robot actuation: motors stepper motors servo motors physics “review” dc motors electric fields...

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+ -

N

S

N S

Torque is a good scrabble word. Author: CIS

Stepper Motors

N

S stator

rotor

electromagnets

Stepper Motors

N

S stator

rotor

S

N

electromagnets“variable reluctance”

stepper motor

How does rotor angle affect the torque?

Stepper Motors

N

S stator

rotor

S

N


stepper motor

angle

torque

Stepper Motors

N

S stator

rotor

S

N

SN


stepper motor on to the next

teeth…

Stepper Motors

N

S

electromagnets

stator

rotor

S

N

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

S

S

N

N

energizing more than one pair of stator teeth


Half-stepping

S

S

N

Nangle

torque



Half-stepping

S

S

N

Nangle

torque

More teeth



Half-stepping

S

S

N

Nangle

torque

More 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

N

S

N S

stator

rotor

permanent magnets

commutator on shaft

V

+

-

brushes

DC motor basics

N

S

N S

stator

rotor

permanent magnets

commutator on shaft

V

+

-

N SS N

V

+

-

brushes

DC motor basics

N

S

N S

stator

rotor

permanent magnets

commutator on shaft

V

+

-

N SS N N SN S

V

+

-

V

+

-

brushes

Who pulls more weight?

N

S

N S

stator

rotor

DC motorStepper motor

N

Selectro-magnets stator

rotor

Who pulls more weight?

N

S

N S

stator

rotor

DC motorStepper motor

N

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...


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

0

1

2

3

4

5

6

7

8

9

# Binary

0

1

10

11

100

101

110

111

1000

1001

000

001

011

010

110

111

101

100

Gray Code

0

1

2

3

4

5

6

7

8

9

# Binary

0

1

10

11

100

101

110

111

1000

1001

000

001

011

010

110

111

101

100

1100

1101

with FPS applications !

Gray Code

0

1

2

3

4

5

6

7

8

9

# Binary

0

1

10

11

100

101

110

111

1000

1001

among others...

000

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

grating

light emitter

light sensor

decode circuitry

A

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...

A

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

N

S

N

S

N S

N S SN

stator

rotor

permanent magnets

N SS N N SN S

Control

What you want to control = what you can control

For DC motors: speed voltage

N

S

N SV

V

Controlling speed with voltage

DC motor model

V e

“back emf”

R

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


DC motor model

V e

R



e = ke

= k I

kke


DC motor model

V e

R



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



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



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:


DC motor model

V e

R



e = ke

= k I



Pe = PR + em

actuator’s power





DC motor model

V e

R



e = ke

= k I



Pe = PR + em (ac’s)




PR = I2R E & M lives on !

Pe = VI


DC motor model

V e

R



e = ke

= k I







VI = I2R + em (ac’s)PR = I2R

E & M lives on !

Pe = VI


DC motor model

V e

R



e = ke

= k I







VI = I2R + em (ac’s)PR = I2R

E & M lives on !

Pe = VI VI > em (ac’s)

Finally ! Scientific proof !


DC motor model

V e

R



e = ke

= k I



Pe = PR +

actuator’s power





Pe = VI


DC motor model

V e

R



e = ke

= k I



Pe = PR +


Pe = VI

VI = I2R +





DC motor model

V e

R



e = ke

= k I



Pe = PR +


Pe = VI

VI = I2R +




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



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


VMotor

and world

“the plant”

gearing up...

should be gearing down...

Another example of feedback control

Nomad going to a designated spot


DC motor model

V e

R



e = ke

= k I



Pe = PR +





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

robot actuation: motors stepper motors servo motors physics “review” dc motors electric fields...

Documents

n s n s torque

v v motor

pair of stator teeth

rotor angle

plant slide

week slide

cis slide

shaft v brushes slide