B.Tech-B.Tech Electrical Engineering 6th Sem 6EE 1 Modern Control Theory 6E3109(Rajasthan Technical University-2012)

6E3109
B.Tech VI Sem. (Main/Back) Exam. April-May, 2012
Electrical Engg.
6EE 1 Modern Control Theory

Time: 3 Hours Maximum Marks: 80 Min. Passing Marks : 24

Unit-I

1 (a) Give the Condition of liner dependency over the field of Rational numbers of set of vectors. Also Explain how it is different from Real numbers. [10]

(b) Explain the Concept of Linear vector space Linear Independence.  [6]

OR

1 (a) Given:-

 

 

 

 

 

Find the Representation of x with respect to the basis  [10]
{Y, XY, X²Y}

(b) Explain the Concept of Linearity and Causality.   [6]

Unit- II

2 (a) A system is describe by the state equation

 

 

 

 

 

Using Laplace Transform Technique. Transform of state equation into a set of Liner equation in the from

 

 

(b) Explain the difference between Modern Control Theory and Conventional Control Theory  [6]

OR

2 (a) Construct the state model for a system characterized by the differential equation   [8]

 

 

 

(b) Explain the following terms:-

(i) State space equation [4]

(ii) State vector [4]

Unit-III

3 (a) A feed back system is characterized by the closed loop transfer function

 

 

 

 

 

 

Draw a suitable signal fliw graph and there form construct a state model of the system. [10]

(b) Derive state space representation using canonical variable's equation [6]

OR

3 (a) For the state equation

 

 

 

 

 

 

3 (b) Derive and state the equation for Jordan canonical form [6]

Unit-IV

4 (a) What is State Transition Matrix ? State and derive the properties of state transition Matrix. [8]

(b) Explain the concept of controllability and observablity and compute these in corporate with State transition Matrix. [8]

OR

4 (a) State and Derive the Ackermari's formula for state equations [8]

4 (b) State and Derive the equations for pole placement by state feed back with nth order state model [8]

Unit-V

5 (a) Given

Z [x(k)] = x (z)

Find the z- transform of

 

 

 

 

(b) Find the Z transform (Inverse) of the following - [8]

 

 

 

 

OR

5 (a) State and explain the initial and final value Theorem for Z-transform [8]

(b) Find the Z- domain transfer function of following S- Domain transfer functions - [8]

 

 

 

 

 

 

Earning:  ₹ 11.00/-