Robot Actuation: Motors
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Transcript of Robot Actuation: Motors
Robot Actuation: Motors
Stepper motors Servo motors
Physics “review”
DC motors
Electric fields and magnetic fields are the same thing.
Nature is lazy.Things seek lowest energy states.• iron core vs. magnet• magnetic fields tend to line up
v+ - v+ -
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Torque is a good scrabble word. Author: CIS
Stepper Motors
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S stator
rotor
electromagnets
Stepper Motors
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S stator
rotor
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electromagnets“variable reluctance”
stepper motor
How does rotor angle affect the torque?
Stepper Motors
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S stator
rotor
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electromagnets“variable reluctance”
stepper motor
angle
torque
Stepper Motors
N
S stator
rotor
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electromagnets“variable reluctance”
stepper motor
angle
torque
Stepper Motors
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S stator
rotor
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electromagnets“variable reluctance”
stepper motor on to the next
teeth…
Stepper Motors
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electromagnets
stator
rotor
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SN
“variable reluctance” stepper motor
• Direct control of rotor position (no sensing needed)
• May oscillate around a desired orientation
• Low resolution
printerscomputer drivesmachining
on to the next teeth…
can we increase our resolution?
Increasing Resolution
Half-stepping
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energizing more than one pair of stator teeth
Increasing Resolution
Half-stepping
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Nangle
torque
energizing more than one pair of stator teeth
Increasing Resolution
Half-stepping
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Nangle
torque
More teeth
energizing more than one pair of stator teeth
Increasing Resolution
Half-stepping
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Nangle
torque
More teeth
energizing more than one pair of stator teeth
on the rotor and/or stator
Question 2 this week…
Motoring along...
• direct control of position
• very precise positioning
• 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…
http://www.ohmslaw.com/robot.htm
Beckman 105 ?
DC motors -- exposed !
DC motor basics
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stator
rotor
permanent magnets
commutator on shaft
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brushes
DC motor basics
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N S
stator
rotor
permanent magnets
commutator on shaft
V
+
-
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V
+
-
brushes
DC motor basics
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stator
rotor
permanent magnets
commutator on shaft
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+
-
N SS N N SN S
V
+
-
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+
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brushes
Who pulls more weight?
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stator
rotor
DC motorStepper motor
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Selectro-magnets stator
rotor
Who pulls more weight?
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stator
rotor
DC motorStepper motor
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Selectro-magnets stator
rotor
• 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 Controller solving for V
VMotor
and world
“the plant”
Bang-bang control
General idea works for any controllable system...
desired speed Controller solving for V
VMotor
and world
desired position Controller
solving for V(t)
V(t)Motor
and world
actual speed
actual position
Returning to one’s sensors
But the real world interferes...
desired speed d Controller
solving for V
VMotor
and world
a
desired speed d actual speed a
Vr = + k R k We don’t know the actual
load on the motor.
Closed-loop control
Compute the error and change in relation to it.
desired dV
The world
a
actual speed a
- compute V using the error e
d a
Error signal e
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
Direct position control in response to the width of a regularly sent pulse.
A potentiometer is used to determinethe motor shaft angle.
modified to run continuously
potentiometer
Optical Encoders
• Detecting motor shaft orientation
potential problems?
Gray Code
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# Binary
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111
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1001
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011
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Gray Code
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# Binary
0
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10
11
100
101
110
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1000
1001
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001
011
010
110
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1100
1101
with FPS applications !
Gray Code
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# Binary
0
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10
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100
101
110
111
1000
1001
among others...
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001
011
010
110
111
101
100
1100
1101
wires?
Absolute Optical Encoders
• Complexity of distinguishing many different states -- high resolution is expensive!
something simpler ?
Relative Encoders
• Track position changes
grating
light emitter
light sensor
decode circuitry
Relative Encoders
• Relative position - calibration ? - direction ?
- resolution ?
grating
light emitter
light sensor
decode circuitry
Relative Encoders
• Relative position - calibration ? - direction ?
- resolution ?
grating
light emitter
light sensor
decode circuitry
Relative Encoders
• Relative position
grating
light emitter
light sensor
decode circuitry
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B
A
B
A lags B
- calibration ? - direction ?
- resolution ?
Relative Encoders
• Relative position
grating
light emitter
light sensor
decode circuitry
A
B A leads B
- calibration ? - direction ?
- resolution ?
quadrature encoding
100 lines -> ?
Ideal
Relative Encoders
• Relative position mask/diffuser
grating
light emitter
light sensor
decode circuitry
Real
A diffuser tends to smooth these signals
With motors and sensors, all that’s left is...
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B
Control
Closed-loop control
Compute the error and change in relation to it.
desired dV
The world
a
actual speed a
- compute V using the error e
d a
Error signal e
Feedback
Initial Feedback
“First” feedback controller
Other Systems
Biological feedback systems
Chemical feedback systems
intelligent hydrogels
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.
Additional Feedback
Chemical feedback systemsfor insulin delivery
Why I’m not a chemist:
ph dependant
Robotic use of EAPs
Short Assignment #3
A second page and picture(s) for Lab Project #1. work in a citation for the paper you read!
Putting the step into stepper motors…
problem 1
problem 2
Implementing one-dimensional PD control (Nomad)problem 3
Remember that these may be done either individually or in your lab groups.
Reading: Choose 1 of these four papers on design/locomotion:
Implementing two-dimensional PD control (Nomad)Extra Credit
• 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
Wednesday
Coming soon! The ancient art of motor arranging...
Controling motion by controlling motors: PID
Spherical Stepper Motor
complete motor
statorrotor
applications
Returning to one’s sensors
But the real world interferes...
desired speed d Controller
solving for V
VMotor
and world
a
desired speed d actual speed a
Vr = + k R k We don’t know the actual
load on the motor.
How robotics got started...
Proportional control
better, but may not reach the setpoint
PI control
better, but will overshoot
but I thought PI was constant...
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
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stator
rotor
permanent magnets
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Control
What you want to control = what you can control
For DC motors: speed voltage
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Controlling speed with voltage
DC motor model
V e
“back emf”
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windings’ resistance
e is a countervoltage generated by the rotor windings
• The back emf depends only on the motor speed.
• The motor’s torque depends only on the current, I.
e = ke
= k I
the following are the DC motor slides
Controlling speed with voltage
DC motor model
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• The back emf depends only on the motor speed.
• The motor’s torque depends only on the current, I.
e = ke
= k I
kke
Controlling speed with voltage
DC motor model
V e
R
• The back emf depends only on the motor speed.
• The motor’s torque depends only on the current, I.
e = ke
= k I
• Consider this circuit’s V: V = IR + eIstall = V/Rcurrent when
motor is stalledspeed = 0
torque = max
How is V related to
V = + ke R k
- or -
= - + R ke V
Speed is proportional to voltage.
speed vs. torque
torque
speed
ke V
at a fixed voltage
R kV
max torque when stalled
no torque at max speed
speed vs. torque
torque
speed
ke V
at a fixed voltage
R kV stall torque
no torque at max speed
Linear mechanical power Pm = F v
Rotational version of Pm =
speed vs. torque
torque
speed
ke V
at a fixed voltage
R kV stall torque
max speed
Linear mechanical power Pm = F v
Rotational version of Pm =
power output
speed vs. torque
speed vs. torque
torque
speed
ke V
R kV
power output
speed vs. torque
gasoline engine
Power loss a good thing ?
DC motor model
V e
R
• The back emf depends only on the motor speed.
• The motor’s torque depends only on the current, I.
e = ke
= k I
• Track power losses: Pe = PR + Pm
Pe = electrical (battery) power
Pm = mechanical (output) power
PR = power loss in resistor
V = IR + e• circuit voltage V:
Power loss a good thing ?
DC motor model
V e
R
• The back emf depends only on the motor speed.
• The motor’s torque depends only on the current, I.
e = ke
= k I
• Track power losses: Pe = PR + Pm
V = IR + e• circuit voltage V:
Pe = PR + em
actuator’s power
Pe = electrical (battery) power
Pm = mechanical (output) power
PR = power loss in resistor
Power loss a good thing ?
DC motor model
V e
R
• The back emf depends only on the motor speed.
• The motor’s torque depends only on the current, I.
e = ke
= k I
• Track power losses: Pe = PR + Pm
V = IR + e• circuit voltage V:
Pe = PR + em (ac’s)
Pe = electrical (battery) power
Pm = mechanical (output) power
PR = power loss in resistor
PR = I2R E & M lives on !
Pe = VI
Power loss a good thing ?
DC motor model
V e
R
• The back emf depends only on the motor speed.
• The motor’s torque depends only on the current, I.
e = ke
= k I
• Track power losses: Pe = PR + Pm
V = IR + e• circuit voltage V:
Pe = PR + em (ac’s)
Pe = electrical (battery) power
Pm = mechanical (output) power
PR = power loss in resistor
VI = I2R + em (ac’s)PR = I2R
E & M lives on !
Pe = VI
Power loss a good thing ?
DC motor model
V e
R
• The back emf depends only on the motor speed.
• The motor’s torque depends only on the current, I.
e = ke
= k I
• Track power losses: Pe = PR + Pm
V = IR + e• circuit voltage V:
Pe = PR + em (ac’s)
Pe = electrical (battery) power
Pm = mechanical (output) power
PR = power loss in resistor
VI = I2R + em (ac’s)PR = I2R
E & M lives on !
Pe = VI VI > em (ac’s)
Finally ! Scientific proof !
Power loss a good thing ?
DC motor model
V e
R
• The back emf depends only on the motor speed.
• The motor’s torque depends only on the current, I.
e = ke
= k I
• Track power losses: Pe = PR + Pm
V = IR + e• circuit voltage V:
Pe = PR +
actuator’s power
Pe = electrical (battery) power
Pm = mechanical (output) power
PR = power loss in resistor
PR = I2R E & M lives on !
Pe = VI
Power loss a good thing ?
DC motor model
V e
R
• The back emf depends only on the motor speed.
• The motor’s torque depends only on the current, I.
e = ke
= k I
• Track power losses: Pe = PR + Pm
V = IR + e• circuit voltage V:
Pe = PR +
PR = I2R E & M lives on !
Pe = VI
VI = I2R +
Pe = electrical (battery) power
Pm = mechanical (output) power
PR = power loss in resistor
Power loss a good thing ?
DC motor model
V e
R
• The back emf depends only on the motor speed.
• The motor’s torque depends only on the current, I.
e = ke
= k I
• Track power losses: Pe = PR + Pm
V = IR + e• circuit voltage V:
Pe = PR +
PR = I2R E & M lives on !
Pe = VI
VI = I2R +
Pe = electrical (battery) power
Pm = mechanical (output) power
PR = power loss in resistor
ke = k
VI = I2R + kIe/ ke
V = IR + ke/ ke
IR + e = IR + ke/ ke
single-parameter summary
torque
speed
k V
R kV stall torque
max speed
Linear mechanical power Pm = F v
Rotational version of Pm =
power output
speed vs. torque
Motor specs
Electrical Specifications (@22°C)For motor type 1624 003S 006S 012S 024
-------------------------- -------- -------- -------- --------- -------nominal supply voltage (Volts) 3 6 12 24armature resistance (Ohms) 1.6 8.6 24 75maximum power output (Watts) 1.41 1.05 1.50 1.92maximum efficiency (%) 76 72 74 74no-load speed (rpm) 12,000 10,600 13,000 14,400no-load current (mA) 30 16 10 6friction torque (oz-in) .010 .011 .013 .013stall torque (oz-in) .613 .510 .600 .694velocity constant (rpm/v) 4065 1808 1105 611back EMF constant (mV/rpm) .246 .553 .905 1.635torque constant (oz-in/A) .333 .748 1.223 2.212armature inductance (mH) .085 .200 .750 3.00
k
the preceding were the DC motor slides
Bang-bang control
An “open-loop” strategy
desired speed Controller solving for V
VMotor
and world
“the plant”
gearing up...
should be gearing down...
Another example of feedback control
Nomad going to a designated spot
Power loss a good thing ?
DC motor model
V e
R
• The back emf depends only on the motor speed.
• The motor’s torque depends only on the current, I.
e = ke
= k I
• Track power losses: Pe = PR + Pm
V = IR + e• circuit voltage V:
Pe = PR +
Pe = electrical (battery) power
Pm = mechanical (output) power
PR = power loss in resistor
PR = I2R E & M lives on !
Pe = VI
Back to control
Basic input / output relationship:
(1) Measure the system: R, k
(2) Compute the voltage needed for a desired speed
(3) Go !
We want a particular motor speed .V = + k
R k
We can control the voltage applied V.
Back to control
Basic input / output relationship:
(1) Measure the system: R, k
(2) Compute the voltage needed for a desired speed
(3) Go !
We want a particular motor speed .
V is usually controlled via PWM -- “pulse width modulation”
V = + k R k
We can control the voltage applied V.
Vt
Vt
(half Vmax)
(1/6 Vmax)
V
V
t
t