1. Lecture 8 Motors, Actuators, and Power Drives Forrest Brewer

2. Motors, Actuators, Servos Actuators are the means for embedded systems to modify the physical world –Macroscopic Currents and power levels –Thermal Management –Power Efficiency (often vs. Performance) Motor Types –DC Brush/Brushless –AC (shaded pole and induction) –Stepper Motors –Servo (variety of DC motor) –Peisio-electric (Kynar, Canon ultra-sonic) –Magnetic Solenoid –Electro-static (MEMS)

3. DC Motor Model Torque (force) ~ Current Max Current = V/R Max RPM = V/B emf B emf = L dI/dt In general: Torque ~ (V – B emf )/R

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

5. 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   = -  + R  k e V Speed is proportional to voltage. Jizhong Xiao

6. Electrostatic MEMS Actuation Electrostatic Drives (MEMS) –Basic equations –Rotation Drive –Comb Drive

7. Electrostatic Actuator Analysis Consider the capacitance of the two figures: –To good approximation, the capacitance is double in the second figure: Imagine that the charge is fixed in the top figure: The stored energy is not the same! The difference must be the work done by the motion of the plate: Plate-1 Plate-2 Plate-3 V (volts) d Plate-1 Plate-3 V (volts) d Plate-2

8. Electrostatic Actuators Plate-1 Plate-2 Plate-3 V (volts) x y d Consider parallel plate 1 & 2 Force of attraction (along y direction) F p = (½  V 2  A/g 2 ) 1nN@15V dimensionless Consider plate 2 inserted between plate 1 and 3 (Popularly known as a COMB DRIVE) F c = (½  V 2 )(2t/g) Force of attraction (along x direction) Constant with x-directional translation

9. Paschen Curve Distance*pressure (meter*atm) Breakdown voltage E bd ~100MV/m ~200V ~2um@ 1atm

10. Side view of SDMTop view of SDM First polysilicon motors were made at UCB (Fan, Tai, Muller), MIT, ATT Typical starting voltages were >100V, operating >50V Side Drive Motors

11. A Rotary Electrostatic Micromotor 1  8 Optical Switch Micro Electro Mechanical Systems Jan., 1998 Heidelberg, Germany A Rotary Electrostatic Micromotor 1  8 Optical Switch A. Yasseen, J. Mitchell, T. Streit, D. A. Smith, and M. Mehregany Microfabrication Laboratory Dept. of Electrical Engineering and Applied Physics Case Western Reserve University Cleveland, Ohio 44106 Fig. 3 SEM photo of an assembled microswitch with vertical 200  m-tall reflective mirror plate. Fig. 4 Insertion loss and crosstalk measurements for multi- mode optics at 850  m.

12. Comb Drives Sandia cascaded comb drive (High force) Close-up Tang/Nguyen/Howe

13. Layout of electrostatic-combdrive Ground plate Folded beams (movable comb suspension) Anchors Stationary comb Moving comb Tang, Nguyen, Howe, MEMS89

14. Electrostatic instability Parallel-Plate Electrostatic Actuator Pull-in s0s0 k m x V V x s0s0 1/3 s 0 V snap

15. Electrostatic spring Adjustable stiffness (sensitivity) and resonance frequency

16. Stepper Motors Overview Operation – full and half step Drive Characteristics

17. VR Stepper Motor M. G. Morrow, P.E.

18. Actual Motor Construction M. G. Morrow, P.E.

19. Multi-pole Rotation, Full-Step A = S B = OFF M. G. Morrow, P.E.

20. A = OFF B = S M. G. Morrow, P.E. Multi-pole Rotation, Full Step

21. A = N B = OFF M. G. Morrow, P.E. Multi-pole Rotation, Full Step

22. A = OFF B = N M. G. Morrow, P.E. Multi-pole Rotation, Full Step

23. A = S B = OFF Multi-pole Rotation, Full Step M. G. Morrow, P.E.

24. “Full-Step” Stepping

25. “Full-Step, 2-on” Stepping

26. Half-stepping M. G. Morrow, P.E.

27. Unipolar motor M. G. Morrow, P.E.

28. Bipolar motor M. G. Morrow, P.E.

29. Torque v.s. Angular Displacement

30. Stepping Dynamics

31. Load Affects the Step Dynamics

32. Drive Affects the Step Dynamics a

33. Stepper Motor Performance Curves

34. Current Dynamics

35. Drive Circuits Inductive Loads AC Motor Drive (Triac) H-bridge Snubbing and L/nR Stepper Drive PWM Micro-Stepping

36. Inductive Load Drive Circuits BJTs –V CEsat ~ 0.4V –P D = I C *V CE MOSFETs –V DS = I D * R DSon –P D = I D *V DS M. G. Morrow, P.E.

37. Switching Characteristics V IN VCVC M. G. Morrow, P.E.

38. Switching Characteristics V IN VCVC M. G. Morrow, P.E.

39. AC Motor Drive M. G. Morrow, P.E.

40. H-bridge Q1Q2Q3Q4 ON **Don’t use - short circuit **ON Don’t use - short circuit OFF **Motor off **OFF Motor off ONOFF ONForward OFFON OFFReverse ONOFFONOFFBrake OFFONOFFONBrake An H-bridge consists of two high-side switches (Q1,Q3) and two low-side switches (Q2,Q4) BJTs or FETs M. G. Morrow, P.E.

41. H-Bridge/Inductor operation V = IRV = V+ V = 0 (V = -IR) V = IR

42. L/nR Drive

43. Current Rise in Detail

44. Performance Improvement with L/nR Drive

45. Pulse-Width Modulation Pulse-width ratio = t on /t period Never in “linear mode” –Uses motor inductance to smooth out current –Saves power! –Noise from T period t on t period Benjamin Kuipers

46. Pulse-Code Modulated Signal Some devices are controlled by the length of a pulse- code signal. –Position servo-motors, for example. 0.7ms 20ms 1.7ms 20ms Benjamin Kuipers

47. Back EMF Motor Sensing Motor torque is proportional to current. Generator voltage is proportional to velocity. The same physical device can be either a motor or a generator. Alternate Drive and Sense (note issue of Coils versus Induction) Drive as a motorSense as a generator 20ms Benjamin Kuipers

48. Back EMF Motor Control Benjamin Kuipers

49. Microstepping Use partial Drive to achieve fractional steps Stepper is good approximation to Sine/Cosine Drive –2  cycle is 1 full step! Usually PWM to reduce power loss –Fractional voltage drop in driver electronics IBIB Full Step position Half Step position I B = -1, I A = 0 IAIA I A = 2 I B I A = I B

50. Microstepping Block Diagram Easy to synthesize the PWM from Microcontroller –Lookup table + interpolation –  /2 phase lag = table index offset Need to monitor winding current: –Winding L,R –Motor Back EMF PWM Frequency tradeoff –Low Freq: resonance (singing) –High Freq: Winding Inductance and switching loss PWM H Bridge PWM H Bridge

51. PWM Issues Noise/Fundamental Period –Low Freq: Singing of motor and resonance –High Freq: Switching Loss Can we do better? –Not unless we add more transitions! (Switching Loss) If we bite bullet and use MOS drives can switch in 2- 50nS… Then can choose code to optimize quantitization noise vs. switching efficiency –Modulated White Noise –Sigma-Delta D/A Requires higher performance Controller

52. Motors and Actuators -- Software Embedded motor control is huge, growing application area –Need drive(sample) rates high enough to support quiet, efficient operation –Rates roughly inversely proportional to motor physical size –Stepper Motors are usually micro-stepped to avoid ‘humming’ and step bounce –Typical: 1kHz rate, 50kHz micro-step; slow HP motors 300Hz-1kHz Upshot- 1 channel “fast” or micro-stepped motor is substantial fraction of 8-bit processor throughput and latency –Common to run up to 3 “slow” motors from single uP –Common trend to control motor via single, cheap uP –Control multiple via commands send to control uPs