Controls Lecture 1
controls lecture 1
modeling and identification of a dc motor
• 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
– presentation on the week 2 (free-free beam) lab at 10 am friday,
– 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
controls lab 1
modeling and identification of a
brushless dc motor
controls lab 2
control of a brushless dc motor
dc motor model
kirchoff voltage law (kvl):
back-electromotive force (emf)
moment balance on load: jl t
combine algebraically, or…
motor can be represented in the form of
a block-diagram showing “internal feedback”
in many cases, la is very small, allowing reduction to 1st-order system:
motor time constant motor gain
see how time constant and motor gain depend on physical parameters
inverse laplace transform
wss= vin km
w = 0.632 wss
t/tm = 1 t/tm
km = 1 2% settling time
t/tm t/tm = 4
negative deadzone positive deadzone
system identification, continued
note phase lag
steady-state harmonic excitation, harmonic response
mag phase lag
due to nonlinearity, we use a biased sinusoid as input
form bode plot
wc =“corner frequency”
45o phase lag
(note: plot shows
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
r e m
***or actuator plant
(includes unit conversion)
proportional control (p-control)
r e m q
open-loop transfer function:
closed-loop transfer function:
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