Robot Actuation: Motors

1
Robot Actuation Motors
Stepper motors
Servo motors
DC motors
Physics review
Things seek lowest energy states.
Nature is lazy.

• iron core vs. magnet

N
S

• magnetic fields tend to line up

Electric fields and magnetic fields are the same
thing.
Author CIS
Torque is a good scrabble word.
2
Stepper Motors
S
stator
rotor
N
electromagnets
3
Stepper Motors
S
stator
rotor
N
variable reluctance stepper motor
electromagnets
How does rotor angle affect the torque?
4
Stepper Motors
S
stator
rotor
N
variable reluctance stepper motor
electromagnets
torque
angle
5
Stepper Motors
S
stator
rotor
N
variable reluctance stepper motor
electromagnets
torque
angle
6
Stepper Motors
S
stator
N
S
rotor
N
variable reluctance stepper motor
on to the next teeth
electromagnets
7
Stepper Motors
S
stator
N
S
rotor
N
variable reluctance stepper motor
on to the next teeth
electromagnets
printers computer drives machining

• Direct control of rotor position (no sensing
  needed)
• May oscillate around a desired orientation
• Low resolution

can we increase our resolution?
8
Increasing Resolution
S
N
S
N
Half-stepping
energizing more than one pair of stator teeth
9
Increasing Resolution
torque
S
N
S
angle
N
Half-stepping
energizing more than one pair of stator teeth
10
Increasing Resolution
torque
S
N
S
angle
N
Half-stepping
energizing more than one pair of stator teeth
More teeth
11
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
12
Motoring along...

• direct control of position

• very precise positioning

http//www.ohmslaw.com/robot.htm

• What if maximum power is supplied to the motors
  circuit accidently ?

• Underdamping leads to oscillation at low speeds
• At high speeds, torque is lower than the primary
  alternative

Beckman 105 ?
13
DC motors -- exposed !
14
DC motor basics
permanent magnets
N
S
rotor
stator
brushes

V
commutator on shaft
-
15
DC motor basics
permanent magnets
N
S
rotor
N
S
stator
brushes


V
V
commutator on shaft
-
-
16
DC motor basics
permanent magnets
N
S
rotor
N
S
N
S
stator
brushes



V
V
V
commutator on shaft
-
-
-
17
Who pulls more weight?
electro-magnets
stator
S
rotor
N
Stepper motor
DC motor
18
Who pulls more weight?
electro-magnets
stator
S
rotor
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 theyre cheaper
• Smoother at low speeds

19
Open-loop control
An open-loop strategy
desired speed w
V
w
Motor and world
Controller solving for V
the plant
20
Bang-bang control
General idea works for any controllable system...
desired speed w
V
w
Motor and world
Controller solving for V
actual speed
desired position q
V(t)
q
Motor and world
Controller solving for V(t)
actual position
21
Returning to ones sensors
But the real world interferes...
desired speed wd
V
wa
Motor and world
Controller solving for V
desired speed wd ? actual speed wa
t R
Vr k w
We dont know the actual load on the motor.
k
22
Closed-loop control
Compute the error and change in relation to it.
Error signal e
wd - wa
wa
V
desired wd
compute V using the error e
-
The world
actual speed wa
how do we get the actual speed?
23
Proprioceptive Sensing

• Resolver
• measures absolute shaft orientation

• Potentiometer
• measures orientation by varying resistance, it
  has a range of motion lt 360º

Power/Contact
24
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
25
Optical Encoders

• Detecting motor shaft orientation

potential problems?
26
Gray Code

Binary
0 1 2 3 4 5 6 7 8
9
0 1 10 11 100 101 110 111 1000 1001
000 001 011 010 110 111 101 100
27
Gray Code

Binary
0 1 2 3 4 5 6 7 8
9
0 1 10 11 100 101 110 111 1000 1001
000 001 011 010 110 111 101 100 1100 1101
with FPS applications !
28
Gray Code

Binary
0 1 2 3 4 5 6 7 8
9
0 1 10 11 100 101 110 111 1000 1001
000 001 011 010 110 111 101 100 1100 1101
among others...
wires?
29
Absolute Optical Encoders

• Complexity of distinguishing many different
  states -- high resolution is expensive!

something simpler ?
30
Relative Encoders

• Track position changes

light sensor
decode circuitry
light emitter
grating
31
Relative Encoders

• Relative position

- calibration ?
- direction ?
light sensor
- resolution ?
decode circuitry
light emitter
grating
32
Relative Encoders

• Relative position

- calibration ?
- direction ?
light sensor
- resolution ?
decode circuitry
light emitter
grating
33
Relative Encoders

• Relative position

- calibration ?
- direction ?
light sensor
- resolution ?
decode circuitry
light emitter
grating
A
A
A lags B
B
B
34
Relative Encoders

• Relative position

- calibration ?
- direction ?
light sensor
- resolution ?
decode circuitry
light emitter
grating
A
B
A leads B
quadrature encoding
100 lines -gt ?
35
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 thats left is...
36
Control
37
Closed-loop control
Compute the error and change in relation to it.
Error signal e
wd - wa
wa
V
desired wd
compute V using the error e
-
The world
actual speed wa
Feedback
38
Initial Feedback
First feedback controller
39
Other Systems
Biological feedback systems
Chemical feedback systems
intelligent hydrogels
40
Additional Feedback
Chemical feedback systems for insulin delivery
ph dependant
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.
Why Im not a chemist
41
Robotic use of EAPs
42
Short Assignment 3
Remember that these may be done either
individually or in your lab groups.
Choose 1 of these four papers on
design/locomotion
Reading

• 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

A second page and picture(s) for Lab Project 1.
work in a citation for the paper you read!
problem 1
Putting the step into stepper motors
problem 2
Implementing one-dimensional PD control (Nomad)
problem 3
Implementing two-dimensional PD control (Nomad)
Extra Credit
43
Wednesday
Controling motion by controlling motors PID
Coming soon! The ancient art of motor arranging...
44
Spherical Stepper Motor
complete motor
stator
rotor
applications
45
Returning to ones sensors
But the real world interferes...
desired speed wd
V
wa
Motor and world
Controller solving for V
desired speed wd ? actual speed wa
t R
Vr k w
We dont know the actual load on the motor.
k
46
How robotics got started...
47
Proportional control
better, but may not reach the setpoint
48
PI control
but I thought PI was constant...
better, but will overshoot
49
PID control
Derivative feedback helps damp the system
other damping techniques?
50
And Beyond
Why limit ourselves to motors?
Nitinol -- demo stiquito robot ? Electroactive
Polymers EAP demo Wiper for Nanorover
dalmation
51
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
52
DC motors
Basic principles
stator
N
S
rotor
N
S
N
S
permanent magnets
53
Control
For DC motors
speed
voltage
w
V
V
N
S
54
Controlling speed with voltage
DC motor model
e ke w

• The back emf depends only on the motor speed.
• The motors torque depends only on the current,
  I.

t kt I
windings resistance

R
e
V
back emf
e
is a countervoltage generated by the rotor
windings
55
the following are the DC motor slides
56
Controlling speed with voltage
e ke w

• The back emf depends only on the motor speed.
• The motors torque depends only on the current,
  I.

t kt I
R
e
V
DC motor model
57
Controlling speed with voltage
e ke w

• The back emf depends only on the motor speed.
• The motors torque depends only on the current,
  I.

t kt I
Istall V/R
V IR e

• Consider this circuits V

current when motor is stalled
How is V related to w ?
speed 0 torque max
t R
V ke w
R
kt
e
V
- or -
V
R
w - t
ke
kt ke
DC motor model
Speed is proportional to voltage.
58
speed vs. torque
at a fixed voltage
speed w
V
no torque at max speed
ke
max torque when stalled
ktV
torque t
R
59
speed vs. torque
at a fixed voltage
Linear mechanical power Pm F ? v
speed w
Rotational version of Pm t ? w
V
no torque at max speed
ke
ktV
stall torque
torque t
R
60
speed vs. torque
at a fixed voltage
Linear mechanical power Pm F ? v
speed w
Rotational version of Pm t ? w
V
ke
max speed
power output
speed vs. torque
ktV
stall torque
torque t
R
61
speed vs. torque
speed w
V
gasoline engine
ke
power output
speed vs. torque
ktV
torque t
R
62
Power loss a good thing ?
e ke w

• The back emf depends only on the motor speed.
• The motors torque depends only on the current,
  I.

t kt I
Pe electrical (battery) power Pm mechanical
(output) power PR power loss in resistor
V IR e

• circuit voltage V

Pe PR Pm

• Track power losses

R
e
V
DC motor model
63
Power loss a good thing ?
e ke w

• The back emf depends only on the motor speed.
• The motors torque depends only on the current,
  I.

t kt I
Pe electrical (battery) power Pm mechanical
(output) power PR power loss in resistor
V IR e

• circuit voltage V

Pe PR Pm

• Track power losses

Pe PR em
R
e
V
actuators power
DC motor model
64
Power loss a good thing ?
e ke w

• The back emf depends only on the motor speed.
• The motors torque depends only on the current,
  I.

t kt I
Pe electrical (battery) power Pm mechanical
(output) power PR power loss in resistor
V IR e

• circuit voltage V

Pe PR Pm

• Track power losses

Pe PR em (acs)
R
PR I2R
e
V
E M lives on !
Pe VI
DC motor model
65
Power loss a good thing ?
e ke w

• The back emf depends only on the motor speed.
• The motors torque depends only on the current,
  I.

t kt I
Pe electrical (battery) power Pm mechanical
(output) power PR power loss in resistor
V IR e

• circuit voltage V

Pe PR Pm

• Track power losses

Pe PR em (acs)
R
PR I2R
e
V
VI I2R em (acs)
E M lives on !
Pe VI
DC motor model
66
Power loss a good thing ?
e ke w

• The back emf depends only on the motor speed.
• The motors torque depends only on the current,
  I.

t kt I
Pe electrical (battery) power Pm mechanical
(output) power PR power loss in resistor
V IR e

• circuit voltage V

Pe PR Pm

• Track power losses

Pe PR em (acs)
R
PR I2R
e
V
VI I2R em (acs)
E M lives on !
Pe VI
VI gt em (acs)
DC motor model
Finally ! Scientific proof !
67
Power loss a good thing ?
e ke w

• The back emf depends only on the motor speed.
• The motors torque depends only on the current,
  I.

t kt I
Pe electrical (battery) power Pm mechanical
(output) power PR power loss in resistor
V IR e

• circuit voltage V

Pe PR Pm

• Track power losses

Pe PR tw
R
PR I2R
e
V
actuators power
E M lives on !
Pe VI
DC motor model
68
Power loss a good thing ?
e ke w

• The back emf depends only on the motor speed.
• The motors torque depends only on the current,
  I.

t kt I
Pe electrical (battery) power Pm mechanical
(output) power PR power loss in resistor
V IR e

• circuit voltage V

Pe PR Pm

• Track power losses

Pe PR tw
R
PR I2R
VI I2R tw
e
V
E M lives on !
Pe VI
DC motor model
69
Power loss a good thing ?
e ke w

• The back emf depends only on the motor speed.
• The motors torque depends only on the current,
  I.

t kt I
Pe electrical (battery) power Pm mechanical
(output) power PR power loss in resistor
V IR e

• circuit voltage V

Pe PR Pm

• Track power losses

Pe PR tw
R
PR I2R
VI I2R tw
e
V
E M lives on !
VI I2R ktIe/ ke
Pe VI
V IR kte/ ke
IR e IR kte/ ke
DC motor model
ke kt
70
single-parameter summary
Linear mechanical power Pm F ? v
speed w
Rotational version of Pm t ? w
V
k
max speed
power output
speed vs. torque
k V
stall torque
torque t
R
71
Motor specs
Electrical Specifications (_at_22C) For motor type
1624   003S 006S 012S 024 ------------------------
-- -------- -------- -------- ---------
------- nominal supply voltage (Volts) 3 6 12 24 a
rmature resistance (Ohms) 1.6 8.6 24 75 maximum
power output (Watts) 1.41 1.05 1.50 1.92 maximum
efficiency () 76 72 74 74 no-load speed
(rpm) 12,000 10,600 13,000 14,400 no-load
current (mA) 30 16 10 6 friction
torque (oz-in) .010 .011 .013 .013 stall
torque (oz-in) .613 .510 .600 .694 velocity
constant (rpm/v) 4065 1808 1105 611 back EMF
constant (mV/rpm) .246 .553 .905 1.635 torque
constant (oz-in/A) .333 .748 1.223 2.212 armature
inductance (mH) .085 .200 .750 3.00
k
72
the preceding were the DC motor slides
73
Bang-bang control
An open-loop strategy
desired speed w
V
w
Motor and world
Controller solving for V
the plant
74
gearing up...
should be gearing down...
75
Another example of feedback control
Nomad going to a designated spot
76
Power loss a good thing ?
e ke w

• The back emf depends only on the motor speed.
• The motors torque depends only on the current,
  I.

t kt I
Pe electrical (battery) power Pm mechanical
(output) power PR power loss in resistor
V IR e

• circuit voltage V

Pe PR Pm

• Track power losses

Pe PR tw
R
PR I2R
e
V
E M lives on !
Pe VI
DC motor model
77
Back to control
Basic input / output relationship
We can control the voltage applied V.
We want a particular motor speed w .
t R
V k w
k
(1) Measure the system t, R, k (2) Compute the
voltage needed for a desired speed w. (3) Go !
78
Back to control
Basic input / output relationship
We can control the voltage applied V.
We want a particular motor speed w .
t R
V k w
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
(half Vmax)
V
V
t
t
V
V
(1/6 Vmax)
t
t