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Posted Date: 23 Apr 2012 Posted By:: praveen Member Level: Bronze Points: 5 (Rs. 1)
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2011 Jawaharlal Nehru Technological University, Anantapur B.Tech Electrical and Electronics Engineering 4 th year ADVANCED CONTROL SYSTEMS Question paper
IV B.Tech II Semester Examinations,APRIL 2011
ADVANCED CONTROL SYSTEMS
Electrical And Electronics Engineering
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. Write short notes on the following for optimal control system design:
(a) Minimum-Time problem.
(b) State regular problem.
(c) In nite - time state regulator problem. [6+6+4]
2. Describe the minimization of functions in the optimal control system design.
[16]
3. A linear time invariant system is described by the following state model. Obtain
the canonical form of the state model: [16]
x_ 1
x_ 2
=
0 1
??4 ??5
x1
x2
+
0
1
u and y =
1
3 ??1
3
x1
x2
4. A system has a nonlinear element, with describing function, KN = (1=X) < ??450
in cascade with, G(j!) = 10
p
2
j!(1+j0:5!) . Determine the limit cycle of the system. [16]
5. Consider the system de ned by x_ = Ax + bu
y = Cx
where A =
2
4
??1 0 1
1 ??2 0
0 0 ??3
3
5 ; B =
2
4
0
1
1
3
5 ; C =
1 1 1
Transform the system equations into the controllable canonical form. [16]
6. A single input system is described by the following state equation
x_ =
2
4
??1 0 0
1 ??2 0
0 1 ??3
3
5 [x] +
2
4
10
1
0
3
5 [u].
Design a state feedback controller which will give closed loop poles at ??1j2; ??6.
[16]
7. A simple servo is described by the following equations
Reaction torque = c + 0:5 _c
Drive torque = 2 sign (e + 0:5e_)
e = R ?? c
e(0) = 2 and e_(0) = 0
Construct the phase trajectory using the delta method. [16]
4
Code No: 07A80202 R07 Set No. 1
8. Prove the linear system x_ = Ax is globally asymptotically state at the origin if and
only if for any given symmetric positive de nite matrix Q, there exists a symmetrix
de nite matrix `P' that satis es the matrix equation.
ATP + PA = ??Q. [16]
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