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AIN SHAMS UNIVERSITYFACULTY OF ENGINEERINGM un ufuct urin g E ng in e ering Pr o gr umMAIYF Junior
Attempt to answer the followins QUESTIONS* Assume an), missing data
Question (I) [t5 MarkJ
a- Find the equations of motion for a DC motor given that motor has an electricalconstant Kn, a torque constant K,, an armature inductance Lo, and a resistanceR,. The rotor has inertia J,, and viscous friction coefficient &. Also, find thetransfer function relating the input voltage to the motor position outputneglecting the inductance effect.
b- Use block-diagram algebra to determine the transfer function between R(s) and,Y(s) in the figure below.
R(s)
i" r..--....-*-----*i*ll
i
I
"\:."t".. \.L \ ''---w
.Ni*) *i-;il {*i---\'i-l
I
i
!_--*-*rY{s}
...1
N' Iiiir-rii _ _.,- I H1 l.{___i--_ii
Using Routh's stability criterion, find the range of K for which all the roots ofthe following polynomial are in the LHP:
Course Code: MANF 481 Time : 3.00 Hrs
The Exam Consists of Three Questions in Two Pages. fOfa, MarkS.. 40 Ma,rkS 1/2
s'+5so +10s3 +10s2 +5s+ K =O
P.T.O >
AIN SHAMS UNIVERSITY, FACULTY OF ENGINEERINGMANUFACTURING ENGINEERING PROGRAM, JUNIOR MANF
Course Code: MANF 481 Time : 3.00 Hrs
The Exam Consists of Three euestioni in two pagEl
Question (ID f$use the following general system block diagram below to solve:
w{s}i")
I
..""u .'* i--*--_*-r Yis)
. i *. \ i ^/ . I-.F, : , __" t:(sj i_--__l_,__-_s.+llj
a- Ignoring disturbance and noise,
D(s)= Ur*u,/ +K,,s where the plant
locate the poles ats = (-1,0),(-1,/), (-1,-.0.
b- For Grst = ,+t zo , D(s , = U! and unity feedback,
i- What is the system type and effor constant with respect to step & rampreference tracking?
ii- What is the system type and error constant with respect to step & rampdisturbance tracking?
D{s}
l
I
.g + V{s)) i+-r-"...J 1
Question (IID fiorSketch the root locus withshowing the (=9.5 and an:2
a- KL(s) = K(s +2)(s+l+ i)6+t- 11
Useful Formulas
, 180 + 36011- 1'r
Qr = --'- '',1 =1,2.....n-nn-m
Fr -f ,--L-/'t
L/ I
find the PID controller gains1
G1s; = -= and unity feedback wills'+1
respect to K for the following equations I+ KL(s)radls lines where:
b- rzls; = K(s +2)s(s+1)(s+5)(s+10)
Qdr,a"p =Zv, -ZO,- I 80 - 360(/ - 1)
QVr,o,, =ZO -Zw,+180+ 360(t -1)
1 80 + 360(/ - 1)
q
n-m(, aa db\I b__a_ l=0\ ds ds)
Co urse Examinatio n CommitteeDr. Mohamed Abdeluziz
Exam. Dste: I June 2013 /9.00 AM