Gujarat Technological University 2010 M.E Control engineering - Question Paper

GUJARAT TECHNOLOGICAL UNIVERSITY
M.E Sem-I exam January 2010
Subject code: 710301 Subject ame: Control Engineering

Total Marks: 60
Instructions:
1. Attempt all ques..
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a)
where , g =
Design the deadbeat observer
10
(b) describe subsequent terms
a) Equilibrium point
b) Autonomous system
02
Q.2 (a) .
.
. explain the stability.
06
(b) explain full order state observer form. 06
OR
(b) Enumerate and explain the design factors of an optimum controller. 06
Q.3 (a) .
x(t) = Ax(t) + Bu(t)
y(t) = Cx(t) + Du(t). Prove that this state model is Bounded Input Bounded
Output stable if and only if H(t) = C.eat.B. satisfies.
06
(b) .
.
. Check the stability of system by using variable
gradient method.
06
OR
Q.3 (a)
Determine stability of the equilibrium state using direct method of
Lyapunov for linear autonomous system.
06
(b) How pole placement is decided in state feedback? 06
2
Q.4 (a) .
x(t) = Ax(t) + Bu(t)
y(t) = Cx(t) + Du(t). Prove that this state model is completely controllable,
completely observable and Bounded input Bounded Output stable then it is
asymptotically stable.
06
(b)
find equivalent observable companion form.
06
OR
Q.4 subsequent data for field controlled DC motor ( Ward Leonard System)
Rf= 400 ohm, Lf = 100 H, Ra= three ohm, KT=Kb= 1.5 newton-m/amp,
J = six kg-m2 , Kg= 50 volts/Amp, B= 12 newton-m per rad/sec. Design
state feedback using state feedback legal regulations so that poles are located at left
hand side of s plane.
12
Q.5 (a) Single input state formula is as under
Design an observer to located observer pole at -4.
08
(b) How Lyapunov function is used to estimate the transient? provide your
ans with justification.
04
OR
Q.5 (a)
Show that the stable linear continuous time system becomes unstable upon
the introduction of sampler and ZOH.
06
(b)
obtain 2 dimensional observers with Eigenvalues -2, -2.
06
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Earning:   Approval pending.