Tsai Et Al. - 2011 - Model Construction and Verification of A BLDC Motor Using MATLABSIMULINK and FPGA Control
Tsai Et Al. - 2011 - Model Construction and Verification of A BLDC Motor Using MATLABSIMULINK and FPGA Control
Tsai Et Al. - 2011 - Model Construction and Verification of A BLDC Motor Using MATLABSIMULINK and FPGA Control
978-1-4244-8756-1/11/$26.00 2011
c IEEE 1797
Fig. 3 Back-emf function modeling block.
1 5 4 6 2 3 1
Fig. 2 The BLDC motor waveforms with trapezoidal model.
5*pi /3 up
u 2
2*pi /3 lo
y
Interval Test
Dynamic
pi /3 up
u
0 lo
Interval Test
Dynamic 2 OR 3
z
Logical
2*pi up
u
Operator 1 Fig. 6 The dynamic modeling block
4*pi /3 lo
Interval Test
Dynamic 3
Te = ¦ kt ik f k (θ r ) (4)
a
k b
The motor mechanical movement equation is as follows. c
dωm
Te − TL = J + Bωm (5)
dt
Besides, the electrical rotor speed and position have the
g
following relationship.
Fig. 7 The three-phase inverter modeling block.
dθ r P
= ωm (6)
dt 2
1
where Ib = [vbn − eb ] (11)
Ls s + R
Te is the electromagnetic torque,
1
TL is the load torque, Ic = [vcn − ec ] (12)
Ls s + R
ωm is the motor rotation speed,
J is the rotor inertia, Taking the Laplace Transform of (5) yields:
B is the damping constant,
k t is the torque constant,
P is the number of poles, Te − TL = ( J s + B ) ωm . (13)
θ r is the electrical angle.
Then, the motor speed can be obtained as (14).
Combining all the relevant equations, the system in state-space
1
form is: ωm = (Te − TL ) . (14)
Js + B
dia 1
= [van − ea − Ria ] (7)
The dynamic modeling block then can be constructed as
dt Ls
shown in Fig. 6.
dib 1
= [vbn − eb − Rib ] (8)
dt Ls
B. Three phase inverter and PWM control
dic 1
= [vcn − ec − Ric ] (9) The power stage is a three-phase inverter for electrical
dt Ls commutation. The simulation block, as shown in Fig. 7, is
where Ls = L − M . Taking the Laplace Transform of (7), (8), constructed by using the power electronic library in the
and (9) yields SimPowerSystems tool set of the MATLAB system. As shown
in Fig. 7, it is necessary to transfer the three-phase output
1
Ia = [van − ea ] (10) voltages with respect to the ground into the three-phase
Ls s + R
2 6 0 1 1 0 0 0 Q3 = x ⋅ y (18)
3 2 1 1 0 0 0 0 Q4 = y ⋅ z (19)
Q5 = x ⋅ z (20)
1 3 1 0 0 0 0 1
Q6 = x ⋅ y (21)
5 1 0 0 0 0 1 1
TL wm Te
Te
15 Q1 pwm1
v* ia
va
ib
va
Q2 pwm2
ic
ctr
ea iabc
Q3 pwm3 eb
Repeating
X vb vb
Sequence ec
Q4 pwm4 x eabc
Y y
Q5 pwm5 z
vc
vc
Z pwm6
Q6 BLDC motor 1
clockwise inveter
Fig. 8 The SIMULINK simulation block linked with ModelSim for PWM control of BLDC motor.
Q1 = x ⋅ z (22)
Q2 = x ⋅ y (23)
Q3 = y ⋅ z (24)
Q4 = x ⋅ z (25)
Q5 = x ⋅ y (26)
Q6 = y ⋅ z (27)
Q2
Q3
Q4
Time, sec.
(a) (a)
Q1
Q2
Q3
Q4
Time, sec.
(b) (b)
Fig. 12 Switching signals in clockwise direction with different duties: (a)
Fig. 10 Simulation results of motor speed (rad/s) in counter-clockwise D=0.25, (b) D=0.50
rotation: (a) with duties D = 1, 0.8, 0.6, 0.4 while TL = 0; (b) load conditions
TL = 0, 0.1, 0.2, 0.3 (Nt-m) while D = 1. REFERENCES
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Fig. 11 The BLDC motor three-phase voltage response IEEE Trans. Industrial Electronics, vol. 56, no. 8, pp. 3040-3049, Aug.
2009.