# Robot Actuation Motors Stepper motors DC motors Servo

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 - 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 Half-stepping energizing more than one pair of stator teeth

Increasing Resolution torque 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 - N S

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

Who pulls more weight? electromagnets S stator N N rotor S S stator N Stepper motor DC motor

Who pulls more weight? electromagnets S stator N N 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 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. t R Vr = + k w 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 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 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 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 B B A lags 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 p. H 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 p. H 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 Poly. Bot 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. t R Vr = + k w 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 N N S permanent magnets N N S S S N S S

Control What you want to control = what you can control For DC motors: 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 ? t R V = + ke w kt R V • Consider this circuit’s V: e - or - V R w = - 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 kt. V 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 kt. V 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 t kt. V R stall torque

speed vs. torque speed w V ke gasoline engine power output speed vs. torque t kt. V 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 V = IR + e • circuit voltage V: Pm = mechanical (output) power PR = power loss in resistor • Track power losses: R V e DC motor model 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 V = IR + e • circuit voltage V: Pm = mechanical (output) power PR = power loss in resistor • Track power losses: R V e DC motor model Pe = PR + Pm Pe = PR + em 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 V = IR + e • circuit voltage V: Pm = mechanical (output) power PR = power loss in resistor • Track power losses: R V e PR = I 2 R 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 V = IR + e • circuit voltage V: Pm = mechanical (output) power PR = power loss in resistor • Track power losses: R V e PR = I 2 R E & M lives on ! Pe = VI DC motor model Pe = PR + Pm Pe = PR + em (ac’s) VI = I 2 R + 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 V = IR + e • circuit voltage V: Pm = mechanical (output) power PR = power loss in resistor • Track power losses: R V e PR = I 2 R E & M lives on ! Pe = VI DC motor model Pe = PR + Pm Pe = PR + em (ac’s) VI = I 2 R + em (ac’s) VI > em (ac’s) Finally ! Scientific proof !

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 V = IR + e • circuit voltage V: Pm = mechanical (output) power PR = power loss in resistor • Track power losses: R V e PR = I 2 R E & M lives on ! Pe = VI DC motor model Pe = PR + Pm Pe = PR + tw 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 V = IR + e • circuit voltage V: Pm = mechanical (output) power PR = power loss in resistor • Track power losses: R V e PR = I 2 R E & M lives on ! Pe = VI DC motor model Pe = PR + Pm Pe = PR + tw VI = I 2 R + 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 V = IR + e • circuit voltage V: Pm = mechanical (output) power PR = power loss in resistor • Track power losses: R V e DC motor model Pe = PR + Pm Pe = PR + tw PR = I 2 R VI = I 2 R + tw E & M lives on ! VI = I 2 R + kt. Ie/ ke Pe = VI 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 t k V R stall torque

Motor specs Electrical Specifications (@22°C) For motor type 1624 003 S 006 S 012 S ------------- --------- ------- 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) (m. A) (oz-in) (rpm/v) (m. V/rpm) (oz-in/A) (m. H) 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. 750 024 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 V = IR + e • circuit voltage V: Pm = mechanical (output) power PR = power loss in resistor • Track power losses: R V e PR = I 2 R E & M lives on ! Pe = VI DC motor model Pe = PR + Pm Pe = PR + tw

Back to control Basic input / output relationship: t R V = + k w 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. 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” V V t t (half Vmax) V (1/6 Vmax) V t t

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