• Controls Lecture 1


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  • FileName: me4053_cont1_Sp10.pdf [read-online]
    • Abstract: me4053controls lecture 1modeling and identification of a dc motordr. f***i announcements!•  vibrations reports are next week•  you will be assigned to do one of the following

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me4053
controls lecture 1
modeling and identification of a dc motor
dr. f***i
announcements!


•  vibrations reports are next week

•  you will be assigned to do one of the following

–  presentation on the week 1 ( 2dof) lab at 10 am weds april 14th
–  extended abstract on the the week 1 (2dof) lab due by 4 pm on weds
april 14th
–  presentation on the week 2 (free-free beam) lab at 10 am friday,
april 16th
–  extended abstract on the the week 2 (free-free beam) lab due by 4 pm
on friday, april 16th
•  assignments will available on the website on friday

•  room assignments will be posted

•  deposit extended abstracts in the bin outside the lab

•  e-mail electronic copies of presentations and abstracts to
[email protected]

me4053
controls lab 1
modeling and identification of a
brushless dc motor
controls lab 2
control of a brushless dc motor
dc motor model
ra la
ia
eo(t) eb
q
b
jl
kirchoff voltage law (kvl):
back-electromotive force (emf)
torque-current constant
moment balance on load: jl t
bw
laplace transforms
laplace transforms
combine algebraically, or…
motor can be represented in the form of
a block-diagram showing “internal feedback”
kvl
torque-current relation
moment summation
back emf
r c
g
h
letting and
or
in many cases, la is very small, allowing reduction to 1st-order system:
or
where
motor time constant motor gain
see how time constant and motor gain depend on physical parameters
step response:
inverse laplace transform
wss= vin km

w

w = 0.632 wss

t/tm = 1 t/tm
km = 1 2% settling time
vin =4
vin =3
w

vin =2
vin =1
t/tm t/tm = 4
deadzone
wss
km
vin
negative deadzone positive deadzone
system identification, continued
motor
a
b
note phase lag
steady-state harmonic excitation, harmonic response
mag phase lag
-3db
due to nonlinearity, we use a biased sinusoid as input
thigh
vhigh
vlow
dt
a
tinp
form bode plot
3db point
wc =“corner frequency”
-20db/dec
45o phase lag
phase lead
(note: plot shows
phase lead)
wc
simulink : measurement model
simulink : simulation model
review of feedback control…
system id was done using the motor/flywheel speed, but
for servo-control, we first need to obtain the transfer function
from voltage to rotation angle
recall = transfer function from applied
voltage to motor speed
what about position?
= transfer function from applied
voltage to motor angular position
change system performance through use of feedback control
commanded
output
angle
angle
r e m
motor q

controller
***or actuator plant
signal
unity feedback
h=1
(includes unit conversion)
proportional control (p-control)
r e m q

kp
***or actuator
open-loop transfer function:
r c
g
h
closed-loop transfer function:
cl


Use: 0.5771