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Southern Taiwan University of
Science and Technology
Reporter: Nguyen Phan Thanh
ID Student: DA220202
FEEE
Ensuring Enhanced Education
Permanent Magnet Synchronous Motors
Contents
• Introduction
• Mathematical model of PMSM
• Sensor Control Architechture
• High performance motor control application
2
FEEE
Ensuring Enhanced Education
Permanent Magnet Synchronous Motors
Introduction
 PM synchronous motors are widely used in industrial
servo-applications
due
to
its
high-performance
characteristics.
Compact
High efficiency (no excitation current)
Smooth torque
Low acoustic noise
Fast dynamic response (both torque and speed)
 A synchronous motor differs from an asynchronous
motor in the relationship between the mechanical speed
and the electrical speed.
3
FEEE
Ensuring Enhanced Education
Permanent Magnet Synchronous Motors
Introduction
4
FEEE
Ensuring Enhanced Education
Permanent Magnet Synchronous Motors
Introduction
2-axis reference frame:The
stator and rotor equations are
referred to a common frame of
reference
• Stator (stationary) reference
frame : non-rotating
• Synchronous reference
frame: d, q axis rotates with
the synchronous angular
velocity
5
FEEE
Ensuring Enhanced Education
Permanent Magnet Synchronous Motors
Introduction
• The stator reference axis for the
a-phase direction: maximum mmf
when a positive a-phase current
is supplied at its maximum level.
• The rotor reference frame:
-D-axis: permanent magnet flux
-Q-axis: 90 degree ahead of d-axis
The d-q model has been used to
analyze reluctance synchronous
machines.
6
FEEE
Ensuring Enhanced Education
Permanent Magnet Synchronous Motors
Introduction
• As the motor spins, there is an
angle between rotor magnetic
field and stator magnetic field
• If these two magnetic fields are
not ninety degrees from each
other, there will be an offset angle
between Back EMF and Current:
=>the torque production at a
given input power will not be
the maximum
7
FEEE
Ensuring Enhanced Education
Permanent Magnet Synchronous Motors
Introduction
• With this animation we can see
how the commutation angle is
always ninety degrees ahead
of the rotor.
• On the left we see how the
motor spins with Field Oriented
Control.
• On the voltage diagrams we
show how the output voltages
have a sinusoidal shape.
• On the lower right we see the
rotor angle changing from
minus pi (minus one eighty
degrees) to plus pi (plus one
eighty degrees).
8
FEEE
Ensuring Enhanced Education
Permanent Magnet Synchronous Motors
Introduction
• With this animation we can see
how the commutation angle is
always ninety degrees ahead
of the rotor.
• On the left we see how the
motor spins with Field Oriented
Control.
• On the voltage diagrams we
show how the output voltages
have a sinusoidal shape.
• On the lower right we see the
rotor angle changing from
minus pi (minus one eighty
degrees) to plus pi (plus one
eighty degrees).
9
FEEE
Ensuring Enhanced Education
Permanent Magnet Synchronous Motors
Introduction
• With this animation we can see
how the commutation angle is
always ninety degrees ahead
of the rotor.
• On the left we see how the
motor spins with Field Oriented
Control.
• On the voltage diagrams we
show how the output voltages
have a sinusoidal shape.
• On the lower right we see the
rotor angle changing from
minus pi (minus one eighty
degrees) to plus pi (plus one
eighty degrees).
10
FEEE
Ensuring Enhanced Education
Permanent Magnet Synchronous Motors
Introduction
• With this animation we can see
how the commutation angle is
always ninety degrees ahead
of the rotor.
• On the left we see how the
motor spins with Field Oriented
Control.
• On the voltage diagrams we
show how the output voltages
have a sinusoidal shape.
• On the lower right we see the
rotor angle changing from
minus pi (minus one eighty
degrees) to plus pi (plus one
eighty degrees).
11
FEEE
Ensuring Enhanced Education
Permanent Magnet Synchronous Motors
Introduction
• With this animation we can see
how the commutation angle is
always ninety degrees ahead
of the rotor.
• On the left we see how the
motor spins with Field Oriented
Control.
• On the voltage diagrams we
show how the output voltages
have a sinusoidal shape.
• On the lower right we see the
rotor angle changing from
minus pi (minus one eighty
degrees) to plus pi (plus one
eighty degrees).
12
FEEE
Ensuring Enhanced Education
Permanent Magnet Synchronous Motors
Introduction
• With this animation we can see
how the commutation angle is
always ninety degrees ahead
of the rotor.
• On the left we see how the
motor spins with Field Oriented
Control.
• On the voltage diagrams we
show how the output voltages
have a sinusoidal shape.
• On the lower right we see the
rotor angle changing from
minus pi (minus one eighty
degrees) to plus pi (plus one
eighty degrees).
13
FEEE
Ensuring Enhanced Education
Permanent Magnet Synchronous Motors
Mathematical model of PMSM
The mathematical model of PMSM is constructed based on the rotating
d-q frame fixed to the rotor, described by the following equations:
Where:
•vd, vq are the d and q axis voltages
•id, iq are the d and q axis currents
•Rs is the phase winding resistance
•Ld, Lq are the d and q axis inductance
•
is the rotating speed of magnet flux
•
is the permanent magnet flux linkage.
14
FEEE
Ensuring Enhanced Education
Permanent Magnet Synchronous Motors
Mathematical model of PMSM
15
FEEE
Ensuring Enhanced Education
Permanent Magnet Synchronous Motors
Operation of PMSM
Motor
+
Command Pulse
+
Kp
Deviation Counter
_
Gain
_
Position Gain
+
Kv
_
Speed Gain
M
Ki
Current
Current Feedback
Speed Feedback
Speed detection
E
Pulse Feedback
Encoder
Closed_loop Control
16
FEEE
Permanent Magnet Synchronous Motors
Ensuring Enhanced Education
Sensor Control Architechture

*
r
Speed loop
Speed
Controller
+
Current
controller
iq*
PI
+
—
id*  0
vq
Park-1
v
d,q
—
vd
, 
v
PI
+
Current loop
modify
Clark-1 vref 1
, 
vref 2
SVPWM
v
a,b,c ref 3
DC
Power
PWM1
PWM2
PWM3
PWM4
PWM5
PWM6
Inverter
—
iq
d,q
id
, 
Park
r
sin /cos of
Flux angle
1-Z-1
PI, Fuzzy, Neural
network are used to
the speed loop of
PMSM drive
i
, 
i
a,b,c
ia
ib
ic
iu
A/D
convert
iv
Clark
e
r
QEP
A
B
Z
Encoder
Vector control is used to the current
loop of PMSM drive to let it reach the
linearity and decouple characteristics.
17
PMSM
FEEE
Permanent Magnet Synchronous Motors
Ensuring Enhanced Education
Sensor Control Architechture

*
r
Speed loop
Speed
Controller
+
Current
controller
iq*
PI
+
—
id*  0
vq
Park-1
v
d,q
—
vd
, 
v
PI
+
Current loop
modify
Clark-1 vref 1
, 
vref 2
SVPWM
v
a,b,c ref 3
DC
Power
PWM1
PWM2
PWM3
PWM4
PWM5
PWM6
Inverter
—
iq
d,q
id
, 
Park
r
sin /cos of
Flux angle
1-Z-1
i
, 
i
a,b,c
ia
ib
ic
iu
A/D
convert
iv
Clark
e
r
QEP
A
B
Z
PMSM
Encoder
The entire process is illustrated in this block diagram, including coordinate
transformations, PI iteration, transforming back and generating PWM
18
FEEE
Permanent Magnet Synchronous Motors
Ensuring Enhanced Education
Sensor Control Architechture

*
r
Speed loop
Speed
Controller
+
Current
controller
iq*
PI
+
—
id*  0
vq
Park-1
v
d,q
—
vd
, 
v
PI
+
Current loop
modify
Clark-1 vref 1
, 
vref 2
SVPWM
v
a,b,c ref 3
DC
Power
PWM1
PWM2
PWM3
PWM4
PWM5
PWM6
Inverter
—
iq
d,q
id
, 
Park
r
sin /cos of
Flux angle
1-Z-1
i
, 
i
a,b,c
ia
ib
ic
iu
A/D
convert
iv
Clark
e
r
QEP
A
B
Z
PMSM
Encoder
•The Id reference controls rotor magnetizing flux
•The Iq reference controls the torque output of the motor
•Id and Iq are only time-invariant under steady-state load conditions
19
FEEE
Permanent Magnet Synchronous Motors
Ensuring Enhanced Education
Sensor Control Architechture

*
r
Speed loop
Speed
Controller
+
Current
controller
iq*
PI
+
—
id*  0
vq
Park-1
v
d,q
—
vd
, 
v
PI
+
Current loop
modify
Clark-1 vref 1
, 
vref 2
SVPWM
v
a,b,c ref 3
DC
Power
PWM1
PWM2
PWM3
PWM4
PWM5
PWM6
Inverter
—
iq
id
d,q
, 
Park
r
sin /cos of
Flux angle
1-Z-1
i
, 
i
a,b,c
ia
ib
ic
iu
A/D
convert
iv
Clark
e
r
QEP
A
B
Z
PMSM
Encoder
•The outputs of the PI controllers provide Vd and Vq, which is a voltage
vector that is sent to the motor.
•A new coordinate transformation angle is calculated based on the motor
speed, rotor electrical time constant,
20 Id and Iq.
FEEE
Permanent Magnet Synchronous Motors
Ensuring Enhanced Education
Sensor Control Architechture

*
r
Speed loop
Speed
Controller
+
Current
controller
iq*
PI
+
—
id*  0
vq
Park-1
v
d,q
—
vd
, 
v
PI
+
Current loop
modify
Clark-1 vref 1
, 
vref 2
SVPWM
v
a,b,c ref 3
DC
Power
PWM1
PWM2
PWM3
PWM4
PWM5
PWM6
Inverter
—
iq
d,q
id
, 
Park
r
sin /cos of
Flux angle
1-Z-1
i
, 
i
a,b,c
ia
ib
ic
iu
A/D
convert
iv
Clark
e
r
QEP
A
B
Z
PMSM
Encoder
•The Vd and Vq output values from the PI controllers are rotated back
to the stationary reference frame, using the new angle.
•This calculation provides quadrature voltage values vα and vβ.
21
FEEE
Permanent Magnet Synchronous Motors
Ensuring Enhanced Education
Sensor Control Architechture

*
r
Speed loop
Speed
Controller
+
Current
controller
iq*
PI
+
—
id*  0
vq
Park-1
v
d,q
—
vd
, 
v
PI
+
Current loop
modify
Clark-1 vref 1
, 
vref 2
SVPWM
v
a,b,c ref 3
DC
Power
PWM1
PWM2
PWM3
PWM4
PWM5
PWM6
Inverter
—
iq
d,q
id
, 
Park
r
sin /cos of
Flux angle
1-Z-1
i
, 
i
a,b,c
ia
ib
ic
iu
A/D
convert
iv
Clark
e
r
QEP
A
B
Z
PMSM
Encoder
•The vα and vβ values are transformed back to 3-phase values va, vb, vc.
•The 3-phase voltage values are used to calculate new PWM duty-cycle
values that generate the desired voltage vector.
22
FEEE
Permanent Magnet Synchronous Motors
Ensuring Enhanced Education
Sensor Control Architechture

*
r
Speed loop
Speed
Controller
+
Current
controller
iq*
PI
+
—
id*  0
vq
Park-1
v
d,q
—
vd
, 
v
PI
+
Current loop
modify
Clark-1 vref 1
, 
vref 2
SVPWM
v
a,b,c ref 3
DC
Power
PWM1
PWM2
PWM3
PWM4
PWM5
PWM6
Inverter
—
iq
d,q
id
, 
Park
r
sin /cos of
Flux angle
1-Z-1
i
, 
i
a,b,c
ia
ib
ic
iu
A/D
convert
iv
Clark
e
r
QEP
A
B
Z
Encoder
The transformation angle, theta, and motor speed are coming from
an optical encoder mounted on the shaft of the motor.
23
PMSM
FEEE
Ensuring Enhanced Education
Motor
Permanent Magnet Synchronous Motors
Driver
Controller
24
FEEE
Ensuring Enhanced Education
Permanent Magnet Synchronous Motors
High performance motor control application
 Industrial drives, e.g., pumps, fans, blowers, mills, hoists, handling systems
 Elevators and escalators, people movers, light railways and streetcars
(trams), electric road vehicles, aircraft flight control surface actuation
25
FEEE
Ensuring Enhanced Education
Permanent Magnet Synchronous Motors
26