Motors and Control

1
Motors and Control
Capstone Design -- Robotics

• Jizhong Xiao
• Department of Electrical Engineering
• City College of New York
• jxiao_at_ccny.cuny.edu

2
Robot Actuators
Stepper motors DC motors AC motors
Physics review
Things seek lowest energy states.
Nature is lazy.

• iron core vs. magnet

N
S

• magnetic fields tend to line up

Electric fields and magnetic fields are the same
thing.
3
Stepper Motor Basics
stator
rotor
Stator made out of coils of wire called
winding Rotor magnet rotates on bearings
inside the stator
Current switch in winding gtMagnetic
force gthold the rotor in a position
Electromagnet

• Direct control of rotor position (no sensing
  needed)
• May oscillate around a desired orientation
  (resonance at low speeds)
• Low resolution

printers computer drives
4
Increased Resolution
S
torque
N
S
angle
N
Half stepping
5
Increased Resolution
S
N
S
More teeth on rotor or stator
N
Half stepping
6
Increased Resolution
S
N
S
More teeth on rotor or stator
N
Half stepping
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How to Control?
4 Lead Wire Configuration
Clockwise Facing Mounting End
Each step, like the second hand of a clock gt
tick, tick
Increase the frequency of the steps gt continuous
motion
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Motoring along...

• direct control of position

• precise positioning (The amount of rotational
  movement per step depends on the construction of
  the motor)

• Easy to Control

• under-damping leads to oscillation at low speeds
• torque is lower at high speeds than the primary
  alternative

9
DC motors -- exposed !
10
DC motor basics
permanent magnets
N
S
rotor
stator
brush

V
-
commutator attached to shaft
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DC motor basics
permanent magnets
N
S
rotor
N
S
stator


V
V
-
-
12
DC motor basics
permanent magnets
N
S
rotor
N
S
N
S
stator



V
V
V
-
-
-
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Position Sensors

• Optical Encoders
• Relative position
• Absolute position
• Other Sensors
• Resolver
• Potentiometer

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Optical Encoders

• Relative position

- direction
light sensor
- resolution
decode circuitry
light emitter
grating
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Optical Encoders
mask/diffuser

• Relative position

light sensor
decode circuitry
light emitter
grating
A diffuser tends to smooth these signals
Ideal
Real
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Optical Encoders

• Relative position

- direction
light sensor
- resolution
decode circuitry
light emitter
grating
17
Optical Encoders

• Relative position

- direction
light sensor
- resolution
decode circuitry
light emitter
grating
A
A
A lags B
B
B
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Optical Encoders

• Relative position

- direction
light sensor
- resolution
decode circuitry
light emitter
grating
Phase lag between A and B is 90 degree
A
B
A leads B
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Optical Encoders

• Detecting absolute position

something simpler ?
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Optical Encoders

• Detecting absolute position

wires ?
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Gray Code

Binary
0 1 2 3 4 5 6 7 8
9
0 1 10 11 100 101 110 111 1000 1001
000 001 011 010 110 111 101 100
among others...
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Other Sensors

• Resolver
• driving a stepper motor

• Potentiometer
• varying resistance

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Control
Control getting motors to do what you want them
to
For DC motors
speed
voltage
windings resistance
R
w
e
V
back emf
V
N
S
e
is a voltage generated by the rotor windings
cutting the magnetic field emf electromagnetic
force
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Controlling speed with voltage
e ke w

• The back emf depends only on the motor speed.
• The motors torque depends only on the current,
  I.

t kt I
R
e
V
DC motor model
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Controlling speed with voltage
e ke w

• The back emf depends only on the motor speed.
• The motors torque depends only on the current,
  I.

t kt I
Istall V/R
V IR e

• Consider this circuits V

current when motor is stalled
How is V related to w ?
speed 0 torque max
R
e
V
- or -
V
R
w - t
ke
kt ke
DC motor model
Speed is proportional to voltage.
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speed vs. torque
at a fixed voltage
speed w
V
no torque at max speed
ke
max torque when stalled
ktV
torque t
R
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speed vs. torque
at a fixed voltage
Linear mechanical power Pm F ? v
speed w
Rotational version of Pm t ? w
V
no torque at max speed
ke
ktV
stall torque
torque t
R
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speed vs. torque
at a fixed voltage
Linear mechanical power Pm F ? v
speed w
Rotational version of Pm t ? w
V
ke
max speed
power output
speed vs. torque
ktV
stall torque
torque t
R
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speed vs. torque
speed w
V
ke
gasoline engine
max speed
power output
speed vs. torque
ktV
stall torque
torque t
R
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Motor specs
Electrical Specifications (_at_22C) For motor type
1624   003S 006S 012S 024 ------------------------
-- -------- -------- -------- ---------
------- nominal supply voltage (Volts) 3 6 12 24 a
rmature resistance (Ohms) 1.6 8.6 24 75 maximum
power output (Watts) 1.41 1.05 1.50 1.92 maximum
efficiency () 76 72 74 74 no-load speed
(rpm) 12,000 10,600 13,000 14,400 no-load
current (mA) 30 16 10 6 friction
torque (oz-in) .010 .011 .013 .013 stall
torque (oz-in) .613 .510 .600 .694 velocity
constant (rpm/v) 4065 1808 1105 611 back EMF
constant (mV/rpm) .246 .553 .905 1.635 torque
constant (oz-in/A) .333 .748 1.223 2.212 armature
inductance (mH) .085 .200 .750 3.00
kt
ke
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Back to control
Basic input / output relationship
We can control the voltage applied V.
We want a particular motor speed w .
How to change the voltage?
V is usually controlled via PWM -- pulse width
modulation
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PWM

• PWM -- pulse width modulation
• Duty cycle
• The ratio of the On time and the Off time in
  one cycle
• Determines the fractional amount of full power
  delivered to the motor

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Open-loop vs. Close-loop Control
Open-loop Control
V(t)
Controller solving for V(t)
desired speed w
w
Motor
actual speed
If desired speed wd ? actual speed wa,
So what?
Closed-loop Control using feedback
PID controller
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PID Controller
PID control Proportional / Integral / Derivative
control
V Kp (wd - w) Ki ? (wd - w) dt Kd
V Kp ( e Ki ? e Kd )
Error signal e
wd - wa
actual w
V
desired wd
compute V using PID feedback
-
Motor
actual speed w
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Evaluating the response
overshoot
steady-state error
ss error -- difference from the systems desired
value
settling time
overshoot -- of final value exceeded at first
oscillation
rise time -- time to span from 10 to 90 of the
final value
settling time -- time to reach within 2 of the
final value
rise time
How can we eliminate the steady-state error?
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Control Performance, P-type
Kp 20
Kp 50
Kp 500
Kp 200
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Steady-state Errors, P-type
Kp 200
Kp 50
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Control Performance, PI - type
Kp 100
Ki 50
Ki 200
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Youve been integrated...
Kp 100
instability oscillation
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Control Performance, PID-type
Kp 100
Kd 5
Ki 200
Kd 2
Kd 10
Kd 20
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PID final control
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PID Tuning
How to get the PID parameter values ?
(1) If the system has a known mathematical model
(i.e., the transfer function), analytical methods
can be used (e.g., root-locus method) to meet the
transient and steady-state specs.
(2) When the system dynamics are not precisely
known, we must resort to experimental approaches.
Ziegler-Nichols Rules for Tuning PID Controller
Using only Proportional control, turn up the gain
until the system oscillates w/o dying down, i.e.,
is marginally stable. Assume that K and P are the
resulting gain and oscillation period,
respectively.
Then, use
for P control
for PI control
for PID control
Kp 0.45 K
Kp 0.5 K
Kp 0.6 K
Ziegler-Nichols Tuning for second or higher order
systems
Ki 2.0 / P
Ki 1.2 / P
Kd P / 8.0
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Implementing PID
Use discrete approximations to the I and D terms

• Proportional term ei wdesired -
  wactual

at time i
inow

• Integral term S ei

i0

• Derivative term ei - 2ei-1
  ei-2

How could this discretization affect the
performance of a system? Sampling time is
critical!!
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What is proper sampling

• Proper sampling
• Can reconstruct the analog signal from the
  samples
• Aliasing
• The higher frequency component that appears to be
  a lower one is called an alias for the lower
  frequency
• Aliasing the frequency of the sampled data is
  different from the frequency of the continuous
  signal

Aliasing
b. 0.09 of sampling rate might represent, a 90
cycle/second sine wave being sampled at 1000
samples/second in another word, there are 11.1
samples taken over each complete cycle of the
sinusoid d. Aliasing occurs when the frequency of
the analog sine wave is greater than the Nyquist
frequency (one-half of the sampling rate) in
other word, the sampling frequency is not fast
enough. Aliasing misrepresents the information,
so the original signal cannot be reconstructed
properly from the samples.
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Shannons Sampling Theorem

• An analog signal x(t) is completely specified by
  the samples if x(t) is bandlimited to
  , where
• In other word, a continuous signal can be
  properly sampled, only if it does not contain
  frequency components above one-half of the
  sampling rate.
• Definitions
• Given a signal bandlimited to , must sample
  at greater than to preserve information.
  The value is called Nyquist rate (of
  sampling for a given )
• Given sampling rate , the highest frequency
  in the signal must be less than if
  samples are to preserve all the information. The
  value is called the Nyquist
  frequency (associated with a fixed sample
  frequency).
  

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Rule of Thumb

• For a closed-loop control system, a typical
  choice for the sampling interval T based on rise
  time is 1/5 th or 1/10 th of the rise time.
  (i.e., 5 to 10 samples for rise time)

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Motor Drive

• Micro-controller
• Logic Level
• Motor Drive Components
• Power transistors
• H-Bridge Drivers
• etc ...

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Useful Links

• 6.270 MITs Autonomous Robot Design Competition,
  http//web.mit.edu/6.270/www/home.html
• Acroname Inc. for Easy robotics, sensors, kits,
  etc, http//www.acroname.com/
• Interactive C Users Guide, etc.,
  http//www.newtonlabs.com/ic/
• Handy board, http//www.handyboard.com/
• Pitsco Lego Dacta, lego components,
  http//www.pitsco-legodacta.com/intro.htm
• The Electronic Goldmine cheep motors,
  electronics components, http//www.goldmine-elec.c
  om
• Applied Motion Products Step/DC motors and
  drives, http//www.applied-motion.com
• Jameco Electronics http//www.jameco.com

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Assignment

• Refresh you memory
• Control Theory
• (Text book K. Ogata, Modern Control Engineering,
  Prentice Hall)
• Electronics (OP-amp, motor drive)
• Laboratory
• Specs of Motors
• Motor Drive Circuit
• Looking for Drive Components