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