# 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.                [8]

b)            Determine the Describing function of the ideal relay nonlinearity. [10]

OR

Q2) Attempt following:

a)            What is phase plane and what are the characteristics of phase plane method? [8]

b)           Explain saddle point and stable point with neat sketches and suitable examples.        [10]

Q3) Attempt following:

a)            Explain stability analysis by describing function method.                         [6]

b)            Consider a nonlinear system described by                                                  [10]

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.                                                                                                                               [6]

b) A second order system represented by x=Ax where                                       [10]

 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.                                                                                                      [8]

b)           Discuss the essential aspects of an adaptive control system.                     [8]

OR

Q6) Explain Lyapunov and MIT rule approaches for designing of Model reference adaptive controller.                                                                                                          [16]

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.                                                                                       [16]

OR

Q8) Consider the process                                                                                        [16]

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                            [16]

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.                   [16]

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.

[W]

b)      Discuss performance measures for optimal control problems. [9]

OR

Q12) Write short notes on:

a)        Applications of Adaptive control.                                                                   [9]

b)        Optimal control applications.                                                                           [9]

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