From MATLAB® and Simulink® to
Real Time with TI DSPs
Sensored Field Oriented
Control of a Permanent Magnet
Synchronous Motor
(PMSM)
Content developed in partnership with
Tel-Aviv University
© 2007 Texas Instruments Inc,
0-1
Learning objectives
• Review of Electromagnetic laws
• Rotating magnetic fields
• Structure of synchronous motors
• Features of synchronous motors
• BLDC and PMSM synchronous motor types
• BLDC and PMSM control overview
• Electro-mechanical parameters for a
synchronous motor
© 2007 Texas Instruments Inc,
Slide 2
Field generated by a current
I
I
Field
B = k*n*I
• A conductor carrying a current produces a magnetic field around it.
I
• A conductor that is wound into a coil produces a magnetic field
along the axis of the coil.
• The flux produced is proportional to the current through the coil
and the number of turns in the coil.
© 2007 Texas Instruments Inc,
Slide 3
The Current in a Coil
F1
d
B1
I
F2
B2
© 2007 Texas Instruments Inc,
• A coil carrying a current,
placed in a magnetic field
experiences a force that
will cause it to rotate.
• This force is given as the
vector cross product of
the flux produced by the
coil and the flux that is
impressed by the
external magnetic field.
F1  F2  B1 x B2
T  B1  B2   d
Slide 4
Back EMF generation
Magnet flux
N
S




(rad / s )

a
B
e
A
Magnet rotating in front of winding “a” create an inductive
voltage between A and B, e = VA-VB called Bemf (Back
electromotive force)
Magnetic flux seen by the winding is given by:    2 cos t
Bemf is then equal to: 
d
e
(
t
)


  2 sin( t )  E sin( t )

dt

 E   2

© 2007 Texas Instruments Inc,
Slide 5
Pole pairs
2 pole pairs
1 pole pair
N
N
SN
e
e(t )  E sin( t ) with   

S
N
N
S
e(t )  E sin( t ) with   2
For a motor with p poles pairs we have


e
  p
is the electrical frequency (rad/s)
is the mechanical frequency (rad/s) or simply
the speed of the machine.
© 2007 Texas Instruments Inc,
Slide 6
Three phases winding
ia  I s .e jt

2
j t 

3
ib  I S .e

4
jt 
3
i  I .e
c
S

c
ic
N
S
ib
b



ia
a
ea  E.e jpt

2
jpt 

3
eb  E.e

4
jpt 
3
e  E.e
c

For most three phase machines, the winding is stationery, and
magnetic field is rotating
Three phase machines have three stator windings, separated 120°
apart physically
Three phase stator windings produce three magnetic fields, which are
spaced 120°in time
© 2007 Texas Instruments Inc,
Slide 7
Application to Three Phases Machine
Operation Fundamentals
Three stationary pulsating magnetic fields
ia
 The
Fc
C
three phase winding
produces three magnetic
fields, which are spaced 120°
apart physically.
 When excited with three sine
waves that are a 120° apart
in phase, there are three
pulsating magnetic fields.
A`
B
Fa
Fb
B`
C
`
A
Phase currents
1.50
ia
1.00
ib
 The
resultant of the three
magnetic fields is a rotating
magnetic field.
ic
0.50
0.00
1
24 47 70 93 116 139 162 185 208 231 254 277 300 323 346
-0.50
t
-1.00
-1.50
© 2007 Texas Instruments Inc,
Slide 8
Synchronous operation
Three
Three
phase
phaseAC
AC
current
current
Phase
Phase11
Coil
Coil11
Phase
Phase22
Coil
Coil22
Phase3
Phase3
Phase3
Phase3
Coil
Coil
Coil
3333
Coil
© 2007 Texas Instruments Inc,
Slide 9
Theory of operation:
Rotor field
A`
C


N
N
B

S
B`
C
`
S
Stator field
Rotor is carrying a constant
magnetic field created either by
permanent magnets or current fed
coils
The interaction between the
rotating stator flux, and the rotor
flux produces a torque which will
cause the motor to rotate.
A


The rotation of the rotor in this case will be at the same exact
frequency as the applied excitation to the rotor.
This is synchronous operation.
Rotor speed (rad/s) :  

gives
p
f : AC supply frequency (Hz)
60. f
(r.pm)
p

Example: a 2 poles pair
synchronous motor will run
at 1500 r.pm for a 50Hz AC
supply frequency
p : motor poles pair per phase
© 2007 Texas Instruments Inc,
Slide 10
Electromechanical Parameters
V
i

Es
uL
estator
v
I
uL
Simplified equivalent electrical scheme of a
winding of a three phases synchronous motor
Note: stator resistance neglected
Tem 
3VI cos 

© 2007 Texas Instruments Inc,
Tem : electromec hanical torque ( N .m)
V : phase voltage (V )


 I : phase current ( I )

 : motor rotation speed (rad / s)
Slide 11
Synchronous Motor Rotor
Construction
non-salient rotor
pole (p=1)
© 2007 Texas Instruments Inc,
non-salient rotor
pole (p=2)
salient rotor pole
(p=2)
Slide 12
Synchronous machine
classification: BLDC and PMSM
C
F
N
A
`
B
B
`
S
F
A
C
`
•
Both (typically) have permanent-magnet rotor and
a wound stator
•
BLDC (Brushless DC) motor is a permanentmagnet brushless motor with trapezoidal back
EMF
•
PMSM (Permanent-magnet synchronous motor) is
a permanent-magnet brushless motor with
sinusoidal back EMF
Back EMF of BLDC Motor
00
Phase A
300
600
900
1500
2100
2700
3300
300
900
1200
1800
2400
3000
3600
600
ia
Back EMF of PMSM
Ea
e
1.50
ea
eb
ec
1.00
Hall A
0.50
Phase B
e
ib
t
0.00
1
Hall B
24 47 70 93 116 139 162 185 208 231 254 277 300 323 346
-0.50
Phase C
ic
Hall C
© 2007 Texas Instruments Inc,
e
-1.00
-1.50
Slide 13
BLDC vs. PMSM
BLDC
PMSM
• Synchronous machine
• Synchronous machine
• Fed with direct currents
• Fed with sinusoidal currents
• Trapezoidal BEMF
• Sinusoidal BEMF
• Stator Flux position
commutation each 60 degrees
• Continuous stator flux
position variation
• Only two phases ON at the
same time
• Possible to have three
phases ON at the same time
• Torque ripple at
commutations
• No torque ripple at
commutations
© 2007 Texas Instruments Inc,
Slide 14
Conclusion
• Synchronous motors use magnetic interaction
to convert electrical energy to mechanical.
• Rotor must be synchronized with the rotating
stator magnetic field in order to produce
torque
• Pole pair numbers and excitation frequency
determine the mechanical rotation speed
• Synchronous motors are classified in two
categories: BLDC and PMSM
• Each type require an appropriate control
© 2007 Texas Instruments Inc,
Slide 15
PMSM Control
• Synchronous Motors such as PM motors
and SynRMs are getting more popular
because of their high power density and
high efficiency
• PM Assisted SynRM uses advantages of
both PM and Reluctance motor
• The vector control strategy is far more
complicated than control of a DC motor
requiring use of multiple control loops
© 2007 Texas Instruments Inc,
Slide 16
Control System Block-Diagram
ref
Inv. Park
Transformation
+
-

PI
e*
iqs
e*
ids
+
e*
+

PI
-

PI
v qs
e*
v ds
-
Vdc
s*
v qs
dqse
dqss
S
V
PWM
s*
v ds
3-phase
Inverter
r
e
iqs
e
ids
s
dq se
dqss
iqs
s
dqs
s
i ds
abc
Park
Clarke
Transformation Transformation
PMASynRM
Mechanical Speed and
position of rotor
© 2007 Texas Instruments Inc,
Slide 17
Using the DMC Library
Speed
setpoint
ref
fb
PID
_IQ
id_ref =0
Uout
FC_PWM
DRV
ref
fb
PID
_IQ
Ipark_D
PARKI
theta
Ipark_d
Vq
SV_GEN
DQ
_IQ
Ta
mfunc_c1
PWM1B
Tb
mfunc_c2
PWM2A
Tc
mfunc_c3
PWM2B
mfunc_p
PWM3A
Q0 / HW
3-Phase
Inverter
_IQ
ref
fb
Uout
PWM1A
PID
_IQ
Uout
Ipark_Q
Ipark_q
Vd
PWM3B
park_D
PARK
_IQ
park_d
clark_d
theta
CLARK
_IQ
clark_a
Ia_out
clark_b
Ib_out
ILEG2
DRV
LEG_A
LEG_B
_IQ
park_Q
park_q
clark_q
clark_c
Q15
Q15
Q13
Q13
speed_frq
SPEED
FRQ
shft_angle
theta_elec
theta_mech
QEP
THETA
DRV
Ia_gain
Ib_gain
Ia_offset
Ib_offset
QEP
QEP_A
PMSM
QEP_A
Motor
_IQ
speed_rpm
direction
dir_QEP
_IQ
QEP_index
index_sync_flg
© 2007 Texas Instruments Inc,
Slide 18
The Equivalent Simulink® Model
PI
iqs
vqs
*
PI
ids*
PI
*
vds
*
vas
Ta
*
Space Tb
Inv.
Vector
Park vbs* Gen. T
c
PWM
Driver
Voltage
Source
Inverter
qlr
ids
iqs
wr
SMOSPD
speed
estimation
PWM1
PWM2
PWM3
PWM4
PWM5
PWM6
ias
Park
qlr
qm
dir
ibs
Clarke
ias Ileg2_
Bus
ibs Driver
QEP_A
Ramp QEP
Gen. driver
ADCIN1
ADCIN2
ADCIN3
Encoder
PMSM
QEP_B
QEP_inc
TMS320F28x controller
© 2007 Texas Instruments Inc,
Slide 19
Hardware Setup
I/O
Power Supply
5V
P6
Parallel Port
Encoder
Permanent Magnet
Synchronous Motor
analog
eZdsp 2812
DMC 550
P7
P3
P4
P5
Motor phases
Power Supply
24 Volts 4 Amps
+
-
Encoder signal
2 Power inputs:
•5V PSU for the DSP board only (software debug)
•0 - 24V PSU for the power stage
© 2007 Texas Instruments Inc,
Slide 23
Synchronous Reluctance Motor
Two pole singly
salient SynRM
© 2007 Texas Instruments Inc,
Two pole doubly salient
Switched RM
Slide 24
Background
d-q axes voltage and flux equations:
d
ds  Llsids  Lmd ids  Ldsids
vd  rs ids  ds   r qs
vq  rs iqs 
dt
dqs
dt
  r ds
Torque equation:
qs  Llsiqs  Lmqiqs  m  Lqsiqs  m
rs I s
Vds
~
Vs
3P
dsiqs  qsids 
Te 
22
Te 
3P
( Lds  Lqs ) I dsI qs
22
I ds  I s cos 

jX qs I qs
I qs
jX ds I ds

I ds
q-axis
Vqs
~
Is
d-axis
I qs  I s sin 
© 2007 Texas Instruments Inc,
Slide 25
Output Torque in MASynRM
di
vds  rs ids  Lds ds  r ( Lqsiqs  m )
dt
vqs  rs iqs  Lqs
© 2007 Texas Instruments Inc,
diqs
dt
Te 
3 P
mids  ( Lds  Lqs ) idsiqs 
2 2
 r Ldsids
Slide 26
The PMS Motor Model
© 2007 Texas Instruments Inc,
Slide 27
Model-Based Design of a PMSM
• Build Level 1 – Space vector generation
• Build Level 2 - Currents/DC-bus voltage
measurement verification
• Build Level 3 - Tuning of dq-axis current closed loops
• Build Level 4 – Encoder verification
• Build Level 5 – Speed closed loop
© 2007 Texas Instruments Inc,
Slide 28
Space vector generation - Simulation
© 2007 Texas Instruments Inc,
Slide 29
Space vector generation – Real Time
key modules under test
Vq_testing
Vd_testingvds
*
Ta
Inv.
Park vbs*
Space Tb
Vector
Gen. Tc
vas
*
PWM1
PWM2
PWM3
PWM
Driver
Ramp
control
PWM5
PWM6
Voltage
Source
Inverter
rmp_out
speed_ref
PWM4
Ramp
Gen.
PMSM
TMS320F28x controller
© 2007 Texas Instruments Inc,
Slide 30
Currents/DC-bus voltage measurement
verification - Simulation
© 2007 Texas Instruments Inc,
Slide 31
Currents/DC-bus voltage measurement
verification – Real Time
PWM1
*
Ta
Inv.
Vq_testingvds* Park vbs*
Space Tb
Vector
Gen. Tc
Vq_testing
vas
PWM2
PWM3
PWM
Driver
PWM4
PWM5
PWM6
Voltage
Source
Inverter
e
ids
iqs
Speed_ref
ias
Park
ia
ibs Clarke
ib
ADCIN1
Ileg2_
Bus
Driver
ADCIN2
ADCIN3
Encoder
Ramp
control
Ramp
Gen.
rmp_out
PMSM
TMS320F28x controller
© 2007 Texas Instruments Inc,
Slide 32
Tuning of dq-axis current closed loops
- Simulation
© 2007 Texas Instruments Inc,
Slide 33
Tuning of dq-axis current closed loops –
Real Time
key module under test
vqs*
Iq_ref
PI
Id_ref
ids
*
PI
vds*
vas
PWM1
Ta
*
Space Tb
Inv.
Vector
Park vbs*
Gen. Tc
PWM
Driver
PWM2
PWM3
PWM4
PWM5
PWM6
Voltage
Source
Inverter
rmp_out
ids
iqs
Speed_ref
ias
Park
ibs
ia
Clarke
ib
ADCIN1
Ileg2_
Bus
Driver
ADCIN2
ADCIN3
Encoder
Ramp
control
Ramp
Gen.
PMSM
TMS320F28x controller
© 2007 Texas Instruments Inc,
Slide 34
Encoder verification - Simulation
© 2007 Texas Instruments Inc,
Slide 35
Encoder verification – Real Time
vqs
Iq_ref
PI
vds
Id_ref
vas
*
*
PI
Ta
*
Space Tb
Inv.
Vector
Park vbs*
Gen. Tc
PWM
Driver
PWM1
PWM2
PWM3
PWM4
PWM5
PWM6
Voltage
Source
Inverter
rmp_out
ids
iqs
Speed_ref Ramp
control
Ramp
Gen.
Park
ias
ia
ibs Clarke
ib
ADCIN1
Ileg2_
Bus
Driver
Theta_ele
c
 Ramp QEP
m
dir Gen. driver
ADCIN2
ADCIN3
Encoder
QEP_A
PMSM
QEP_B
QEP_inc
TMS320F28x
controller
© 2007 Texas Instruments Inc,
Slide 36
Speed closed loop - Simulation
© 2007 Texas Instruments Inc,
Slide 37
Speed closed loop – Real Time
iqs
*
vqs
PI
PI
ids
*
vds
*
vas
*
PI
Ta
*
Space Tb
Inv.
Vector
Park vbs*
Gen. Tc
PWM
Driver
PWM1
PWM2
PWM3
PWM4
PWM5
PWM6
Voltage
Source
Inverter
r
ias
ids
iqs
r
SMOSPD
speed
estimation
Park
ias
ibs Clarke
ibs

r
QEP
m Ramp
dir Gen. driver
ADCIN1
Ileg2_
Bus
Driver
ADCIN2
ADCIN3
Encoder
QEP_A
PMSM
QEP_B
QEP_inc
TMS320F28x controller
© 2007 Texas Instruments Inc,
Slide 38