Code:
AE11 Subject:
CONTROL ENGINEERING
Time: 3 Hours Max. Marks: 100
NOTE: There are 9 Questions in all.
· Question 1 is compulsory and carries 20 marks. Answer to Q. 1. must be written in the space provided for it in the answer book supplied and nowhere else.
· Out of the remaining EIGHT Questions answer any FIVE Questions. Each question carries 16 marks.
· Any required data not explicitly given, may be suitably assumed and stated.
Q.1 Choose the correct or best alternative in the following: (2x10)
a. Consider the function 
where F(s) = Laplace transform of f(t). The final value of f(t) is equal to
(A) zero (B) infinite
(C) one (D) none of the above
b. For type one system, the steady-state error due to step input is equal to
(A) infinite (B) zero
(C) finite constant (D) none of the above
c. Consider the
equation 
.
The equation has _____ roots in the right half of s-plane.
(A) one (B) two
(C) three (D) four
d. The transfer function of a phase-lag controller is given by
(A)
(B)
(C) 
(D)
e. The transfer function of a P-D controller is
(A)
(B)
(C) 
(D)
None of the above
f. The Nyquist plot of a system passes through the (–1, j0) point, the gain margin of the system is
(A) greater than 1 (B) less than 1
(C) zero (D) Equal to 1
g. For type-2 system, the steady-state error due to ramp input is equal to
(A) zero (B) finite constant
(C) infinite (D) None of the above
h. Given the matrix
, the
eigen values of A are
(A) –1, –2, –3 (B) –1, 2, –3
(C) 0, 0, –6 (D) –6, –11, –6.
i. For a tachometer
if 
is
the rotor displacement, e(t) is the output voltage and Kt is the
tachometer constant, then the transfer function is defined as
(A)
(B)
.
(C) 
(D)
.
j. The system
matrix of a continuous time system is given by 
, the characteristic equation is
given by
(A) 
(B)
(C) 
(D)
Answer any FIVE Questions out of EIGHT Questions.
Each question carries 16 marks.
Q.2 a. Define the transfer function of a linear-time invariant system in terms of its differential equation model. What is the characteristic equation of the system. (8)
b. (i) Explain Mason’s gain formula for signal flow graph.
(ii)
For the electrical circuit shown in Fig.1 find the transfer function 
(8)
Q.3 a. State and explain the Nyquist stability criterion. (6)
b. Consider the unity feedback system whose open-loop transfer function is
. Using the Nyquist
stability criterion, determine the critical value of ‘K’ for stability. (10)
Q.4 a. Define the terms
(i) bounded-input, bounded-output (BIBO) stability.
(ii) asymptotic stability (8)
b. (i) Discuss Routh’s stability criterion.
(ii) The characteristic equation of a control system is given by
Determine the stability of the system. (8)
Q.5 a. Reduce the feedback system given in Fig.2 to an equivalent unity feedback system (8)
b. For the standard second order system with closed loop transfer function as
derive the
expression for unit step response, assuming it to be an underdamped system. (8)
Q.6 a. Consider the system shown in Fig.3.
Sketch the root loci and show that a part of the root locus is circular for 
(12)
b. Explain why root locus always orignates from an open loop pole ad terminates at open loop zero or infinity. (4)
Q.7 Determine the values of K and k of the closed-loop system shown in Fig.4 so that the maximum overshoot in unit-step response in 25% and the peak time is 2 seconds. Assume that J = 1 Kg – m2. (16)
Q.8 a. Sketch
the polar plot of the transfer function given as 
with K=5. Determine the gain
margin and phase margin. (12)
b. Discuss the effect of increasing the value of K to 10. (4)
Q.9 Write short notes on any TWO of the following:
(i) Cascade Lag-lead compensation
(ii) Hydraulic actuators
(iii) Synchros (16)