2014 Texas Instruments Motor Control Training Series
-Vth
Dave Wilson
Maximum Torque Per Amp (MTPA)
Newton-Meters
Maximum torque per amp
(MTPA)
200
V (t r e a c t i o n )
2 00 V
150
1 50 V
Simulated Reactance Torque as
a function of angle delta
from 2005 Prius Traction Motor
100
1 00 V
50
5 0V
0
0V
-50
-5 0 V
-100
-1 0 0 V
-150
-1 5 0 V
-200
-180o
-2 0 0 V
0 .0 s
Dave Wilson
0 .3 s
-150o
0 .6 s
-120o
0 .9 s
-90o
1 .2 s
-60o
1 .5 s
-30o
1 .8 s
0o
2 .1 s
30o
2 .4 s
60o
2 .7 s
90o
3 .0 s
120o
3 .3 s
150o
3 .6 s
180o
TI Spins Motors…Smarter, Safer, Greener.
Field Oriented Control in Real Time
Low Torque
Medium Torque
High Torque
A
B
Interrupt:
Measure rotor flux angle
Regulate current vector to be 90o wrt rotor flux
Exit ISR
C
Interrupt:
Measure new rotor flux angle
Regulate current vector to be 90o wrt rotor flux
Exit ISR
Currents
Constant

Constant
(for now)
3P
Torque 
dr I qs
22
†

Interrupt:
Measure new rotor flux angle
Regulate current vector to be 90o wrt rotor flux
Exit ISR
†
Adjustable
Torque expression based on amplitude invariant form of Clarke Transform.
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
Establishing Space Vector Conventions
+b
Direction of positive rotation
Direction of positive speed
Direction of positive torque
B
A
-a
Phase A leads phase B
Phase B leads phase C
Phase C leads phase A
C
-b
Dave Wilson
+a
Motor shaft axis
TI Spins Motors…Smarter, Safer, Greener.
How Do You Control Torque
on a DC Motor?
3
2
Error Signal
Desired Current +
PI
Controller
PWM
1
Measured Current
Brush DC Motor
4
Power
Stage
Texas Instruments
Dave’s
Motor Control
Center
ADC1
Commutator keeps
rotor and stator fields
properly aligned!
1. Measure current already flowing in the motor.
2. Compare the measured current with the desired current, and generate an error signal.
3. Amplify the error signal to generate a correction voltage.
4. Modulate the correction voltage onto the motor terminals.
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
1. Measure currents already flowing in the motor.
Only 2 phases are measured!
WHY?
A, B, and C axes are “fixed” with
respect to the motor housing. This
reference frame is also called the
“stationary frame” or “stator frame”.
ib
net current vector
ia
B
i c (implied)
A
Texas Instruments
B
ib
Dave’s
Motor Control
Center
ic
C
Controller
with A/D
Dave Wilson
ia
ib
ic
ia
C
TI Spins Motors…Smarter, Safer, Greener.
A
2. Compare the measured current (vector) with the desired
current (vector), and generate error signals.
Commanded
The desired phase currents
can be calculated via these
equations:
is
Error
is
B
ic
ia = -Im sin(q)
ib
ib = -Im sin(q - 120 o)
ia
ic = -Im sin(q - 240 o)
C
Im is proportional to motor torque
q is the angle of the rotor flux
So how do we get the rotor flux angle?
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
A
2. Compare the measured current (vector) with the desired
current (vector), and generate error signals.
q or qd
Magnetic axis for phase A
Usually accomplished with a
resolver or encoder.
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
2. Compare the measured current (vector) with the desired
current (vector), and generate error signals.
The CLARKE transform
allows us to convert
three vectors into two
orthogonal vectors that
produce the same net
vector.
ib
is
B
ic
ib
In other words,
convert a 3-phase
motor into a 2-phase
motor.
i a ia
C
Forward Clarke
A
B
C
aA
b
Dave Wilson
B - C 
A
This is the Amplitude
Invariant form of the
Clarke Transform
a b
3
TI Spins Motors…Smarter, Safer, Greener.
Stationary Frame Servo
b
q
r
rCos(q)
-r
Tracking a rotating reference signal
from a stationary frame is tedious!
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
a
Synchronous Frame Servo
Tracking a rotating reference signal in
the same rotating frame is easy!
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
Take the “Coffee” Test
1. Give your coffee a
good stir so that
bubbles form on
the surface.
2. Holding the cup as
shown here, spin
around in the same
direction that you
stirred the coffee.
3. As soon as you
reach synchronous
speed, the bubbles
stop spinning.
Why?
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
2. Compare the measured current (vector) with the desired
current (vector), and generate error signals.
Jump up on the
rotating reference
frame, whose x-axis
is the rotor flux axis.
ib
B
is
iq
id
ia
This is called the
Park Transform
A
q
C
a b
id  ia cos q  + ib sin q 
iq  -ia sin q  + ib cos q 
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
2. Compare the measured current (vector) with the desired
current (vector), and generate error signals.
and i q are handled independently. Since the comparison is
performed in the synchronous frame, motor AC frequency is not
seen. Thus, they are DC quantities!
id
Under normal conditions, we have all
the flux we need supplied by the
permanent magnets on the rotor. So
commanded id is set to zero.
This is how much torque we want!
i d (commanded) +
i d (measured)
errord (t)
-
i q (commanded) +
i q (measured)
errorq (t)
-
i d can be used to weaken the field of the machine.
i q controls the amount of torque generated by the motor
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
3. (Finally!) Amplify the error signals to generate correction voltages.
PI Controller (d-axis)
Commanded Id
Measured Id
Error
+
Ka
∫
Kb
-
Vd
+
+
PI Controller (q-axis)
Error
+
Commanded Iq
Ka
Kb
-
Measured Iq
∫
Vq
+
+
K a  L  Current Bandwidth (rad / sec), K b  R L
Motor
Rd
Rq
Ld
Lq
PMSM
Rs
Rs
Ls
Ls
ACIM
Rs
Rs+Rr
IPM
Rs
Rs
Dave Wilson
2 

L
Ls 1 - m 
 Lr Ls 


2 

L
m

Ls 1  Lr Ls 


Ls_d
TI Spins Motors…Smarter, Safer, Greener.
Ls_q
4. Modulate the correction voltages onto the motor terminals.
Before we can apply the
voltages to the motor
windings, we must first
jump off of the rotating
reference frame.
vb
B
Voltage vector
vq
vd
q
va A
Part A. Transfer the
voltage vectors back to
the stationary rectangular
coordinate system.
vd (t)
vq(t)
Dave Wilson
C
va  vd cos q  - vq sin q 
a b
vb  vd sin q  + vq cos q 
TI Spins Motors…Smarter, Safer, Greener.
4. Modulate the correction voltages onto the motor terminals.
Part B. Next, we
transform the voltage
vectors from the
rectangular coordinate
system to three phase
vectors.
vb
vc
B
Voltage Vector
vb
v a va A
C
Reverse Clarke Transformation
a b
Dave Wilson
A a
B  - 12 a +
3
2
b
C  - 12 a -
3
2
b
A
B
C
TI Spins Motors…Smarter, Safer, Greener.
4. Modulate the correction voltages onto the motor terminals.
Phase A - top
Phase A - bottom
Phase B - top
Phase B - bottom
Phase C - top
Phase C - bottom
Over time, under steady-state conditions, the correction voltages
va, vb, and vc will be sine waves phase shifted by 120o.
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
FOC in a Nutshell
Va
Wilson
Torque Current
Flux Current
q
Desired Torque +
-
Desired Flux +
-
Dave Wilson
PI
Vb
Reverse
Clarke-Park
Transforms
Vq
q
Vd
+
+
-1
Vc
i
i
i
B
C
A
Forward
Clarke-Park
Transforms
q
PI
TI Spins Motors…Smarter, Safer, Greener.
iq
id
2014 Texas Instruments Motor Control Training Series
d-axis
V3 = 010
V2 = 110
Sector 2
Vref
Sector 3
a
V4 = 011
T2•V2
V1 = 100
T1•V1
q-axis
Sector 6
Sector 4
Sector 5
V5 = 001
V6 = 101
-Vth
Space Vector Modulation
• PWMs treat each phase individually.
• SVM treats the inverter as ONE unit!!
- ALL 6 switches affected.
U
TI
Dave’s
Control
Center
V
• PWMs control the phase voltages.
W
120° offsets between A, B, and C.
• SVM controls the Voltage Vector.
The inverter can be driven to 8 states.
V1 = 001
A
B
A
- 6 voltage
vectors
B
C
V6=110
A
B
V2 = 010
V3 = 011
A
B
C
V4 = 100
C
A
B
A
B
C
V5 = 101
C
A
B
C
C
V0 = 000
V7 = 111
- 2 null vectors
Source: Mahmoud Riaz, Sc.D., Professor of
Electrical Engineering, Department of Electrical and
Computer Engineering, University of Minnesota
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
1 = Top Switch is on
0 = Bottom Switch is on
Space Vector Modulation
V1
V3
V2
V6
V4
V5
V2
120o
V1
V3
60o
C
300
B
V6 180o
0o V1
A
0
60
120 180 240 300
“6-Step” Voltage Waveforms
0
300o
240o
V5
V4
Vector Diagram
Output voltage vector created by repeatedly switching between adjacent vectors and the “null” vector
(all three phases high or all three phases low).
Output angle q determined by relative “on” time between two adjacent vectors.
Output magnitude determined by relative “on” time between two adjacent vectors and the null vector.
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
SVM Implementation
V3 = 011 (Vy)
V2 = 010
• Vref, is created by the two adjacent
state vectors Vx, Vy, and a null
vector in a time averaging fashion:
Vref = Vx•T1 + Vy•T2 + Vnull•T0
Where:
Sector 2
Vref
Sector 3
a
V6 = 110
Vx = lowest angle voltage vector
Vy = highest angle voltage vector
T2•Vy
V1 = 001
(Vx)
T1•Vx
Sector 4
Sector 6
Sector 5
If Vref is represented in POLAR notation ( ma):
T1 = T•m•SIN(60 - a)
T2 = T•m•SIN(a)
T0 = T - T1 - T2
m = vector magnitude (0 to 1)
a = vector angle between Vref and Vx (0 to 60o)
T = switching period
Dave Wilson
V5 = 101
V4 = 100
Example vector reconstruction in sector 1.
SWITCHING PERIOD
T
Vx
Vy
Null
T1
T2
T0
TI Spins Motors…Smarter, Safer, Greener.
SVM Variations
• Choice of Null vectors effects SVM waveform creation
and switching performance but motor still sees sinusoidal
waveform at its phases.
NULL=V7
NULL=V0
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0
60
A
120
180
B
240
300
360
C
0
60
A
120
180
B
Good choice when reduced switching losses
are desired in an inverter with
high-side bootstrap circuits.
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
240
300
C
360
SVM Variations (continued)
Null = V7 in sectors 1,3,5
Null = V0 in sectors 2,4,6
Null = V0 in sectors 1,3,5
Null = V7 in sectors 2,4,6
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0
60
A
120
180
240
B
300
360
0
60
C
120
180
A
240
B
300
360
C
1
0.8
Null = alt-rev
(null alternates every sequence
and sequence reverses.)
Most popular form of SVM
• Similar waveforms
to Third Harmonic
0.6
0.4
0.2
0
0
60
A
Dave Wilson
120
180
B
240
300
360
C
TI Spins Motors…Smarter, Safer, Greener.
SVM Using Center-Aligned PWMs
PWM Period
Sc
Sb
Sa
V1 V3 V7 V3 V1 V0 V1 V3 V7 V3 V1
t1
t2
t0
t2
t1
t0
t1
t2
t0
t2
t1
Alternating-Reversing Sequence
Check out http://www.ipes.ethz.ch/ipes/Raumzeiger/e_RZ4.html for a neat SVM animation!
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
SVM with PWMs
Procedure for implementing SVM with Center-Aligned PWM Module
1 Check which sector the Vref vector is in.
2 Calculate T1, T2, and T0 from block below.
3 Adjust PWMs High times based on table below.
T1 = T•m•SIN(60 - a)
T2 = T•m•SIN(a)
T0 = T - T1 - T2
(5 compares)
(3 multiples)
(1-3 additions)
V0 in 1,3,5
V7 in 2,4,6
Alternating
Reversing
Sequencing
Null = V0
Null = V7
V7 in 1,3,5
V0 in 2,4,6
U = T1+T2
Sector 1 V = T2
W=0
U = 100%
V = T0+T2
W = T0
U = 100%
V = T0+T2
W = T0
U = T1+T2
V = T2
W=0
U = T1+T2+.5T0
V = T2+.5T0
W = .5T0
U = T1
Sector 2 V = T1+T2
W=0
U = T0+T1
V = 100%
W = T0
U = T1
V = T1+T2
W=0
U = T0+T1
V = 100%
W = T0
U = T1+.5T0
V = T1+T2+.5T0
W = .5T0
U=0
Sector 3 V = T1+T2
W = T2
U = T0
V = 100%
W = T0+T2
U = T0
V = 100%
W = T0+T2
U=0
V = T1+T2
W = T2
U = .5T0
V = T1+T2+.5T0
W = T2+.5T0
U=0
Sector 4 V = T1
W = T1+T2
U = T0
V = T0+T1
W = 100%
U=0
V = T1
W = T1+T2
U = T0
V = T0+T1
W = 100%
U = .5T0
V = T1+.5T0
W = T1+T2+.5T0
U = T2
Sector 5 V = 0
W = T1+T2
U = T0+T2
V = T0
W = 100%
U = T0+T2
V = T0
W = 100%
U = T2
V=0
W = T1+T2
U = T2+.5T0
V = .5T0
W = T1+T2+.5T0
U = T1+T2
Sector 6 V = 0
W = T1
U = 100%
V = T0
W = T0+T1
U = T1+T2
V=0
W = T1
U = 100%
V = T0
W = T0+T1
U = T1+T2+.5T0
V = .5T0
W = T1+.5T0
Note: All calculations referenced to top switch
Source: Understanding Space Vector Modulation,
by Peter Pinewski, EDN Products Edition, March 7, 1996
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
Sinusoidal Modulation Limited Amplitude
In sinusoidal modulation the amplitude is limited to half of the DC-bus voltage.
•
The phase to phase voltage is then lower then the DC-bus voltage (although such
voltage can be generated between the terminals).
PWM2
PWM4
PWM6
UDC-BUS
PWM5
A
PWM3
B
PWM1
Uphase-phase
•
C
Animation Source: Leos Chalupa
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
Full Phase-to-Phase Voltage Generation
• Full phase-to-phase voltage can be generated by continuously shifting the
3-phase voltage system.
Uphase-phase
PWM6
Uphase-phase
PWM4
A
PWM2
B
PWM5
A
PWM3
B
PWM1
15%
• The amplitude of the first harmonic can be then increased by 15.5%.
C
C
Animation Source: Leos Chalupa
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
How to Increase Modulation Index
•
Modulation index is increased by adding the “shifting” voltage u0 to first harmonic.
•
“Shifting” voltage u0 must be the same for all three phases, thus it can only contain
3r harmonics!
15%
A
B
Animation Source: Leos Chalupa
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
C
SVM with Field Oriented Systems
Vb
a
T1·Vx
T2·Vy
Va
We could calculate “m” and “a”:
Recall:
Vy
T1 = T•m•SIN(60 - a)
T2 = T•m•SIN(a)
T0 = T - T1 - T2
Vx
…but with FOC, we don’t have
POLAR notation. We have
RECTANGULAR notation
(Va and Vb.
Va 2 + Vb 2
a  tan-1
Vb
Va
Or…
We could use a simple procedure designed
specifically for RECTANGULAR notation:
Reference Voltage Vector
amplitude
m
Components of the Stator Reference Voltage Vector
1 Va
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1 0
Vb
1.
2.
a 60
120
180
240
300
360
angle
Sector 1 Sector 2 Sector 3 Sector 4 Sector 5 Sector 6
Dave Wilson
3.
4.
Perform modified inverse Clarketransform on the voltage vector
Calculate which sector the
voltage vector is in
Determine T1, T2, and T0
Directly calculate the PWM
register values
TI Spins Motors…Smarter, Safer, Greener.
1. Perform Modified Inverse
Clarke Transform
Va
3
+
0.5
Vb
j
-
i
Dave Wilson
i
-
-
0.5
j
k
Vb
3
i
Va 2
2
j  Vb
Vb
3
kVa 2
2
k
TI Spins Motors…Smarter, Safer, Greener.
i
2. Identify the correct sector
based on i, j, and k variables
a. Calculate the following expression:
N  sign(i ) + 2 sign j  + 4 signk 
where sign( + )  1 ; sign( -)  0
b. Use look-up table below to determine the sector from the value of N
N=
1
2
3
4
5
6
Sector =
6
2
1
4
5
3
Alternatively, you can determine the sector by using IF THEN statements to check the polarities of i, j, and k.
i
j
1
Dave Wilson
2
k
3
4
5
TI Spins Motors…Smarter, Safer, Greener.
6
3. Based on the sector, determine T1, T2, and T0
Sector→
Bounded by:
T1
T2
†
†
1
(U0-U60)
2
(U60-U120)
3
(U120-U180)
4
(U180-U240)
5
(U240-U300)
6
(U300-U0)
i
-k
j
-i
k
-j
j
-i
k
-j
i
-k
T0 = 1 – T1 – T2
4. Load the PWM
registers based on
this table
†
Recall that T1 always applies to Vx (the
most clockwise vector), and T2 applies to Vy
(the most counter-clockwise vector) for any
given sector.
Dave Wilson
V0 in 1,3,5
V7 in 2,4,6
Alternating
Reversing
Sequencing
Null = V0
Null = V7
V7 in 1,3,5
V0 in 2,4,6
U = T1+T2
Sector 1 V = T2
W=0
U = 100%
V = T0+T2
W = T0
U = 100%
V = T0+T2
W = T0
U = T1+T2
V = T2
W=0
U = T1+T2+.5T0
V = T2+.5T0
W = .5T0
U = T1
Sector 2 V = T1+T2
W=0
U = T0+T1
V = 100%
W = T0
U = T1
V = T1+T2
W=0
U = T0+T1
V = 100%
W = T0
U = T1+.5T0
V = T1+T2+.5T0
W = .5T0
U=0
Sector 3 V = T1+T2
W = T2
U = T0
V = 100%
W = T0+T2
U = T0
V = 100%
W = T0+T2
U=0
V = T1+T2
W = T2
U = .5T0
V = T1+T2+.5T0
W = T2+.5T0
U=0
Sector 4 V = T1
W = T1+T2
U = T0
V = T0+T1
W = 100%
U=0
V = T1
W = T1+T2
U = T0
V = T0+T1
W = 100%
U = .5T0
V = T1+.5T0
W = T1+T2+.5T0
U = T2
Sector 5 V = 0
W = T1+T2
U = T0+T2
V = T0
W = 100%
U = T0+T2
V = T0
W = 100%
U = T2
V=0
W = T1+T2
U = T2+.5T0
V = .5T0
W = T1+T2+.5T0
U = T1+T2
Sector 6 V = 0
W = T1
U = 100%
V = T0
W = T0+T1
U = T1+T2
V=0
W = T1
U = 100%
V = T0
W = T0+T1
U = T1+T2+.5T0
V = .5T0
W = T1+.5T0
Note: All calculations referenced to top switch
Source: Understanding Space Vector Modulation,
by Peter Pinewski, EDN Products Edition, March 7, 1996
TI Spins Motors…Smarter, Safer, Greener.
Axis Coupling
1/Ld
1/Lq
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
Current Regulator Decoupling
Permanent Magnet Motors
Commanded id
+
-
Ka
+
+
Kb
id
w
Vd
+
-
∫
Vd compensation
Ls
iq
Commanded iq
Vq compensation
+
Ka
+
+
Kb
+
+
+
Vq
∫
KE
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
Too Much Flux???
The larger the flux, the higher the dλ/dt is for a given speed.
dλ/dt is voltage, so the back-EMF is higher for a given speed.
When the back-EMF amplitude reaches the bus voltage, current goes to zero.
When current goes to zero, torque goes to zero.
Therefore, the motor cannot go any faster…all because of too much flux.
Speed
Torque
Flux
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
Weakening the Field…LUT
Id_nominal
Rated Speed
Idref
Speed
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
Weakening the Field…Voltage Limit
Max Limit
==
Vq
Reset

+
0.97
Idref
Min Limit
Slew Value
Vqlim
Vqlim
VEMFq
0.7
Vq
S
+
Reset
Q
Vq
“1” or “0”
Vd
R
Vlim
Vd is given 1st dibs on available voltage
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
Less Flux Means More Speed
Speed
Previous Speed Limit
Torque
Observe how the flux is weakened
Flux
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
2014 Texas Instruments Motor Control Training Series
-Vth
Dave Wilson
-2 K V
Speed-Torque Performance of
Induction Motors
-4 K V
-6 K V
-8 K V
-1 0 K V
Torque (newton-meters)
-1 2 K V
Pull-out Torque
-1 4 K V
V (te m )
5 0V
4 0V
3 0V
2 0V
1 0V
Starting Torque
0V
-1 0 V
-2 0 V
-3 0 V
-4 0 V
-5 0 V
-6 0 V
-7 0 V
00s
2s
0.2
4s
0.4
6s
0.6
8s
0.8
1 01.0
s
11.2
2s
11.4
4s
11.6
6s
% Synchronous Speed
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
11.8
8s
22.0
0s
Stator and Rotor Fields
Source: Mahmoud Riaz, Sc.D., Professor of Electrical Engineering, Department of Electrical and Computer Engineering,
University of Minnesota
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
ACIM Circuit Representation with
Arbitrary Turns Ratio “a”
rs
jw Ls - aLm 

jw a 2 Lr - aLm

jwaLm
General equivalent circuit showing arbitrary value of referral ratio “a” (a=1
corresponds to a turns ratio of Ns/Nr, which yields the conventional circuit.)
If the actual value of rotor current isn’t required, “a”
can be any value except zero or infinity, resulting in
an infinite number of possible circuits!
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
a 2 rr
S
ACIM Circuit Representation with
Turns Ratio a=Lm/Lr
iq
Rotor Flux
current
Torque current
Stator current
id
Rotor leakage reactance now lumped
with mutual and stator leakage reactances!
This implies that a
reference frame
exists where the
stator current can
be resolved into
torque current
and flux current.
Source: Vector Control and Dynamics of AC Drives, by Don Novotny and Tom Lipo, Oxford University Press, 2000
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
Torque Production in an ACIM
~
Lm ~
Ir  I sT
Lr
rotor current
~
One expression for torque is the
cross product between the rotor
current and the rotor flux.
I sT
Stator current is resolved
into flux producing and
torque producing
components.
~
I s
~
Rotor flux is NOT fixed
~
w.r.t. rotor. It is
s “asynchronous” to rotor
position.
I
~
 r  Lm I s
rotor flux
 Lm
 3 L2m
P Er I r 3 P
we Lm I s  I sT   P I s I sT
Te  3

2 2w e 4 we
Lr
4 Lr


rotor flux
rotor current
P is the number of poles
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
Dynamic Response of RotorReferenced FOC
Step change in iqs
iqr  -
Lm
iqs
Lr
Step change in ids
iqs
iqr
iqs
ids
dr
Rotor current (and thus torque) are
instantaneously changed.
Dave Wilson
idr
iqr
iqs
ids
dr
ids
dr
Rotor flux (and thus torque) are
gradually changed.
TI Spins Motors…Smarter, Safer, Greener.
ACIM Slip Frequency Calculation
Texas Instruments
is a
neat company!
Encoder
Dave Wilson’s
Motor Control
Center
qr
Slip Calculator
id
1
1 + Str
Poles/2
tr
qe
D
iq
N
^ slip
w

^q
^
qd
+
slip
+
B
qd
9.9°
Recall that the rotor flux sweeps
across the surface of the rotor at a
speed equal to the slip frequency, i.e.,
it is “asynchronous” to the rotor.
A
C
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
P
+
+
Commanded id
(flux)
+
-
∫
I
Commanded iq
(torque)
+
+
+
Vq
Va
Vb
Vc
θd
+
-
+
-
I
Reverse
Clarke-Park
Transform
P
P
Commanded
Rotor
Speed
+
Vd
∫
∫
I
iq
id
ia
Forward
Clarke-Park
Transform
Speed
Calculator
ib
ic
-
θd
Commanded id
Commanded iq
Slip
Slip
Frequency
Calculator
∫
θd
+
+
Actual Rotor Angle
Control Diagram of an Induction Motor Speed Controller Utilizing Field Oriented Control.
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
Texas Instruments
is a
neat company!
Dave Wilson’s
Motor Control
Center
2014 Texas Instruments Motor Control Training Series
-Vth
Dave Wilson
Buried Magnets Create NEW Torque
Buried rotor magnets
produce different
inductances on the d-q axes.
This results in a NEW torque
component proportional to
the difference in these
inductances.
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
Total Motor Torque
Ids
Iqs
Permanent Magnet Rotor
Reluctance Torque
Reaction Torque



3P
Torque 
dr I qs + Lds - Lqs I ds I qs
22
†
Torque expression based on amplitude invariant form of Clarke Transform.
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.

†
Torque
Torque vs. Angle
Reaction Torque (magnet to magnet)
CCW
Q
D
Stable
CW
0o
Unstable
Stable
45o
90o
Unstable
135o Unstable 180o
Reluctance Torque (magnet to metal)
The magnets exerts force
on the rotor in an effort to
minimize the resistance
(reluctance) of the flux path.
Locked Rotor
Dave Wilson
TI Spins Motors…Smarter, Safer, Greener.
Effect of Saliency on Optimum Torque Angle
Positive Ids
Dave Wilson
Negative Ids
TI Spins Motors…Smarter, Safer, Greener.
MTPA Control of IPM Motors
Commanded Speed
+
-
Limit i
T
i

1 r
id  - 
+
4  Ld - Lq

Commanded d

 r2
2 +
+
8
i
Ld - Lq 2 T  -
Current
Controller
id
Vd
Reverse
Clarke-Park
Transform
Actual Speed
i
Commanded q
Current
Controller
+
-
Vb
IPM
TI
Dave’s
Control
Center
Vc
θd
iq
id
ia
d/dt
Forward
Clarke-Park
Transform
θd
Dave Wilson
Vq
Va
ib
ic
Phase C
Current
Calculation
Rotor Flux Angle
TI Spins Motors…Smarter, Safer, Greener.