MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Depart,rnent of Electrical Engineering ar~rlCornpllt,er Science
Spring Term 2007
Lat) 1C
Introduction
T l ~ egoal of t l ~ i slal~orat,oryis t l ~ edesign of a. posit,ion cor~trolloop t , l ~ r o ~ lthe
g l ~ use of t,lx rr~at,hernati<:al
rr~oclelol]taine(i for t,lx servorr~ecl~ar~isrr~
in la11 1.1. Measl~rernentsare rr~arlein t l ~ e1al)oratorj~t,o verify
reslllts ~:al~:l~laterl
in the prelr~l).
Equipment
For this lal). you will need to pick 111) the follorrir~git,err~sfrorr~the e q ~ ~ i p r n r desk:
nt
five UKC c:al)les, 3 BNC
in the prelal).
T-conne<:tors,ar~rlt,lx capacitor illat you <:al<:~~laterl
Measurements
Configure t l ~ eservo-rnechanisrr~as she\%-n l~elo\%(rerr~ernt)erthe fly\%-heel.)Use the ' . S l l ~ r ~ ~ rA~ iIr ~ g/I COIII~
sect,ior~on the left side of t,lx cor~trolt ~ o x . Set its srrit<:hes to the "flat" sett,ir~gsand rlial in a
~~ensat,or''
<:ornpensatorgain va111e of 8.0.
mput
compemator
power amp
G,
-21-/17
motor
1;"
*
I.,
I
0"
I, 7 5
(3)
1. Drive t l ~ esystern i n p ~ wit11
~ t a s t j r ~ a r r ' v~nor'of voltage ar~rlrrleasure the percent oversl~ootand rir~gir~g
freq~lency)of t,l~en ~ ~ t p shr%ft
l ~ t , 110siti011.Find t,lx vahles of and d,,that
freq~lency(rlarr111e(ir~at,l~ral
corresponrl to your rneas~~rernents.
Corr~pareyour experimental ar~rl~ : a l ~ : ~ ~ lV?%~IIPS.
a t e ( i Be sure thr%t
yo11 d011't river-drive and saturate the systerrl ~vhiletaking your rneas~~rernents. <
2. Drive t l ~ esystern wit11 a sfne ii~avf!of voltage and fir111the peak r r ~ a g r ~ i t ~(gain)
~ r l e of the closecl loop
response and t l ~ efreqllency a t rn11ic:h t l ~ i speak o<:cllrs. Ue very careful r ~ o tto over-drive the syst,err~,as
a srr~alli n p ~ rnagnit~lde
~t
is reql~ireclfor t l ~ i srneasllrernent. Find the va111es of ar~rlw, t l ~ a ct orrespon(i
to yollr rneasllrernents. Cornpare yollr experimental and calc~llat,e(l
V?%~IIPS.
<
p1.ace
. a. <.apacitorof
.. .
t l ~ eva111e r r l ~ i c lyo^^
~ <:al<:~~laterl
across t,lx "(;jco,j7'
terrr~ir~als
nf t,lx ( : ( > I I I ~ I ~ I r%r~d
Is~%~o~
rrlove it,s s\%-it,chto t,lx "lea~l" set,ting. T l ~ esyst,ern is rlow configllrr(i with a. ~~roportional
p111s clerivative
<:ontroller. (Plus an a(irlitiona1 pole rn11ic:h is fast e11o11gl1t,o ignore.)
1. Repeat t l ~ eal~overr~eas~~rerr~er~t,s
(tirne rlorr~air~
ar~rlfreqllency (lornain) on t l ~ eP + D cornpensaterl sys- rrleasure
the ring freq~lencyof t,lx step response. n l ~ y
tern. Not,e t l ~ a it
t is q ~ ~ icliffi<:~~lt
te
to ac<:~~rately
t
is t l ~ i sso? \ I e a s ~ ~ rthe
e ~ l e r c e r ~nvers1100t
x ~ (t,lx
i tirr~eto 11eak. You \%-illnotice t,l~att l ~ err~eas~~recl
( i 1)asecl on t l ~ e and d,,,of a pole pair. IThy? Use
va111es of Po and AI,, rlo not rrlat,cl~the e x ~ ~ e c t eva111es
\IAITL.lU to plot the st,ep and freq~lencyresponses of t,lx rno(iele(1 systern wit11 t l ~ eP + D controller.
Horr rlo t,l~ese~ ~ S I I O I I Sc01r111r%re
~S
tn yn11r IIIP?LSIIIP~res111tsY
<
Cite as: James Roberge, course materials for 6.302 Feedback Systems, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
2. Drive t l ~ esyst,err~wit11 a. triangle wave of volt,age and rrleasllre t l ~ esteady stat,e error t,o a rarnp i n p l ~ t .
By llsirlg the slope of t,lle i r ~ p l ~rarnp.
t
your error rrleasllrerrlerlt to t,llat \%-llich\%-olllrlt)e
r~orrr~alize
ot)t,ainecl frorr~a llr~itsize rr%rrlp.Note illat t,lle errnr is the S I I ~ I Iof the irq)llt
0,. Use tlle '.Char111e1
on t l ~ eoscilloscope t,o ft%cilitateillis rneas~~rernent.
\1at,hn fim<:tior~
Write Up
The \%-rit,e1111 for this la11 sl~ol~lrl
1)e prepared in t l ~ esarrle spirit as last meek's: short, sirnple. arlrl inforrrlal.
Useful Formulae
Cite as: James Roberge, course materials for 6.302 Feedback Systems, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].