# B.E. (Instrumentation and Control) ADVANCED CONTROL SYSTEMS (Elective – I) (2008 Pattern) (Sem. – I)

Time: 3 Hours]                                                                                             [Max. Marks : 100

Instructions to candidates:

1)            Answer any three questions from each Section.

2)            Assume suitable data, if necessary.

3)             Pigures to the right indicate full marks.

SECTION – I

QI) Attempt following:

a)            Explain Inherent and intentional nonlinearities with examples.                

b)            Determine the Describing function of the ideal relay nonlinearity. 

OR

Q2) Attempt following:

a)            What is phase plane and what are the characteristics of phase plane method? 

b)           Explain saddle point and stable point with neat sketches and suitable examples.        

Q3) Attempt following:

a)            Explain stability analysis by describing function method.                         

b)            Consider a nonlinear system described by                                                  

X1 = X2 x = -x –

22

Investigate whether the system is stable or not.

OR

Q4) Attempt following:

a)             Explain positive definite, negative definite and semi definite functions with examples.                                                                                                                               

b) A second order system represented by x=Ax where                                       

 0 1 -1 -1

A=

Assuming matrix Q to be identity matrix, solve for matrix P in the equation A TP + PA = – Q.

Use Liapunov theorem and determine the stability of the system. Write the Liapunov function V(x).

Q5) Attempt following:

a)            Explain in brief direct and indirect model reference adaptive control with block diagram.                                                                                                      

b)           Discuss the essential aspects of an adaptive control system.                     

OR

Q6) Explain Lyapunov and MIT rule approaches for designing of Model reference adaptive controller.                                                                                                          

SECTION – II

Q7) Explain indirect self tuning regulator using least squares estimator for Ay (t) = B (u (t) + v (t))

where y is the output, u is the input of the process, and v is a disturbance. Also give the algorithm for obtaining it.                                                                                       

OR

Q8) Consider the process                                                                                        

G(sy 1

s(s+a)

Where a is an unknown parameter. Assume that the desired closed loop system is

2

r ( n\-____________________________

sr +2l>cos+co

Construct continuous indirect self tuning algorithm for the system.

Q9) A first order system is described by the differential equation                            

x (t)=2 x (t) + u (t)

It is desired to find the control law that minimizes the performance index

1 tf 1 J=- j (3X2+^ u2) dttf = 1 sec.

OR

QI 0) Obtain the control law which minimizes the performance index.                   

J =j (x2 + u2) dt0For the system

 x1 0 1 x1 0 = + X2 0 1 X2 1

QII) Attempt following:

a)      Explain requirements for formulation of an optimal control problem.

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b)      Discuss performance measures for optimal control problems. 

OR

Q12) Write short notes on:

a)        Applications of Adaptive control.                                                                   

b)        Optimal control applications.                                                                           

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