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]
^{X}1 = ^{X}2 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 ^{T}P + 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 (3X^{2}+^ u^{2}) dtt_{f} = 1 sec.
OR
QI 0) Obtain the control law which minimizes the performance index. [16]
J =j (x^{2} + u^{2}) dt0For the system
^{x}1 |
0 |
1 |
^{x}1 |
0 |
|||
= |
+ |
||||||
^{X}2 |
0 |
1 |
^{X}2 |
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]
WWW