases coordinates into a fixed 2-axis stationary complex coordinate system see figure 2.7.
(Ia, Ib, Ic) → (Iα, Iβ)
Figure 2.7: abc-reference frame to αβ transformation
Clarke transformation which transforms the abc-reference frame to the αβ-reference frame can be seen in matrix 2.14. Note that here the zero-sequence calculation is always zero for a balanced system as it was shown in equation 2.13. " I0 Iα Iβ # = r 2 3 1 √ 2 1 √ 2 1 √ 2 1 2 − 1 2 − 1 2 0 √ 3 2 − √ 3 2 "Ia Ib Ic # (2.14)
The inverse Clarke transformation transforms (αβ-frame back to abc-frame) can be done by using 2.15
"Ia Ib Ic # = r 2 3 1 √ 2 1 0 1 √ 2 − 1 2 √ 3 2 1 √ 2 1 2 − √ 3 2 " I0 Iα Iβ # (2.15)
On the next step the αβ coordinate system transforms to the dq-reference frame. The dq-reference frame represent the rotating part in dq-axis. The rotating part rotate with the rotor fluxes. This transformation is called Park transformation see figure 2.8.
αβ → dq-reference-frame
Figure 2.8: Relation between αβ and dq-reference-frame
The Park transformation which transforms the αβ → dq-reference-frame can be seen in matrix 2.16. Note that here the zero-sequence calculation keeps the same value as it has.
"Id Iq I0 # =" cos(ωt) sin(ωt) 0 −sin(ωt) cos(ωt) 0 0 0 1 # "Iα Iβ I0 # (2.16)
Then the inverse of the Park transformation can be done by using matrix 2.17. dq → αβ − ref erencef rame
"Iα Iβ I0 # ="cos(ωt) −sin(ωt) 0 sin(ωt) cos(ωt) 0 0 0 1 # "Id Iq I0 # (2.17) 2.4.5 PMSM Relation in dq Variables
The quantities of the motor in dq-reference frame are expressed in equations below. d dtid= 1 Ld vd− Rs Ld id+ Lq Ld ωeiq (2.18) d dtiq = 1 Lq vq− Rs Lq iq− Lq Ld ωe(Ldid+ φm) (2.19)
Where the ωe is the electrical angular velocity and φm is the permanent magnet flux linkage. Since the rotor in the motor is rounded, then the inductance Ld = Lq, by assuming a steady state and using equation 2.8 and the relation that Ld = Lq, the phase voltage in dq-reference frame can be expressed as below.
vd= Rsid+ did dtLs− ωeLsiq (2.20) vq = Rsiq+ Ls diq dt + ωe(Lsid+ φm) (2.21)
Then the total voltage Udq in a complex form can be expressed as equation 2.22
Chapter 3
3
Simulation
In this part of the thesis the simulation of the control models that were explored in the theory part will be represented. Simulation of the control models simplifies the workflow and helps to get a better understanding of how the theories can be used in practical. The simulation will also configure the design’s functionalities and improvements. As mentioned before Matlab/Simulink will be used for the design of the control models. All those three control models at first will be simulated in Simulink. When the control models have been configured in Simulink and then the models will be implemented to the Arduino Due for further tests on the motor. The results of the simulations will be represented at the end of each case for every control model. The simulation results of all three control models will be compared at the end of the section.
3.1
Simulation Models
3.1.1 Six-step Control System
As was mentioned before the control models are operated with electronic commutation e.g. in this model the motor angular velocity will be controlled by controlling the motor phases voltages. This can be done by controlling the switching ratio in the full-bridge inverter to generate the desired phases voltages. The design of the six-step model shows in the figure 3.1.
Figure 3.1: Six-step control scheme
Figure 3.1 show the blocks which have been used for the design of the six-step control. An equivalent model for the BLDC motor shows in the middle of the block-scheme. The motor feds by three-phase voltage from the inverter. The same equivalent motor model in the simulation will be used for all three control models in the following. This equivalent motor in the Simulink represents the motor which was figured in figure 2.2. Some measurements have been possible to do in this type of motor model in the Simulink e.g. motor’s back-emf, hall-effect sensors signals, electrical torque and rotor angle.
The next block in this control scheme is the full-bridge inverter, this block has been used for inverting of DC voltage to three-phase alternating current (AC). The decoder in the control model decodes the hall-effect sensors’ information about the motor conditions. When the hall-effects sensors affect by the position of the rotor and reveals its position by sending the corresponding data. Then by using these hall-effect sensors data as it was shown in table 1, the mathematical model for this conversion has been simulated and can be seen in figure 3.2.
Figure 3.2: Mathematical conversion of the hall-effect sensors data to driving stator currents
The information from figure 3.2 needed to be decoded that the information could be applicable in the full-bridge inverter. Then the conversion of the information at this step make the switches to generate the right phase voltages. The relationship between hall-effect sensors and phase voltage as it was shown in table 1 and the figure 2.4 have been simulated and can be seen in the figure 3.3.
Figure 3.3: Mathematical conversion of phase control signals to gate pulses
The PI-regulator which can be seen in figure 3.1 controls the angular velocity of the motor. The PI-regulator uses the feedback of the motor angular velocity. Then the PI-regulator controls the applied voltages to the motor by generation a desired duty cycle to the switches in the inverter see figure 3.3. As it was described before that on the 6-step control two phases are active at the same time. Since one of the phase control signal is zero and two others are one plus and one minus at each time see figure 1, then in figure 3.3 can be seen that these phase control signals can be used by comparison to zero which in turn allow that only two switches in the inverter to be active at each time see figure 3.7.
3.1.2 Six-step Simulation Result
In this section, the simulation results of the six-step will be shown. Since this thesis focuses are on the investigation of three different control models, then the values of phases currents, torque ripples and audible noise of the motor will be observed. Note that the motor parameter values will be the same and the motor will be operated at a specified angular velocity during observation. Then the results of the simulations will be compared at the end of the section.
Figure 3.4: Six-step: Motor stator currents, Electrical torque and Electrical angular velocity (reference and actual) in respective
Here the reference electrical angular velocity was chosen at 300 rad/s and the load was set at 10 Nm. Then the simulation was running until the reference angular velocity has been reached. Note that the 300 rad/s electrical angular velocity is equivalent to 716 rpm mechanical revolution per minute for an 8-poles motor. Figure 3.5 shows a closer view of angular velocity, current and torque when the motor has been stabilized and reached the reference angular velocity.
Figure 3.5: Zoomed: Motor stator currents, Electrical torque and Electrical angular velocity (reference and actual) in respective
On the upper part of the figure 3.4 and 3.5 shows the stator currents, in the middle part the electrical torque and in the bottom part the angular velocity response of the six-step control system.
Figure 3.6: Six-step maximum angular velocity
The maximum performance of the motor can be limited by phases voltages and currents. But in this case the performance of the motor has been tested in the form of maximum angular velocity. By assuming that the available terminal voltage is 48 V and then the motor runs until to reach the maximum angular velocity. Figure 3.6 shows the result of the maximum angular velocity. Here the reference angular velocity was chosen at 4000 rad/s and then the simulation was running until the maximum angular velocity was reached. The maximum angular velocity of the six-step control shows in the bottom part of the figure 3.6
Figure 3.7: Six-step gate pulses
Six-step control was running with two phases-currents and the inverter was switching with two switches in parallel at each time. This gate pulses shows in figure 3.7.
Figure 3.8: Six-step hall-sensors and back-emf
Six-step control’s hall-effect sensors and back-emf signals are shown in figure 3.8 above, here on the first half of the figure are shown the form of three hall-effect sensors signals and on the next half of the figure are shown the form of back-emf signals. By exploring the signals forms in the figure 3.8, it can be seen that the hall-effect sensors and back-emf signals are almost in phase.
3.2
Sinusoidal Control System
On sinusoidal control design three-phase voltages need to be generated by the inverter. To be able to drive the motor by this control model a precise rotor position has to be calculated. In figure 3.9 are shown the design of the control models and the signals which have been used for calculations in the control models.
Figure 3.9: Control scheme and control signals
Figure 3.9 shows an overview of all three-control systems and the yellow blocks in the figure represent three different control systems. On the left side of figure 3.9 shows the subsystem block named sinusoidal, in this block the input signals were taken from the motor, PI-regulator and a reference angular velocity. The sinusoidal control was operated by using these inputs in different blocks inside the sinusoidal block.
T =2π ωe
(3.2) When the hall-effect sensor’s data about the motor states are measured, then these data are used in the hall-filter and angular velocity calculator block see figure 3.2.1. In this block the angular velocity and angle of the motor have been calculated. By using hall-sensors period time and equation 3.2 the electrical angular velocity of the motor has been calculated. Then by multiplication of the equation 3.1 and the motor direction signal the right direction for the motor has been determined.
Figure 3.10: Calculation of the motor angle and generation of the sine-wave
3.2.1 Angle and Speed Calculation
As mentioned before a precise rotor position needs to be calculated on this control model. The rotor position calculates by using hall-effect sensor’s information. At first, by knowing in which order the hall-effect sensor’s information comes, then the direction of the motor can be known that if the motor runs clockwise or counterclockwise see figure 3.11.
Figure 3.11: Calculation of the motor angle and angular velocity
In the first step in the calculation of the motor angle in figure 3.11 (upper part) are shown that the hall-effect sensors are used to generate a reset signal. Here the signal that indicates the rotor direction is used, which indicates that if an up or down flank can be used as a reset signal. In the lower part of the figure, the hall-effect sensor’s
period time is used to calculate the motor angular velocity. Then to achieve a precise motor angle the calculated angular velocity (ωe− calc) multiplies by a step time and counts up until a revolution has been completed and then it resets by a flank signal from hall-effect sensors see figure 3.12. Note that in this case the hall-effect sensor number-3 was used, and the step time was 100us. The period time which can be seen in figure 3.11 have been calculated by using equations 3.1 and 3.2.
Figure 3.12: Motor angle and hall-effect sensor signal
Figure 3.13: Generation of sine-waves signals
Figure 3.14: Generation of gates signals
The calculated angle was used in the fundamental control block see figure 3.10, where based on the calculated angle, the sine-waves have been generated see figure 3.13. In this block, the calculated angle has been used as a reference point and the three-phase sinusoidal signals can be created, where the phases between the signals have been shifted by 120◦ from each other.
When the three-phase sine-wave signal was generated then on the next block the signals are used as control signals for the generation of phase voltages. Then to be able to control the applied voltages/currents to the motor, the
generated three-phase signals have been multiplied by the signal which was achieved from PI-regulator, this signal controls the amplitude of the phase currents see figure 3.13. The generated three-phase sinusoidal signals were used as control signals and compared with a high frequency sawtooth triangular signal see figure 2.6 and 3.14.
In order to drive the motor optimally, the phase between the voltages signals must be kept like, that the currents have to lie perpendicular to the rotor fluxes direction see figure 3.20.
3.2.2 Sinusoidal Control Simulation Results
In this part the simulation results of the sinusoidal control will be shown. As mentioned before the motor parameters have been the same as the previous control system, the motor’s reference electrical angular velocity was chosen at 300 rad/s and the load has been chosen at 10 Nm as before.
Figure 3.15: Sinusoidal: Motor phases currents, Electrical torque and Electrical angular velocity (reference and actual) in the respective
Figure 3.16 shows an enlarged model of the figure 3.15 on an interval that the motor has reached the reference angular velocity.
Figure 3.16: Zoomed: Motor stator currents, Electrical torque and Electrical angular velocity (reference and actual) in the respective
The performance of the sinusoidal control model has been also tested and its result can be seen on the figure 3.17 below. Here the reference angular velocity was chosen at 4000 rad/s and then the simulation was running until maximum angular velocity has been reached.
Figure 3.17: Sinusoidal maximum angular velocity
Figure 3.18: Sinusoidal gate pulses
As was described before that the sinusoidal control running with three-phase currents/voltages then the gate pulses of this model will be different. Figure 3.18 show gate pulses that all switches are active in parallel to create a sinusoidal signal.
Figure 3.19: Angle calculation results
As was described in section 3.2.1 an angle was calculated for this control model. In figure 3.19 top part shows the measured angle from the motor, the calculated angle and one of the sine-wave signals which were used as a reference signal for generation of phases currents. Note that here the reference sine-wave signal was adjusted which in turn adjust all three generated phases currents to match the rotor angle see figure 3.13. Since in the mathematical calculation of angle, the hall-effect sensor number-3 was used, here in the middle part of the figure 3.19 shows that the angle resets when the hall-effect sensor number-3 changes. On the bottom part of figure 3.19 shows the back-emf signal of phase-C.
As was described at the beginning of this section that to operate the motor optimally the phases currents must be kept perpendicular to phases voltages. Here in the figure 3.20 shows that difference between the reference signal to the inverter for phase-A and the measured current of phase-A is 90◦ degrees. Note that the form of the phases voltages was not sinusoidal, and its angle was not possible to measure and compare, here the reference signal to the inverter has been used instead of phase voltage.
Figure 3.20: Measured current of phase-A, Reference signal to the inverter and calculated angle
3.3
Field Oriented Control
The third control system is the FOC or vector control. The simulation of this model can be seen in figure 3.9 and the subsystem for the model was named FOC in this figure. This control model is different from two other which were described and simulated above. By using the mathematical equations which was described in section 2.4.4, the three-phase coordinate system transforms into two-coordinate system.
In FOC the two of three phases currents can be measured, and the third one can be calculated by using the Kirchhoff’s current law from equation 2.13. Then the measured phases currents can be transformed by using the equations 2.14 and 2.16. Then the three-phase currents coordinate system can be transformed into Id-direct and Iq-quadrant orthogonal coordinate system. The Id and Iq are the measured currents from the motor. Two PI-regulator can be used to control these currents by using the measured and the reference currents. By using the equations 2.17 and 2.15 the inverse Park and Clarke transformation the system can be transformed back to a three-phase coordinate system see figure 3.21. In this figure the classical model of FOC control has been visualized. Note that the transformation uses an angle based on the rotor position. While the motor is equipped with hall-sensors then by using the information of these hall-effect sensors the angle for transformation has been calculated see section 3.2.1.
Figure 3.21: FOC Control scheme
Simulation model for FOC control shows in figure 3.22, there are three PI-regulator that have been used, but just one of them can be seen in figure 3.22. The first PI-regulator’s output has been used as Iqref. Then the two other PI-regulators are used for regulation of Id and Iq see figure 3.21. These two regulators controlled the fluxes and torque of the motor independently. The rotor fluxes controlled by Id-regulator and the torque has been controlled by Iq-regulator. How the PI-regulators have been used can be seen in the figure 3.21
Figure 3.22: FOC control simulation model
The input phases voltages are calculated by using the equations 2.20 and 2.21. Then by using the currents controller and measured phases currents the motor have been controlled as desired.
3.3.1 FOC Control Simulation Results
In this part the simulation results of the FOC control system will be shown. As mentioned in the two previous control models the motor parameters have been the same as before. Then the reference electrical angular velocity was chosen at 300 rad/s and the load was set at 10 Nm. In this control model the same calculated angle as it was for sinusoidal control has been used.
Figure 3.23: Motor phases currents, Electrical torque and Electrical angular velocity (reference and actual) in respective
Figure 3.24 shows an enlarged view of the previous figure on an interval that the motor has reached the reference angular velocity.
Figure 3.24: FOC control: Motor Phases currents, Electrical torque and Electrical angular velocity (reference and actual) in the respective
Here in the figure 3.25 (bottom part) shows the maximum angular velocity of the motor when it was running with FOC control system. Note that the motor phases currents and electrical torque are also shown here.
Figure 3.25: FOC control maximal angular velocity
The controlled currents and voltages in dq-frame are shown in figure 3.26. Here the controlled dq-currents are shown in the lower part of the figure 3.26 and the dq-voltages on upper part of the figure 3.26. How the dq-currents regulate after reference signal can also be seen in figure 3.26.
Figure 3.26: dq currents and voltages controller response
An enlarged view of the dq-currents and dq-voltages are shown in 3.27. Here the dq-currents and dq-voltages have been plotted in the figure when the motor was regulated after the reference signal.
Figure 3.27: Regulated dq currents and voltages
As was described before, to operate the motor optimally the phase currents must be kept perpendicular to the rotor fluxes. Here in figure 3.20 upper part shows the relationship between phase voltage and current for phase-A. In figure 3.28 can be seen that the difference between phase current and voltage is 90◦ degrees.
Figure 3.28: The phase differences between currents and voltages
3.4
Comparison of the control systems
In this part the results of the simulated control models will be compared. The results of the simulated control models are shown in table 2. As can be seen in table 2 the current and torque ripple of six-step control is higher, and its maximum angular velocity is lower than two other control models. Sinusoidal control results show that its phases currents are higher than FOC control and lower than the six-step control model, then the maximum angular velocity of sinusoidal control is lower than FOC and higher than six-step control. The total performance of the FOC control is better than two other control systems where its phases currents are lower, and the maximum angular velocity is higher in the whole comparison.
Since the commutations of six-step control happen based on the commutations table, it means that the commutation occurs once per 60◦ electrical degrees, then the commutation happens in steps that results in a trapezoidal shape phases currents, these commutations also create a louder audible noise. Then the ripples in the trapezoidal shape phases currents are higher compared to the sinusoidal shape phases currents which in turn increase the torque ripples.
As was shown during the simulation, the results of the sinusoidal and FOC control models in terms of currents shape, gate pulses and the used calculated angle have been almost the same. But as can be seen in the table 2 the performance of the FOC control is better than sinusoidal control. In FOC control design, due to the Park and Clarke conversion for phases currents have been used, then by using these conversions the angle between stator and rotor has been kept perpendicular to each other. Then to control the corresponded dq-currents PI-regulators have been used and this in turns increases the reliability of the FOC control.
On the other hand the sinusoidal control represents a simplified model of the FOC control, where the control model running with three-phase voltages and the same calculated angle as FOC control has been used. Then in the sinusoidal control there have not been used any conversions of the phase currents and no PI-regulator was used to control the currents. Then the phases currents amplitudes controlled by a factor, and there have not been any direct control of the motor fluxes in this control model.
Finally, it can be concluded that the FOC control overcomes these shortcomings of both sinusoidal and six-step control models and the control model uses the mathematical conversion and PI-regulators to control the motor fluxes in separately frames which in turn increase the reliability of the motor, but it should be reminded that the design of the FOC control model is also a little complicated than two others control models.
Table 2: Observed values of all three control models
Control type Current A Torque Nm Angular velocity rad/s Max angular velocity rad/s
Six-step 131 7-13.4 300 1210
Sinusoidal 127 8.5-12.5 300 1300
Chapter 4
4
Hardware
The hardware that was used for implementations of the control systems will be presented in this section.
4.1
Hardware Specifications
As mentioned before the BLDC motor was an Arduino Due based motor and a control board was available for implementation of the control systems. The control board was equipped with two Arduino Due board, relays, converter, inverter and an emergency stop bottom. The detailed description of hardware and the connection of the system can be seen in the Appendix A. The motor that was used for implementation have the specification and rated parameter values as it shows in the table 3.
Table 3: Motor parameters values
P W 5000 n rpm 3000 wm rad/s 314 T Nm 16 p 8 R mohm 6 L µH 68 Frequency Hz 200 mf 21 fsw Hz 4200 H s 2.5 J N m/s2 0.253
Two battery systems were available one 12 V and one 48 V. 12 V battery was used for the power supplying of control electronics. Then the motor voltages have been applied by the 48 V battery system. The data about battery systems shows in table 4 and 5.
Table 4: 12 Volt Battery system specification
Nominal voltage 12 V Max voltage 14.4 V Rated capacity 100 Ah
DoD 0.6 %
Stored energy 720 Wh Max charging current 30 A
Weight 31.8 kg
Volume 12.2 l
Table 5: 48 Volt Battery system specification
No of cells 16 Unit Nominal voltage 51.2 V Max voltage 60.8 V Min voltage 40 A Rated capacity 60 Ah DoD 0.78 % Ri 0.032 Ω Stored energy 2304 Wh Imax 180 A
Max charging current 20 A
Weight 27 kg
Volume 15 l
4.2
Implementation of Control Systems to Hardware
The designed control models have been implemented in an Arduino Due and the functionalities of control models have been configured. The first implemented model was the six-step control. Here in the figure 4.1 are shown the results of the six-step control implementation. The values which can be seen in figure 4.1 are the phases currents
of phases-A and phase-B, gate pulses and hall-effect sensors in the respective order from the top down. The values which can be seen in the bottom of the figure 4.1 represent that the value of each square in the figure are equal to 160 A. Note that the motor was running at 700 rpm and load to the motor was at 5 Nm when the values have been measured/captured.
The audible noise of the control models has been recorded by a mobile and then have been plotted in Matlab. The results of the audible noise can be seen in the figures 4.2, 4.4 and 4.6.
Note that the motor was running without load when the audible noises have been recorded.
Figure 4.1: Implementation results of six-step control model
Figure 4.2: Six-step control’s audible noise level
Figure 4.3 shows the configurations results of sinusoidal control model. The values which can be seen here are the phases currents from two phases, gate pulses, the calculated angle and hall-effect sensors in the respective order from the top down.
Figure 4.3: Implementation results of sinusoidal control model
Figure 4.4: Sinusoidal control’s audible noise level
The FOC control configurations results can be seen in figure 4.5. Here are shown the same values that were shown and described for two other control models above. Some distortions have been captured in hall-effect sensors, some loose connections in the measurement components caused these distortions.
Figure 4.5: Implementation result of the FOC control model
Figure 4.6: FOC control’s audible noise level
The audible noise of the control models which have been recorded and were shown in the figures 4.2, 4.4 and 4.6 have been compared and their results can be seen in the table 6.
Table 6: Audible noise level of all three control models
Control models Six-step Sinusoidal FOC Audible noise level in dB ≈ −12 ≈ −25.9 ≈ −16.5 Audible noise Power ratio ≈ 0.66 ≈ 0.288 ≈ 0.37
Chapter 5
5
Discussion
5.1
Method
At the beginning of the thesis, it was decided to go through previous studies about control systems to understand how the control of the electric motors work. After having acquired basic knowledge about the motor controls, those three types of control models for electric drive systems have been investigated. If I look back to the time of this thesis, it could be better to choose one of the control models to keep the focus on. After that investigate the corresponded control model, then simulate and implement the control model to the hardware. Thereafter a better understanding of how the whole process of the thesis should be done. When a better understanding of equipment and devices has been gained at an earlier time of the thesis, then the process of thesis would go better and faster, then a lot of time would be saved during the process of the thesis.
5.2
Simulation
The simulation was used as a configuration of the control models. The results of the simulation showed the properties of the control models. Since the components in Simulink considered to be ideal, then the simulation results have not guaranteed that the implementation of control models would have the same properties on hardware. The other benefit of the simulation was that the motor currents and voltages have been quite high and dangerous, then the simulation of the control models in the Simulink was a better way for configuration and test of control models, this ,in turn, has reduced the amount of direct work with the motor and high currents and voltages.
5.3
Simulation Results
The simulation results of the control models have been shown in the form of figures, then the motor performance conditions values have been shown for every control model. Since this thesis focuses were on the investigation of some conditions that are crucial for an electric motor, then the motor performance observed under such conditions. The currents and torque of the three control models have been presented. The results of all those three control models showed that there are ripples both in currents and torques. The minimization of these ripples need some improvements for these control models. The improvements need more time, since this thesis has a limited time, these improvements have been left to future work.
5.4
Implementation to Hardware
The implementation results of control models to the hardware have been shown in the figures that were captured by an oscilloscope in section 4.2. The results that were shown in the section 4.2 were quite similar to the simulation results. when we explore the figures 4.3 and 4.5 then we can conclude that the functionality of the FOC and sinusoidal control are more similar to each other. Generally, the FOC control could be better, that in this control model the motor currents can be controlled depending on the load, but some improvements were needed for this control model e.g. PI-regulators that were used as currents controller needed to be improved.
There were some restrictions on the implementation of the control models. The control frequency in the simulation was chosen at 10 kHz and in the hardware it was limited at 1 kHz. This limitation in turn could have an impact on the results. The impact of a lower control frequency means less samples per electrical period time and a higher ripple both in torque and currents. When we compare the number of the samples per electrical period between hardware implementation and simulation at 700 rpm, then by using equation 2.4 it shows that the number of samples in the simulation is 213 and in the hardware is 21 samples per electrical period. Then this shortage in the hardware could be the reason that the FOC control did not work when the motor was running at higher angular velocity.
Chapter 6
6
Conclusion
The purpose of this work has been to investigate and design three different control models to operate an electric motor. Then determine which of the control models are more effective. The basic theory about the BLDC motors have been described in the theory section. Then Matlab/Simulink has been used for design and simulations of these control models. The control models have been simulated and then its results have been presented during the thesis. The results from simulations showed that the FOC control model had a better performance compared to the two other control models. The simulated control models have been implemented on an Arduino Due based BLDC motor which verified the functionalities of the designed control models. The results of hardware implementations showed that the motor can be controlled by these control models. Generally, the performance of the FOC control model has been better in simulation compared to the two other control models. But in the hardware implementation the performance of the sinusoidal was better, that the sinusoidal control was smoother and its audible noise was lower. The FOC control implementation has worked as well but the control model needed some improvements.
The commutations techniques that were used for six-step control cause higher ripples in the phases currents which in turn gives higher torque ripples and louder audible noise. Then the six-step control also requires more currents for the same load see table 2. In the FOC control there have been used some mathematical conversions of stator currents. Then it was possible, that by using PI-regulators the stator fluxes in dq-frame could be controlled as desired. As can be seen in the table 2, that the results of the sinusoidal control lands between FOC and six-step control models. As mentioned before, the sinusoidal control represents a simplified model of the FOC control, wherein the sinusoidal control, there are no direct control of the fluxes in the stator respect to the rotor. These shortcomings of the sinusoidal control mean that its reliability becomes lower than FOC control. Finally, it should be clarified that the control frequency in the hardware implementation was too low and this in turn decreases the number of the samples per electrical period which could affect the hardware implementation and the final results.
6.1
Future Work
Some improvements that are needed to be investigated further, thereafter the implementations of the control systems should work better. The first one is to compensate the control models with other methods to reduce the currents and torques ripples. The second one in the FOC control model is to develop a transfer function for the entire system to determine the optimal PI-regulator parameters. In the third one, it could be desirable to implement and test these control models to the other types of motors and control boards.
References
[1] Ward Brown. Brushless dc motor control made easy. AN857, 2002.
[2] A.E. Fitzgerald, Charles Kingsley Jr., and Stephen D.Umans. Electric Machinery. McGraw-Hill Companies, 2003.
[3] Xianhu Gao. Bldc motor control with hall sensors based on frdm-ke02z. AN4776, 2013.
[4] Meghana N Gujjar and Pradeep Kumar. Comparative analysis of field oriented control of bldc motor using spwm and svpwm techniques. In 2014 6th European Embedded Design in Education and Research Conference (EDERC). IEEE, 2017.
[5] Bo Li and Chen Wang. Comparative analysis on pmsm control system based on spwm and svpwm. In 2016 Chinese Control and Decision Conference (CCDC), pages 5071–5075. IEEE, 2016.
[6] Matlab. Permanent magnet synchronous motor with sinusoidal flux distribution.
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[9] Libor Prokop. Using motor control eflexpwm (mcpwm) for bldc motors. Freescale Semiconductor, 2011. [10] Microchip Seminars. Sensorless foc for pmsm. 2007.
[11] MICRO SWITCH Sensing and Control. HALL EFFECT SENSING AND APPLICATION. Honeywell. [12] Bist Vashist. Field oriented control (foc) made easy for brushless dc (bldc) motors using ti smart gate drivers.
TI, January 2018.
[13] GUO Xiaoli. How does a dc motor work. NXP, 2012.
[14] Jufeng Yang Feifei Bu Yong Zhao, Wenxin Huang and Saide Liu. A pmsm rotor position estimation with low-cost hall-effect sensors using improved pll. 2016.
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Appendix
Overview of the control system
BLDC motor data
• Rated power: 5 kW @ 3500 rpm • Rated voltage: 48 V
• Rated torque: 16 Nm • No of poles: 8
• Nominal electrical frequency: 200 Hz • Winding data (R/L): 6 mohm/68 µH • H factor: 2.5 kJs/kVA
• Inertia (J): 0.253 Nm/s2
• Manufacturer: Golden motor • Type: HPM48-5000
HPM48-5000
Ud
Id
Pin
Te
n
Pout
Eff
we
PM
BEMF
Description V A W mNm rpm W % rad/s Vs V
No-load point 47.99 8.2 392 360 4389 165 42.2 1838 0.01305 24.0
Max efficiency
point 47.57 73.7 3501 7729 3861 3096 88.4 1617 0.01305 21.1
Max Po. point 47.34 175 8308 21277 2892 6662 80.2 1211 0.01305 15.8
Max torque point 47.42 176 8367 24118 2389 6034 72.1 1001 0.01305 13.1
Rated speed point 47.38 133 6297 14541 3476 5421 86.1 1456 0.01305 19.0
