1. 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

2. Stepper Motors N S stator rotor electromagnets

3. Stepper Motors N S stator rotor S N electromagnets “variable reluctance” stepper motor How does rotor angle affect the torque?

4. Stepper Motors N S stator rotor S N electromagnets “variable reluctance” stepper motor angle torque

5. Stepper Motors N S stator rotor S N electromagnets “variable reluctance” stepper motor angle torque

6. Stepper Motors N S stator rotor S N S N electromagnets “variable reluctance” stepper motor on to the next teeth…

7. Stepper Motors N S electromagnets stator rotor S N S N “variable reluctance” stepper motor Direct control of rotor position (no sensing needed) May oscillate around a desired orientation Low resolution printers computer drives machining on to the next teeth… can we increase our resolution?

8. Increasing Resolution Half-stepping S S N N energizing more than one pair of stator teeth

9. Increasing Resolution Half-stepping S S N N angle torque energizing more than one pair of stator teeth

10. Increasing Resolution Half-stepping S S N N angle torque More teeth energizing more than one pair of stator teeth

11. Increasing Resolution Half-stepping S S N N angle torque More teeth energizing more than one pair of stator teeth on the rotor and/or stator Question 2 this week…

12. 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 ?

13. DC motors -- exposed !

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

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

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

17. Who pulls more weight? N S NS stator rotor DC motor Stepper motor N S electro- magnets stator rotor

18. Who pulls more weight? N S NS stator rotor DC motor Stepper motor N S electro- 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

19. Open-loop control An “open-loop” strategy desired speed  Controller solving for V V Motor and world  “the plant”

20. Bang-bang control General idea works for any controllable system... desired speed  Controller solving for V V Motor and world  desired position  Controller solving for V(t) V(t) Motor and world  actual speed actual position

21. Returning to one’s sensors But the real world interferes... desired speed  d Controller solving for V V Motor and world aa desired speed  d  actual speed  a V r = + k   R k We don’t know the actual load on the motor.

22. Closed-loop control Compute the error and change in relation to it. desired  d V The world aa actual speed  a - compute V using the error e  d  a Error signal e 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 < 360º Power/Contact

24. Servomotors 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 potentiometer

25. Optical Encoders Detecting motor shaft orientation potential problems?

26. 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

27. 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 !

28. 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?

29. Absolute Optical Encoders Complexity of distinguishing many different states -- high resolution is expensive! something simpler ?

30. Relative Encoders Track position changes grating light emitter light sensor decode circuitry

31. Relative Encoders Relative position - calibration ? - direction ? - resolution ? grating light emitter light sensor decode circuitry

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

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

34. Relative Encoders Relative position grating light emitter light sensor decode circuitry A B A leads B - calibration ? - direction ? - resolution ? quadrature encoding 100 lines -> ?

35. 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

36. Control

37. Closed-loop control Compute the error and change in relation to it. desired  d V The world aa actual speed  a - compute V using the error e  d  a Error signal e Feedback

38. Initial Feedback “First” feedback controller

39. Other Systems Biological feedback systems Chemical feedback systems intelligent hydrogels

40. 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 systems for insulin delivery Why I’m not a chemist: ph dependant

41. Robotic use of EAPs

42. 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

43. Wednesday Coming soon! The ancient art of motor arranging... Controling motion by controlling motors: PID

44. Spherical Stepper Motor complete motor statorrotor applications

45. Returning to one’s sensors But the real world interferes... desired speed  d Controller solving for V V Motor and world aa desired speed  d  actual speed  a V r = + k   R k We don’t know the actual load on the motor.

46. How robotics got started...

47. Proportional control better, but may not reach the setpoint

48. PI control better, but will overshoot but I thought PI was constant...

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 N S N S NS N S S N stator rotor permanent magnets NS S NNS N S

53. Control What you want to control = what you can control For DC motors: speedvoltage N S NS V  V

54. 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 = k e   = k  I

55. the following are the DC motor slides

56. 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 = k e   = k  I

57. k  k e 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 = k e   = k  I Consider this circuit’s V: V = IR + e I stall = V/R current when motor is stalled speed = 0 torque = max How is V related to  V = + k e   R k  - or -  = -  + R  k e V Speed is proportional to voltage.

58. speed vs. torque torque  speed   k e V at a fixed voltage  R k  V max torque when stalled no torque at max speed

59. speed vs. torque torque  speed   k e V at a fixed voltage  R k  V stall torque no torque at max speed Linear mechanical power P m = F  v Rotational version of P m = 

60. speed vs. torque torque  speed   k e V at a fixed voltage  R k  V stall torque max speed Linear mechanical power P m = F  v Rotational version of P m =  power output speed vs. torque

61. torque  speed   k e V  R k  V power output speed vs. torque gasoline engine

62. 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 = k e   = k  I Track power losses: P e = P R + P m P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor V = IR + e circuit voltage V:

63. 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 = k e   = k  I Track power losses: P e = P R + P m V = IR + e circuit voltage V: P e = P R + e m actuator’s power P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor

64. 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 = k e   = k  I Track power losses: P e = P R + P m V = IR + e circuit voltage V: P e = P R + e m ( ac’s ) P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor P R = I 2 R E & M lives on ! P e = VI

65. 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 = k e   = k  I Track power losses: P e = P R + P m V = IR + e circuit voltage V: P e = P R + e m ( ac’s ) P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor VI = I 2 R + e m ( ac’s ) P R = I 2 R E & M lives on ! P e = VI

66. 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 = k e   = k  I Track power losses: P e = P R + P m V = IR + e circuit voltage V: P e = P R + e m ( ac’s ) P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor VI = I 2 R + e m ( ac’s ) P R = I 2 R E & M lives on ! P e = VI VI > e m ( ac’s ) Finally ! Scientific proof !

67. 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 = k e   = k  I Track power losses: P e = P R + P m V = IR + e circuit voltage V: P e = P R +  actuator’s power P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor P R = I 2 R E & M lives on ! P e = VI

68. 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 = k e   = k  I Track power losses: P e = P R + P m V = IR + e circuit voltage V: P e = P R +  P R = I 2 R E & M lives on ! P e = VI VI = I 2 R +  P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor

69. 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 = k e   = k  I Track power losses: P e = P R + P m V = IR + e circuit voltage V: P e = P R +  P R = I 2 R E & M lives on ! P e = VI VI = I 2 R +  P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor k e = k  VI = I 2 R + k  Ie/ k e V = IR + k  e/ k e IR + e = IR + k  e/ k e

70. single-parameter summary torque  speed   k V  R k  V stall torque max speed Linear mechanical power P m = F  v Rotational version of P m =  power output speed vs. torque

71. Motor specs Electrical Specifications (@22°C) For motor type 1624 003S006S012S024 ----------------------------------------------------------- ------- nominal supply voltage(Volts)361224 armature resistance(Ohms)1.68.62475 maximum power output(Watts)1.411.051.50 1.92 maximum efficiency(%)76727474 no-load speed (rpm)12,00010,60013,00014,400 no-load current(mA)3016106 friction torque(oz-in).010.011.013.013 stall torque(oz-in).613.510.600.694 velocity constant(rpm/v)406518081105611 back EMF constant(mV/rpm ).246.553.9051.635 torque constant(oz-in/A).333.7481.2232.212 armature inductance (mH).085.200.7503.00 k

72. the preceding were the DC motor slides

73. Bang-bang control An “open-loop” strategy desired speed  Controller solving for V V Motor and world  “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 ? 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 = k e   = k  I Track power losses: P e = P R + P m V = IR + e circuit voltage V: P e = P R +  P e = electrical (battery) power P m = mechanical (output) power P R = power loss in resistor P R = I 2 R E & M lives on ! P e = VI

77. 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.

78. 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. V t V t (half V max ) (1/6 V max ) V V t t