Jawaharlal Nehru Technological University Anantapur 2011 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: three hours Max Marks: 80
ans any 5 ques.
All ques. carry equal marks
1. Write short notes on the subsequent for optimal control system design:
(a) Minimum-Time issue.
(b) State regular issue.
(c) Innite - time state regulator issue. [6+6+4]
2. define the minimization of functions in the optimal control system design.
[16]
3. A linear time invariant system is defined by the subsequent state model. find
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 one 1

Transform the system equations into the controllable canonical form. [16]
6. A single input system is defined by the subsequent state formula
x_ =
2
4
??1 0 0
1 ??2 0
0 one ??3
3
5 [x] +
2
4
10
1
0
3
5 [u].
Design a state feedback controller which will provide closed loop poles at ??1j2; ??6.
[16]
7. A simple servo is defined by the subsequent equations
Reaction torque = c + 0:5 _c
Drive torque = two sign (e + 0:5e_)
e = R ?? c
e(0) = two 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 provided symmetric positive denite matrix Q, there exists a symmetrix
denite matrix `P' that satises the matrix formula.
ATP + PA = ??Q. [16]

Earning:   Approval pending.