CHAPTER 4 START-UP STARTEGY AND PROCEDURE FOR BLDC MOTORS.32
4.1.2 Inductive sense start-up method
The main idea of this method is to utilize the fact that the inductance of the motor winding varies as the rotor position changes. The magnetic flux generated by the current in the stator winding can increase or decrease the flux density in the stator depending on the rotor position, leading to decrease or increase in induction due to the saturation of the stator. The relationship between inductance and flux linkage is shown
as
+
Li
= PM
Phase λ
λ (4-1)
where λPhase is the summation of the flux from the permanent magnet, λ , and the PM flux from the current i. L is the inductance of the excited phase. Supply the current with positive or negative direction to the phase, as shown in Fig.4.1 [10]. The
variations of the inductance are derived as
where and are the inductance and flux linkage variation corresponding to the positive current is provided; , and is opposite. It is obvious that is smaller than due to is smaller than . Consider the response of a phase voltage and current to the variation of the inductance. The phase voltage equation is expressed as
L
+ ∆λ+The back-EMF can be neglect when a motor is at standstill. Then, solve the differential equation; the phase current can be derived as
⎟⎟⎠
According to (4-5), the phase current has a different transient dependent on the inductance variation, which is determined by the relative position of the magnet and the direction of the current. It should be noted that has a faster response than due to the time constant is larger than , as shown in Fig.4.2 [10].
Therefore, the position information can be obtained by monitoring the phase current and in an appropriate time interval.
i
+i
−R/L
+R/L
−i
+i
−∆λ
−∆λ
+ λPMi
+i i
−λphase
Fig.4.1 The flux linkage with positive or negative current
∆i R
v
ani
| i− |
i
+T t
Fig.4.2 The responses of current with positive or negative direction
By applying positive and negative voltage pulses sequentially and measuring the difference in inductance, it can be determined which magnetic polarity the phase
winding is facing (Appendix A). Therefore, the initial position can be detected by the difference of the current pulse.
After identifying the initial position when a motor is at standstill, the correct phases winding on the stator are excited and the maximum electromagnetic torque is produced so that motor starts to rotate. Necessarily, the next commutation position should be detected for next excitation when the rotor rotates with 60 electrical degrees.
However, the method proposed in previous section is not suitable while the rotor is rotating due to the time delay caused by the period of six voltage pulses and the negative direction torque produced by exciting incorrect segments. The start-up procedure proposed by G. H. Jang, J. H. Park and J. H. Chang [10] will be detailed illustrated in Appendix A.
However, the success of this algorithm strongly depends on how sensitive the inductance of the phase winding to the direction of the applied current at the given position. Therefore, the prototype motor which was unsuccessful with the inductive sense start-up algorithm will be investigated using finite element method (FEM) analysis for the identification of the root cause [13].
4.2 Start-up Procedure
In the section will verify the method introduced in Section 4.1 and represent the start-up procedure which will be used in the experiment for the BLDC motor since the start-up procedure is highly dependent on the characteristics of the motor.
4.2.1 Initial position detection
By using the initial position detection mentioned in Section 4.1, the relation of each segments of an electrical cycle will be implemented. As shown in Table 4.1, the three-phase motor has six segments of an electrical cycle, in which any two phases out of three currents. In order to verify the feasibility of this method, measured the current response with a delay 500µs. Besides, by using (4-5), the inductance is determined whenever a rotor moves the electrical angle of 12°. Therefore, Fig.4.3 could be plotted to show the relative rotor position with respect to the stator produces different response of the current i1+
and i1-
. In addition, Fig.4.4 shows the variation of the difference
responses , which can provide information on the rotor position because the polarity of changes every electrical angle of 60°, where didi
di
1=i1+− i
1− , di2= anddi
− +
−
22 i
i
3=
i
3+− i
3− . The equilibrium positions (P1~P6), which means the relative magnitudes of the excitation currents in the two phases.Table 4.1 Six segments of an electrical cycle
Segment Symbol of current
B
0 60 120 180 240 300 360 -0.8
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
electrical angle (deg)
cur re n t di ( A m p )
di1
di2 di3
P1 P2 P3 P4 P5 P6
Fig.4.4 First difference of current responses to the rotor position
However, it is very difficult to identify the polarity of di near the magnetic equilibrium where a rotor tends to stop, because one of three di is zero in these positions. In these case, the polarity of second different of the current response, ddi, can be effectively used to identify the rotor position. Fig.4.5 shows the for electrical period, where ddi
ddi
1= di1
-di
2,ddi
2= di2-di3, and ddi3= di3-di
1. Therefore, the polarity of ddi provides information on the rotor position near the equilibrium positions as shown in Table 4.2. Consequently, the stationary rotor position can be detected by ministering the polarity of di and ddi to energize the correct phases of the motor.0 60 120 180 240 300 360
Fig.4.5 Second difference of current responses to the rotor position
Table 4.2 Polarity of ddi on rotor position
Electrical position
dd i
1dd i
2dd i
34.2.2 Start-up from standstill
Consider the sampling rate is not high enough to implement the start-up algorithm proposed in [10] (see Appendix A.2), the open-loop method is used form standstill to the low angular velocity. After using the initial position detection to ensure the starting point, the next position should be right to avoid the initial backward rotation. However, the conventional open-loop method could not make the motor rotating smoothly from standstill since the torque input from software is too high. Therefore, the modified open-loop start-up method is proposed by using voltage pulse as shown in Fig.4.6.
Define the six segments as sector 0~5 which are shown in Table 4.3. After detecting the initial sector, a set of position sequence will import the system and the motor will start to rotate in right direction. However, time delay is caused since the command instant is always faster than the motor arriving instant. Fig.4.7 shows the relation between the command signal and the circuit signal with initial sector 0. At
t t
tc 2tc 3tc 4tc
B
A A C
BCB A
B
A A C
v v
0 0 tc 2tc
Fig.4.6 The modified open-loop start-up method
starting, the delay time is almost beyond a commutation time. After a period of time, the delay time will become less and approach to a constant. Then the system will switch to the commutation algorithm because there are enough back-EMFs to be detected.
As mentioned before, if there is no initial position detection, the initial backward will be incurred. For example, when the rotor initial position is in the sector 3 but the command is started in the sector 1, the rotor will rotate backward at the first commutation period as shown in Fig.4.8.
In addition, the angular velocity could be estimated by the commutation period because six commutation periods are equal to an electrical cycle. The mathematical equation is shown as
6 2 60
t p ˆ
c× ×
ω = (4-6)
where p is pole number and tc is the commutation period. Since the velocity is changed by tuning the duty ratio, Table 4.4 will show the relation between the duty ratio and estimated angular velocity of the motor. By using the table, the open-loop start up method can be used from standstill to accelerate the velocity with decreasing time interval in the command signal.
Table 4.3 The definition of the position sector Segment Electrical position Sector
B
Table 4.4 The relation between the duty ratio and estimated angular velocity Duty ratio
2 12.8997 9.6901
10 13.0691 9.5645
20 49.0097 3.5105
30 76.0586 1.6435
40 100.1600 1.2480
50 117.1875 1.0667
60 130.7909 0.9557
70 140.1903 0.8916
80 148.6549 0.8409
90 155.6351 0.8032
100 170.4790 0.7332
0 1 2 3 4 5 6 7 8 9 10 0
1 2 3 4 5
time
Se c to r
command signal circuit signal
Fig.4.7 The relation between the command signal and the circuit signal
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5
time
Se c to r
command signal circuit signal
Fig.4.8 The relation signals without initial position detection
Chapter 5
Hardware Setup and Implementation of Sensorless Drivers
The theories and sensorless control strategies for the BLDC motor have been introduced in Chapter 3 and 4. In order to fulfill the control strategies, it is required to design sensorless drivers with good performance. Hence, this chapter will focus on the implementation of sensorless drivers. Besides, some experiments using PC-based drive system will be set up to verify the developed sensorless control strategies.
5.1 Experimental System Descriptions
The whole experimental system shown in Fig.5.1 consists of a BLDC motor, a driver circuit, AD/DA card, a PC-based control unit and a set of low-pass filters. The motor divers will be discussed in Section 5.2.
BLDC Motor Driver
Circuit
xPC Control unit
Sensorless control algorithm & PWM
AD/DA card PCI-6024E
Filter
Velocity transducer
Fig.5.1 The complete hardware PC-based control system
A 3-phase BLDC axial-flux wheel motor, Crystalyte 4011, is used as the experimental plant, which is a low speed and high torque direct-drive motor with
specifications listed in Table 5.1.
Table 5.1 The specification of the BLDC motor
Weight (kg) 6
Outer diameter of rotor (mm) 188 Outer diameter of stator (mm) 148
Length of PM (mm) 40
Pole numbers 16
Slot numbers 48
Coil numbers per phase 11
Phase resistance (Ω) 0.5
Phase inductance (mH) 0.001025
Operation voltage (volt) 36
Maximum unload speed (rpm) 177
In the second part, the AD/DA card, which is named PCI-6024E, is an I/O broad with 16 single analog input (A/D) channels, 2 analog output (D/A) channels, 8 digital input and output lines. The maximum input sampling rate is 200kHz and the output sampling rate is 10kHz.
On the other hand, the control unit and AD/DA card are connected by the xPC target environment [12] which is shown in Fig.5.2, using two PC connected by
Ethernet line. One is a target PC; the other is a host PC. In addition, xPC target does not require DOS, Windows, Linux or any another operating system on the target PC. It is a kind of Real-Time environment with high sampling rate up to 20kHz. Furthermore, the PWM generator and sensorless control algorithm including the start-up algorithm and commutation control algorithm are realized in the host PC by software. In Section 5.3, the software design of these parts will be described in detail. Thus, the three inputs of the AD/DA card are the analog motor voltage, and six outputs are digital six-step drive signals.
Host PC Target PC
Besides, after using pulse width modulation (PWM), the voltage signal will produce unwanted noises for detecting position in sensorless control algorithm.
Therefore, a set of low pass-filters is needed to eliminate these inherent noises. Section 5.4 will analyze this part explicitly.
Fig.5.2 The block diagram of the xPC Target environment TCP/IP
Windows xPC Real-Time
Matlab®−Simulink® Kernel
PCI-6024E Plant
Real time AD/DA card
5.2 The Driver Circuit Unit
The use of the driver circuit unit is to realize the sensorless controller of a BLDC motor. The driver circuit unit consists of three parts: signal amplifier, half bridge driver unit and power MOSFET, whose block diagram is shown in Fig.5.3. There are six digital inputs required to control the current flow in the driver circuit unit, which are provided by the AD/DA card. The signal amplifier is needed due to the fact that the output high voltage of the AD/DA card is 5V [15] and the input of the half bridge driver unit is 15V [14].
The half bridge driver unit is composed of three driver ICs, IR2113, which are high voltage, high speed power MOSFET drivers with independent high and low side reference channels. The floating channel at high side can be used to drive an N-channel power MOSFET which operates up to 600V. Besides, the gate drive supply ranges from 10 to 20V. The functional block diagram is shown in Fig.5.4. Each channel contains an under-voltage detect to ensure sufficient gate bias for the power MOSFET.
6 digital inputs 3-phase
6-arms Signal Half Power
Amplifier
AD-DA card Bridge
Driver Unit
Fig.5.3 The block diagram of driver circuit unit
MOSFET
Another problem inherent to the half-bridge driver in the dead-time required between switching events. If there is not enough dead-time between turning one set of MOSFETs off and the next set on, a short circuit will appear across the dc bus. This creates large current spikes and will have a negative impact on circuit operation. To control the dead-time, the IR2113 has Schmitt trigger inputs. This allows the use of a simple RC circuit to control the time delay between receiving a gate signal input and the chip actually seeing that input.
Fig 5.4 The functional block diagram of IR2113 [14]
Fig.5.5 shows the typical connection of IR2113 to power MOSFET. Each phase of motor is driven by two power MOSFETs (IRF640N) [16]. One of the most critical issues in a high power motor driver is to construct a circuitry a circuitry that will be able to drive the high side power MOSFET. Since the source of this device is connected to one end of the phase coil, the voltage level of this node is floating due to
the induced voltage on the phase coil. So, the gate voltage of the high side power MOSFET must be set accordingly to provide proper operation of this device.
In Fig.5.5, the bootstrap principle is applied to the floating channel. First, suppose that the bootstrap capacitor C1 has been charged enough voltage ( ) by an external source over a bootstrap diode during the period when S
cc
c1
V
V
≈V
cc 1 is OFF. WhenHIN is high, M1 turns on and M2 turns off, and then will charge the capacitor between the drain and source of S1 through M1, i.e., works as a voltage source at this time. When HIN is low, M1 turns off and M2 turns on, and then the charge in S1 will be released rapidly through R1 and M1. Finally, S1 is OFF, and LIN changes to high voltage after passing the dead-time.
V
c1V
c1Fig.5.5 The typical connection of IR2113 to power MOSFET
The total driver circuit will be shown in Fig.5.6 and the photo of motor drive circuit will be displayed in Fig.5.7. There are six inputs connected to AD/DA card and
three outputs connected to the three phase of the motor.
Fig.5.6 The three phase motor driver circuit
Fig.5.7 The motor driver circuit
5.3 The Sensorless Control Unit
The sensorless control unit is fulfilled by the software package simulink○R, including control algorithm, 3-to-6 signal transformation and pulse width modulation (PWM). The block diagram of the sensorless control unit is shown in Fig.5.8.
Sensorless control unit
The control algorithm block is to realize the start-up method mentioned in Section 4.2 and sensorless commutation control method given as (3-17) to (3-26) with inputs of the motor’s phase voltages and outputs of the three-phase commutation signals. Then the 3-to-6 signal transformation block fulfills the phase commutation sequence as shown in Table 5.2, where the six outputs (aup
, a
down, b
up, b
down, c
up, and c
down) are determined by the inputs of the three-phase commutation signals (Sa, Sb, and Sc). These3-phase Voltage
Fig.5.8 The block diagram of sensorless control unit
six outputs are used as the switches to turn on or turn off the power MOSFET in driver circuit unit. Fig.5.9 shows the results of the trapezoidal back-EMFs and the phase current generated by the switching.
Table 5.2 the phase commutation sequence
Commutation signal MOSFET switch
segment Sa Sb Sc
a
upa
downb
upb
downc
upc
downB
C 0 0 1 0 0 0 1 1 0
B
A 1 0 1 1 0 0 1 0 0
C
A 1 0 0 1 0 0 0 0 1
C
B 1 1 0 0 0 1 0 0 1
A
B 0 1 0 0 1 1 0 0 0
A
C 0 1 1 0 1 0 0 1 0
As usual, in a PWM signal, the frequency of the waveform is a constant while the duty cycle varies (from 0% to 100%) according to the amplitude of the original signal.
In addition, the PWM is used to control the power applied to the motor. It can control the voltage on the motor with a fixed PWM duty cycle. The PWM usually can be applied in three ways: on the high side, on the low side, and on both sides [17]. Among them, PWM on the high side is more useful since the back-EMF can be read.
For example, in Fig.5.10(a), when the related switches T2 and T3 are ON, the current passes through the two switches and two motor windings. The potential on the point M is HV/2 and the back-EMF can not be read because the voltage is too high.
bdown
Fig.5.9 The ideal trapezoidal back-EMFs and torque production in a Y-connected three phase BLDC motor
When the high side is switched OFF in Fig.5.10(b), the current inside the motor continues to flow in the same direction. While the switch is off, the current can only use the diode D5. Assume that Von is the turn ON voltage of the switch, and Vf is the forward voltage of a diode. In this case, the potential in A is the Von of switch T3, the potential in B is –Vf of D5, and the potential in M is (Von-Vf)/2. It is close to zero because in most cases Von=Vf. Thus the complete back-EMF referred to the ground terminal on the phase C can be read by voltage measurement.
(a) (b)
Fig.5.10 PWM on the high side: (a) current during ON time, (b) Current during OFF time
5.4 Filter Circuit Unit
The purpose of the low-pass filter is to eliminate the noise generated by the PWM.
A Fourier analysis of a typical PWM signal is shown in Fig. 5.11. There is a strong peak at frequency
F
n = 1T
, and other strong harmonics also exist atF
=K T
, where K is an integer. These peaks are unwanted noises and should be eliminated by low-pass filter.Therefore, the band-width of the desired signal should be smaller than the fundamental component at
F
PWM = 1T
. As shown in Fig.5.12, chosen the band-width frequencyF
BW to satisfyF
BW <<F
PWMsuch thatBW
PWM
K F
F
= ⋅ (5-1)where K is a constant and K>>1. The value of K should dependent upon the number dB such that the inherent fundamental noise component of PWM will be rejected.
FPWM=1/T 2/T 3/T Frequency Frequency
spectrum of baseband signal
Fundamental
component Harmonics
Fig.5.11 Frequency spectrum in a PWM signal
In the experiment, the frequency of PWM is 1KHz, so it is required to design a simple RC low-pass filter to obtain an analog voltage output. To analyze the value of K
in (5-1), the bode plot of the RC low-pass filter will be shown in Fig.5.13. First, choose
K=2, thus
of the low-pass filter will equal to 500Hz. So, the fundamental noisepeak will be filtered at 1KHz. In this figure, the main peak of PWM signal is cut-off about -7dB. Generally, this rejection of -7dB will not suffice. When K=4, the main peak of PWM signal is cut-off about -12.3dB. However, the phase delay is more than the first case. Since it is a real-time feedback control system, the phase delay would affect the accuracy in the experiment. Thus, when K is large, the rejection of the main peak would be better but the phase delay would be more.
F
BWFBW FPWM=1/T 2/T 3/T Frequency Unwanted spectra
due to PWM pulses
Fig.5.12 External low-pass filter
101 102 103 104 -90
-45 0
Phase (deg)
-40 -30 -20 -10 0
Magnitude (dB)
K=2 K=4 Bode Diagram
Frequency (rad/sec)
Fig.5.13 Bode plot of the external low-pass filter
Design a low-pass filter to suffice K=4, the band-width frequency is equal to 250Hz. Using relation
RC = 1 2
πf
, R is chosen as 6.4KΩand C is chosen as 0.1μF.The design circuit is shown in Fig.5.14. The voltage follower is used as a buffer between devices to avoid loading errors.
Voltage Follower
Fig.5.14 The external low-pass filter circuit