dt u U x J + = 2 1 ) ( 2 1

OR Code No: 420258 IV B.Tech II-Semester Supplementary Examinations April/May 2004 ADVANCED CONTROL SYSTEMS (Electrical and Electronics Engineering) Max. Marks: 70 Answer any Five questions All questions carry equal marks ---

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Time: 3 hours

State when linear time invariant dynamical system are equivalent. Explain any two of them.

2. a) b)

State and prove two Liapunov stability theorems. Consider a system described by the following equations 

x1  - 3x1  x 2 

or ld

1.

x 2  x1 - x 2 - x 32 Investigate the stability of equilibrium state. 3. a) b)

Explain the linear system with full-order state observer with neat block diagram. Design a full-order state observer for the given state model.

 1 ; C  [1, 0] 1 

uW

 1 Given A   2

and given values are 1 = -5, 2 = -5 4. a) b)

Explain Tracking Problem. Explain Minimum fuel Problem.

5. a)

Find the optional control U*(t) for the system. *

x U

x(0) = 1 to minimize

nt

1 2 14 2 J  x (U )   u dt 2 20

b)

Derive the H J B equation in the continues time care.

Aj

6.

Formulate the optional control problem in terms of Hamiltonian.

7.

Explain the method of getting Bode plot using MATLAB Illustrate with examples.

8.

Explain how functions work in MATLAB with examples. ###