Lecture 8Lecture 8Motors, Actuators, and Power DrivesMotors, Actuators, and Power Drives

Forrest Brewer

Motors, Actuators, ServosMotors, 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)

DC Motor ModelDC Motor Model

•Torque (force) ~ Current

•Max Current = V/R

•Max RPM = V/Bemf

Bemf = L dI/dt

In general:

Torque ~ (V – Bemf)/R

R

+

-

Torque

Bemf

In-oz/Amp

V/krpm

L

Output

RPM

Vo

ltag

e

torque

speed

ke V

R kV

max speed

Linear mechanical power Pm = F v

Rotational version of Pm =

power output

speed vs. torque

Jizhong Xiao

speed vs. torque, fixed voltage

stall torque

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

= - + R ke V

Speed is proportional to voltage.

Jizhong Xiao

Electrostatic MEMS ActuationElectrostatic MEMS Actuation

Electrostatic Drives (MEMS)– Basic equations– Rotation Drive– Comb Drive

Electrostatic Actuator AnalysisElectrostatic 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

2211 VCVCQ

2/21 CC

)2

1(

2

1

2

1 2222

2111 VCEVCE

2Vdx

dEFFdxE

Electrostatic ActuatorsElectrostatic Actuators

Plate-1

Plate-2

Plate-3

V (volts)

x

yd Consider parallel plate 1 & 2

Force of attraction (along y direction)

Fp = (½ V2A/g2)

1nN@15Vdimensionless

Consider plate 2 inserted between plate 1 and 3(Popularly known as a COMB DRIVE)

Fc = (½ V2 )(2t/g)Force of attraction (along x direction)

Constant with x-directional translation

Paschen CurvePaschen Curve

Distance*pressure(meter*atm)

Breakdown voltage

Ebd~100MV/m

~200V

~2um@1atm

Side view of SDM Top view of SDM

First polysilicon motors were made at UCB (Fan, Tai, Muller), MIT, ATTTypical starting voltages were >100V, operating >50V

Side Drive MotorsSide Drive Motors

A Rotary Electrostatic Micromotor 1A Rotary Electrostatic Micromotor 18 Optical Switch8 Optical Switch

Micro Electro Mechanical SystemsJan., 1998 Heidelberg, Germany

A Rotary Electrostatic Micromotor 18 Optical Switch

A. Yasseen, J. Mitchell, T. Streit, D. A. Smith, and M. MehreganyMicrofabrication Laboratory

Dept. of Electrical Engineering and Applied PhysicsCase 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.

Comb DrivesComb Drives

Sandia cascaded comb drive(High force)

Close-upTang/Nguyen/Howe

Layout of electrostatic-combdrive

Ground plate

Folded beams (movable comb

suspension)

Anchors

Stationarycomb

Movingcomb

Tang, Nguyen, Howe, MEMS89

Electrostatic instability

Parallel-Plate Electrostatic Actuator Pull-inParallel-Plate Electrostatic Actuator Pull-in

s0

0

30

0

00

20

20

27

8

30

2

2

A

ksV

sx

x

V

xskx

V

kxxs

VF

snap

snap

k

m

x

V

V

x

s0

1/3 s0

Vsnap

Electrostatic springElectrostatic spring

00

02

00

20

300

20

00

02

00

20

00

02

00

20

20

20

21

2

212

2122

xs

x

xs

Vx

xs

Vkxm

xs

xx

xs

VkxxmF

xs

xx

xs

V

xs

VF

Adjustable stiffness (sensitivity) and resonance frequency

Stepper MotorsStepper Motors

Overview Operation – full and half step Drive Characteristics

VR Stepper MotorVR Stepper Motor

M. G. Morrow, P.E.

Actual Motor ConstructionActual Motor Construction

ROTOR

STATOR

A

S

N

N

N

S

A

A

/A

/A

/B

/B

B

B

M. G. Morrow, P.E.

Multi-pole Rotation, Full-StepMulti-pole Rotation, Full-Step

ROTOR

STATOR

A

S

N

N

N

S

A

A

/A

/A

/B

/B

B

B

A = S

B = OFF

M. G. Morrow, P.E.

ROTOR

STATOR

A

S

N

N

N

S

A

A

/A

/A

/B

/B

B

B

A = OFF

B = S

M. G. Morrow, P.E.

Multi-pole Rotation, Full StepMulti-pole Rotation, Full Step

ROTOR

STATOR

A

S

N

N

N

S

A

A

/A

/A

/B

/B

B

B A = N

B = OFF

M. G. Morrow, P.E.

Multi-pole Rotation, Full StepMulti-pole Rotation, Full Step

A = OFF

B = N

ROTOR

STATOR

/A

/A

/B

/B

AS

N

N

N

S

A

A

B

B

M. G. Morrow, P.E.

Multi-pole Rotation, Full StepMulti-pole Rotation, Full Step

A = S

B = OFF

Multi-pole Rotation, Full StepMulti-pole Rotation, Full Step

ROTOR

STATOR

A

S

N

N

N

S

A

A

/A

/A

/B

/B

B

B

M. G. Morrow, P.E.

““Full-Step” SteppingFull-Step” Stepping

““Full-Step, 2-on” SteppingFull-Step, 2-on” Stepping

Half-steppingHalf-stepping

M. G. Morrow, P.E.

Unipolar motor Unipolar motor

M. G. Morrow, P.E.

Bipolar motorBipolar motor

M. G. Morrow, P.E.

Torque v.s. Angular DisplacementTorque v.s. Angular Displacement

Stepping DynamicsStepping Dynamics

Load Affects the Step DynamicsLoad Affects the Step Dynamics

Drive Affects the Step DynamicsDrive Affects the Step Dynamics

a

Stepper Motor Performance CurvesStepper Motor Performance Curves

Current DynamicsCurrent Dynamics

Drive CircuitsDrive Circuits

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

Inductive Load Drive CircuitsInductive Load Drive Circuits

M M MM

i < ~30mAV M = V CC

V M V M V M V M

i < ~150mAi < ~1A

V CCPROTPROTPROT

PROT

BJTs– VCEsat ~ 0.4V

– PD = IC*VCE

MOSFETs– VDS = ID * RDSon

– PD = ID*VDS

                     

M. G. Morrow, P.E.

Switching CharacteristicsSwitching Characteristics

V IN

V C

+5V

VIN

VC

M. G. Morrow, P.E.

Switching CharacteristicsSwitching Characteristics

V IN

V C

+5V

VIN

VC

M. G. Morrow, P.E.

AC Motor DriveAC Motor Drive

M

VAC

PROT

VCC

M. G. Morrow, P.E.

H-bridgeH-bridge

Q1 Q2 Q3 Q4

ON ON * * Don’t use - short circuit

* * ON ON Don’t use - short circuit

OFF OFF * * Motor off

* * OFF OFF Motor off

ON OFF OFF ON Forward

OFF ON ON OFF Reverse

ON OFF ON OFF Brake

OFF ON OFF ON Brake

+M-

V M

Q1

Q2 Q4

Q3

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.

H-Bridge/Inductor operationH-Bridge/Inductor operation

V = IR V = V+

V = 0(V = -IR)

V = IR

L/nR DriveL/nR Drive

Current Rise in DetailCurrent Rise in Detail

0

Performance Improvement with L/nR DrivePerformance Improvement with L/nR Drive

Pulse-Width ModulationPulse-Width Modulation

Pulse-width ratio = ton/tperiod

Never in “linear mode”– Uses motor inductance to smooth out current– Saves power!

– Noise from Tperiod

ton

tperiod

Benjamin Kuipers

Pulse-Code Modulated SignalPulse-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

Back EMF Motor SensingBack 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 motor Sense as a generator

20ms

Benjamin Kuipers

Back EMF Motor ControlBack EMF Motor Control

Benjamin Kuipers

MicrosteppingMicrostepping

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

IB

Full Step position

Half Step positionIB = -1, IA = 0

IA

IA = 2 IB

IA = IB

Microstepping Block DiagramMicrostepping 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 HBridge

PWM HBridge

PWM IssuesPWM 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

Motors and Actuators -- SoftwareMotors 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