MASSACHUSETTS lNSTITUTE OF TECHNOLOGY
Dep;lrt,rrlent of Electrici~lErlgirlewirlg x ~ C~r~lpnt,er
d
SC.~PIICP
Sprir~g:Terrr~2007
Prol~lernSet 8
Problem 1: .X systerrl wit11 rrlirlor loop corrly)rns;Liion is shown l)el1>717
IC
(a) Do rre want H ( J )= I i s or H(s) = -!
S
(I)) Find Ii
S I I ~ tI hat
*.,
=
10" rps arlrl $hi = 45'.
( c ) TT11at is t,lle rlyr~arr~ic
t,racking:error
((1) yollr cllstorrlerrrTarlt,sU, = 10" rps,
~~-11ich
satifies all of tl~esecriteria.
10-"4'
Hl(s) =
10-"s
1
+
= 45" and
c2x
10-5at 10%rl)s. Clloose t,l~eH(s)
H~(s=
)
+
10r"s
1
lo-"<'
Cite as: James Roberge and Kent Lundberg, course materials for 6.302 Feedback Systems, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Problem 2: For each plant trarlsfer filr~ctior~
Gr,(s) in t l ~ eleft colilrrlr~(1-G), select t,lle "l)esti' c:orr~per~sat(x
trarlsfer fim<:tionG,(.s) frorr~the right cc~lil~rlr~
(a-g). ,4(irlitionally, specify t l ~ freqi~ency
e
or freqilen<:ies
rrl~erethe loop t,rar~sferfilr~ctior~
is ilnity. and give t,lle phase rrlargir~at tllese freqilencies. Sorrle of t l ~ e
t , otllers rrlaji rlot l)e I I S P ~ .
cornpensator t,rar~sferfilr~ctior~s
rrlaji t)e 1)est for I I I O ~ Ptllar~(me p l a ~ ~r%-hile
'4s wit11 all design ~SSIIPS.
\%-hatis .'t)est," is oft,er~a cornprornisr t)et,meen cornpet,ing consirlerations. Yo11
rrqi~irernentt)et,meen 30" and 90°, t l ~ e
shoi~lcl<:onsi(ierthe fc~llorrir~g
t,llree criteria: a. phase rr~argir~
rvidest l)an~lr%-i~lth
<:onsistent with illis range of phase rnargin, arlrl high open-loop gain at freqilen<:irs
t)elom <:rossover.
a.
1.
Gp(,s) =
10'
(J
1
G,:(s) = -
+ 1)(10-"s + 1)
S
1).
2.
G,,(s) =
Jiir x 10"
.s"lO-i,s + 1)
G,(s) = 7
c.
3.
G,:(,s) = 1Ofi
GI,(s) = f'-"
4.
G,,(J) =
lo7
1
.s(lO-"is
G,,(J) =
(0.1s + l)(O.l.s - l)(lo-i,s
G,:(s) =
+ 1)
(S
+ 113
10r"s
10-"s
+1
+1
f.
G,(.s) = 10
,s
G,(J) = 1o4-
0.1,s + 1
G,(.s) = 100
+ 1)
Jiijx 10"
6.
+1
11.
e.
5.
10-7,~
g.
G,:(s) =
10
,s2
Cite as: James Roberge and Kent Lundberg, course materials for 6.302 Feedback Systems, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Problem 3: For r l ~ esyst,ern sllorrr~I~elo\%-,
me are tolrl that the plant is
It is reql~iredillat the irlajnr loop crossover occllr close to
tllar~or eqllal t,o 60 rlegrees.
d,: =
100 rps \%-it,ha. phase rrlargirl greater
(a) d s s ~ ~ r n
for
e this first part the GI ( 3 ) = I l l , a (:nr~str~r~t,.
Find
(I)) No\%-assllrrle
= 0. Fir111a. series
~ O I I I I I P ~ I GI(,?)
S ~ ~ , ~tn~ Irleet
t,n Irleet tllese s~~ecifications.
the S I I ~ ~ S .
( c ) S l ~ ~ ~the
~ ~DC
o s gr1i11
e of G2( 3 ) is i11c:rer~sedfrorr~100 to 1000. tYhat, 11r%ppe11s
t,n
the phase rrlargirl
in t l ~ etwo cases (:onsi(iere(iin parts (a) and (I))? ((i) Using hI.4TLdU. fir111t l ~ eclosecl-loo11st,ep response for the syst,ern \%-henrrlirlor loop c o r n ~ ~ e n s a t i o ~ ~
is 11sec1. Corrlrrler~ton the ~ O I I I I S ~ ~nf
I ~ the
S S t\%-ndesigns.
Cite as: James Roberge and Kent Lundberg, course materials for 6.302 Feedback Systems, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].