value xo =system .is — -] Bu where

5. (a) Prove that a system is completely controllable if and only if its controllability (4)
matrix is full rank.

(0) Solve .'h(t) = where (5)

w= (3 4)

6. (a) Prove that zeros of a closed loop transfer function are unaffected with a state (4) feedback
controller.

b Determine the controllable and uncontrollable modes of the system represcntcd (5)

by
._{ -2 1 5 5
2-1 ‏۶إ وہ‎ 1
y=(01 )2
Also obtain the controllable sub realization of the systenl.

PART C(MOdules V and VI)

7. (a) Explain the optimality criterion for choosing observer poles. (4)

(b) Consider the system + = A.c + Bu. y Cr where, (8)

२७०० 3)" (1). ८=(\ 9)
20.60 3

By using state feedback control technique it is desired to have the closed loop poles
at s —1.8 + 32.4. Assume that the desired eigen values of the observer matrix arc VI
1 = --8. Design an observer-controller.

8. (a) With the help of a suitable example explain any one companion form for ۸۱۱۱۸10 (4)
systems.

(b) Explain the direct transfer function design procedure of observer-controller. (8)

9. (a) Show that in an observed state feedback control system, the observer design and (4)
the statc feedback design can be carried out, independently.

(b) Consider the system Ax + Bu, y = CT where, (8)

५-10 -11 அணா
0 1-6

Design a rcdutcd order observer so that the observer poles are at 8
= -2 + j3.46-

Page 2