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Robot Actuation: Motors
Stepper motors
DC motors
Servo motors
Physics “review”
Nature is lazy.
Things seek lowest energy states.
• iron core vs. magnet
• magnetic fields tend to line up
N
N
Electric fields and magnetic
fields are the same thing.
Torque is a good scrabble word.
S
+ v -
+ v -
Author: CIS
S
Stepper Motors
S
rotor
N
electromagnets
stator
Stepper Motors
S
stator
S
rotor
N
N
electromagnets
“variable reluctance”
stepper motor
How does rotor angle
affect the torque?
Stepper Motors
stator
S
S
rotor
N
N
electromagnets
“variable reluctance”
stepper motor
torque
angle
Stepper Motors
stator
S
S
rotor
N
N
electromagnets
“variable reluctance”
stepper motor
torque
angle
Stepper Motors
S
stator
S
N
S
rotor
N
N
electromagnets
“variable reluctance”
stepper motor
on to the next teeth…
Stepper Motors
S
stator
S
N
S
rotor
N
N
electromagnets
“variable reluctance”
stepper motor
• Direct control of rotor position (no sensing needed)
on to the next teeth…
printers
computer drives
machining
• May oscillate around a desired orientation
• Low resolution
can we increase
our resolution?
Increasing Resolution
S
N
S
N
Half-stepping
energizing more than one
pair of stator teeth
Increasing Resolution
torque
S
N
S
N
Half-stepping
energizing more than one
pair of stator teeth
angle
Increasing Resolution
torque
S
N
S
angle
N
Half-stepping
energizing more than one
pair of stator teeth
More teeth
Increasing Resolution
torque
S
N
S
angle
N
Half-stepping
energizing more than one
pair of stator teeth
More teeth
on the rotor
and/or stator
Question 2 this week…
Motoring along...
• direct control of position
• very precise positioning
http://www.ohmslaw.com/robot.htm
• What if maximum power is supplied
to the motor’s circuit accidently ?
• Underdamping leads to oscillation at low speeds
• At high speeds, torque is lower than the primary alternative…
Beckman 105 ?
DC motors -- exposed !
DC motor basics
permanent
magnets
N
N
rotor
S
S
stator
brushes
+
V
-
commutator
on shaft
DC motor basics
permanent
magnets
N
N
rotor
S
N
S
S
stator
brushes
+
+
V
-
commutator
on shaft
V
-
DC motor basics
permanent
magnets
N
N
rotor
S
N
S
N
S
S
stator
brushes
+
+
V
-
commutator
on shaft
+
V
-
V
-
Who pulls more weight?
electromagnets
S
stator
N
N
rotor
rotor
S
S
stator
N
Stepper motor
DC motor
Who pulls more weight?
electromagnets
S
stator
N
N
rotor
rotor
S
S
stator
N
Stepper motor
DC motor
• Position control
• High holding torque
• Durability (no brushes)
• Energy used is prop. to speed
• Higher torque at faster speeds
• More popular, so they’re cheaper
• Smoother at low speeds
Open-loop control
An “open-loop” strategy
desired speed w
V
Controller
solving for V
“the plant”
Motor
and
world
w
Bang-bang control
General idea works for any controllable system...
desired speed w
V
Controller
solving for V
desired position q
V(t)
Controller
solving for V(t)
Motor
and
world
Motor
and
world
w
actual speed
q
actual position
Returning to one’s sensors
But the real world interferes...
desired speed wd
V
Controller
solving for V
Motor
and
world
desired speed wd  actual speed wa
We don’t know the actual
load on the motor.
Vr =
tR
+kw
k
wa
Closed-loop control
Compute the error and change in relation to it.
Error signal e
wd - wa
desired wd
-
compute V
using the error e
V
wa
The world
actual speed wa
how do we get the
actual speed?
Proprioceptive Sensing
• Resolver
= measures absolute
shaft orientation
• Potentiometer
= measures orientation by
varying resistance, it has
a range of motion < 360º
Power/Contact
Servomotors
potentiometer
Direct position control in response
to the width of a regularly sent pulse.
A potentiometer is used to determine
the motor shaft angle.
modified to run continuously
Optical Encoders
• Detecting motor shaft orientation
potential problems?
Gray Code
#
0
1
2
3
4
5
6
7
8
9
Binary
0
000
1
001
10
011
11
010
100
110
101
111
110
101
111
100
1000
1001
Gray Code
#
0
1
2
3
4
5
6
7
8
9
Binary
0
000
1
001
10
011
11
010
100
110
101
111
110
101
111
100
1000
1100
1001
1101
with FPS applications !
Gray Code
#
0
1
2
3
4
5
6
7
8
9
Binary
0
000
1
001
10
011
11
010
100
110
101
111
110
101
111
100
1000
1100
1001
1101
among others...
wires?
Absolute Optical Encoders
• Complexity of distinguishing many different states -high resolution is expensive!
something simpler ?
Relative Encoders
• Track position changes
light sensor
light emitter
grating
decode
circuitry
Relative Encoders
- calibration ?
• Relative position
light sensor
light emitter
grating
decode
circuitry
- direction ?
- resolution ?
Relative Encoders
- calibration ?
• Relative position
light sensor
light emitter
grating
decode
circuitry
- direction ?
- resolution ?
Relative Encoders
- calibration ?
• Relative position
light sensor
light emitter
- direction ?
- resolution ?
decode
circuitry
grating
A
A
A lags B
B
B
Relative Encoders
- calibration ?
• Relative position
light sensor
- direction ?
- resolution ?
decode
circuitry
light emitter
grating
A
B
quadrature
encoding
A leads B
100 lines -> ?
Relative Encoders
mask/diffuser
• Relative position
light sensor
A
decode
circuitry
light emitter
grating
B
A diffuser tends to
smooth these signals
Ideal
Real
With motors and sensors,
all that’s left is...
Control
Closed-loop control
Compute the error and change in relation to it.
Error signal e
wd - wa
desired wd
-
compute V
using the error e
V
wa
The world
actual speed wa
Feedback
Initial Feedback
“First” feedback controller
Other Systems
Biological feedback systems
Chemical feedback systems
intelligent hydrogels
Additional Feedback
Chemical feedback systems
for insulin delivery
ph dependant
Why I’m not a
chemist:
at low pH values, the carboxylic acid groups of PMAA tend to be protonated, and
hydrogen bonds form between them and the ether oxygens on the PEG chains. These
interpolyer complexes lead to increased hydrophobicity, which causes the gel to collapse.
At high pH values, carboxylic groups become ionized, the complexes are disrupted, and
the gel expands because of increased electrostatic repulsion between the anionic chains.
Robotic use of EAPs
Short Assignment #3
Remember that these may be done either individually or in your lab groups.
Reading:
Choose 1 of these four papers on design/locomotion:
• Designing a Miniature Wearable Visual Robot
• An Innovative Locomotion Principle for Minirobots Moving in the Gastrointestinal Tract
• Get Back in Shape! A reconfigurable microrobot using Shape Memory Alloy
• Walk on the Wild Side: The reconfigurable PolyBot robotic system
problem 1
A second page and picture(s) for Lab Project #1.
work in a citation for the paper you read!
problem 2
Putting the step into stepper motors…
problem 3
Implementing one-dimensional PD control (Nomad)
Extra Credit
Implementing two-dimensional PD control (Nomad)
Wednesday
Controling motion by controlling motors: PID
Coming soon! The ancient art of motor arranging...
Spherical Stepper Motor
complete motor
rotor
stator
applications
Returning to one’s sensors
But the real world interferes...
desired speed wd
V
Controller
solving for V
Motor
and
world
desired speed wd  actual speed wa
We don’t know the actual
load on the motor.
Vr =
tR
+kw
k
wa
How robotics got started...
Proportional control
better, but may
not reach the
setpoint
PI control
but I thought PI was constant...
better, but will
overshoot
PID control
Derivative
feedback helps
damp the system
other damping
techniques?
And Beyond
Why limit ourselves to motors?
Nitinol -- demo stiquito robot ?
Electroactive Polymers
EAP demo
Wiper for Nanorover
dalmation
Control
Knowing when to stop...
DC servo motor -- what you control and
what you want to control are not nec. the
same thing
motor model -- equivalent circuit
to control velocity
to control position
DC motors
Basic principles
stator
N
N
rotor
S
N
S
S
permanent
magnets
N
S
N
S
N
N
S
S
Control
What you want to control
For DC
motors:
what you can control
speed
N
V
=
N
voltage
w
S
S
V
Controlling speed with voltage
DC motor model
• The back emf depends only on the motor speed.
e = ke w
• The motor’s torque depends only on the current, I.
t = kt I
windings’
resistance
R
V
e
“back emf”
e
is a countervoltage generated
by the rotor windings
the following are the
DC motor slides
Controlling speed with voltage
• The back emf depends only on the motor speed.
e = ke w
• The motor’s torque depends only on the current, I.
t = kt I
R
V
e
DC motor model
Controlling speed with voltage
• The back emf depends only on the motor speed.
e = ke w
• The motor’s torque depends only on the current, I.
t = kt I
Istall = V/R
current when motor
is stalled
speed = 0
torque = max
V = IR + e
How is V related to w ?
tR
V=
+ ke w
kt
R
V
• Consider this circuit’s V:
e
- or -
V
w=- R t+
ke
kt ke
DC motor model
Speed is proportional to voltage.
speed vs. torque at a fixed voltage
speed w
V
ke
no torque at max speed
max torque when stalled
torque t
ktV
R
speed vs. torque at a fixed voltage
speed w
V
ke
no torque at max speed
Linear mechanical power Pm = F  v
Rotational version of Pm = t  w
torque t
ktV
R
stall torque
speed vs. torque at a fixed voltage
speed w
V
ke
Linear mechanical power Pm = F  v
Rotational version of Pm = t  w
max speed
power output
speed vs.
torque
torque t
ktV
R
stall torque
speed vs. torque
speed w
V
ke
gasoline engine
power output
speed vs.
torque
torque t
ktV
R
Power loss a good thing ?
• The back emf depends only on the motor speed.
e = ke w
• The motor’s torque depends only on the current, I.
t = kt I
Pe = electrical (battery) power
• circuit voltage V:
V = IR + e
Pm = mechanical (output) power
PR = power loss in resistor
R
V
e
DC motor model
• Track power losses:
Pe = PR + Pm
Power loss a good thing ?
• The back emf depends only on the motor speed.
e = ke w
• The motor’s torque depends only on the current, I.
t = kt I
Pe = electrical (battery) power
• circuit voltage V:
V = IR + e
Pm = mechanical (output) power
PR = power loss in resistor
Pe = PR + Pm
Pe = PR + em
R
V
• Track power losses:
e
DC motor model
actuator’s power
Power loss a good thing ?
• The back emf depends only on the motor speed.
e = ke w
• The motor’s torque depends only on the current, I.
t = kt I
Pe = electrical (battery) power
• circuit voltage V:
V = IR + e
Pm = mechanical (output) power
PR = power loss in resistor
• Track power losses:
R
V
e
PR = I2R
E & M lives on !
Pe = VI
DC motor model
Pe = PR + Pm
Pe = PR + em (ac’s)
Power loss a good thing ?
• The back emf depends only on the motor speed.
e = ke w
• The motor’s torque depends only on the current, I.
t = kt I
Pe = electrical (battery) power
• circuit voltage V:
V = IR + e
Pm = mechanical (output) power
PR = power loss in resistor
• Track power losses:
Pe = PR + em (ac’s)
R
V
Pe = PR + Pm
e
PR = I2R
E & M lives on !
Pe = VI
DC motor model
VI = I2R + em (ac’s)
Power loss a good thing ?
• The back emf depends only on the motor speed.
e = ke w
• The motor’s torque depends only on the current, I.
t = kt I
Pe = electrical (battery) power
• circuit voltage V:
V = IR + e
Pm = mechanical (output) power
PR = power loss in resistor
• Track power losses:
R
V
e
PR = I2R
E & M lives on !
Pe = VI
DC motor model
Pe = PR + Pm
Pe = PR + em (ac’s)
VI = I2R + em (ac’s)
VI
>
Finally ! Scientific proof !
em (ac’s)
Power loss a good thing ?
• The back emf depends only on the motor speed.
e = ke w
• The motor’s torque depends only on the current, I.
t = kt I
Pe = electrical (battery) power
• circuit voltage V:
V = IR + e
Pm = mechanical (output) power
PR = power loss in resistor
• Track power losses:
Pe = PR + tw
R
V
Pe = PR + Pm
e
PR = I2R
E & M lives on !
Pe = VI
DC motor model
actuator’s power
Power loss a good thing ?
• The back emf depends only on the motor speed.
e = ke w
• The motor’s torque depends only on the current, I.
t = kt I
Pe = electrical (battery) power
• circuit voltage V:
V = IR + e
Pm = mechanical (output) power
PR = power loss in resistor
• Track power losses:
Pe = PR + tw
R
V
Pe = PR + Pm
e
PR = I2R
E & M lives on !
Pe = VI
DC motor model
VI = I2R + tw
Power loss a good thing ?
• The back emf depends only on the motor speed.
e = ke w
• The motor’s torque depends only on the current, I.
t = kt I
Pe = electrical (battery) power
• circuit voltage V:
V = IR + e
Pm = mechanical (output) power
PR = power loss in resistor
• Track power losses:
Pe = PR + tw
R
V
Pe = PR + Pm
e
PR = I2R
E & M lives on !
Pe = VI
DC motor model
VI = I2R + tw
VI = I2R + ktIe/ ke
V = IR + kte/ ke
IR + e = IR + kte/ ke
ke = kt
single-parameter summary
speed w
V
k
Linear mechanical power Pm = F  v
Rotational version of Pm = t  w
max speed
power output
speed vs.
torque
torque t
kV
R
stall torque
Motor specs
Electrical Specifications (@22°C)
For motor type 1624
003S
006S
012S
024
--------------------------
--------
--------
--------
---------
-------
nominal supply voltage
armature resistance
maximum power output
maximum efficiency
no-load speed
no-load current
friction torque
stall torque
velocity constant
back EMF constant
torque constant
armature inductance
(Volts)
(Ohms)
(Watts)
(%)
(rpm)
(mA)
(oz-in)
(oz-in)
(rpm/v)
(mV/rpm)
(oz-in/A)
(mH)
3
1.6
1.41
76
12,000
30
.010
.613
4065
.246
.333
.085
6
8.6
1.05
72
10,600
16
.011
.510
1808
.553
.748
.200
12
24
1.50
74
13,000
10
.013
.600
1105
.905
1.223
.750
24
75
1.92
74
14,400
6
.013
.694
611
1.635
2.212
3.00
k
the preceding were the
DC motor slides
Bang-bang control
An “open-loop” strategy
desired speed w
V
Controller
solving for V
“the plant”
Motor
and
world
w
gearing up...
should be gearing down...
Another example of feedback control
Nomad going to a designated spot
Power loss a good thing ?
• The back emf depends only on the motor speed.
e = ke w
• The motor’s torque depends only on the current, I.
t = kt I
Pe = electrical (battery) power
• circuit voltage V:
V = IR + e
Pm = mechanical (output) power
PR = power loss in resistor
• Track power losses:
Pe = PR + tw
R
V
Pe = PR + Pm
e
PR = I2R
E & M lives on !
Pe = VI
DC motor model
Back to control
Basic input / output relationship:
tR
V=
+kw
k
We can control the
voltage applied V.
We want a particular
motor speed w .
(1) Measure the system: t, R, k
(2) Compute the voltage needed for a desired speed w.
(3) Go !
Back to control
We can control the
voltage applied V.
Basic input / output relationship:
We want a particular
motor speed w .
tR
V=
+kw
k
(1) Measure the system: t, R, k
(2) Compute the voltage needed for a desired speed w.
(3) Go !
V is usually controlled via PWM -- “pulse width modulation”
V
V
t
t
(half Vmax)
V
(1/6 Vmax)
V
t
t