Gati Shakti Vishwavidyalaya, Vadodara
End-Semester Examination, April2025
Duration :2 Hours Maximum marks :50
Programme : B.Tech EE (Rail Engineering) Semester :1V
Course Title :Linear Control Systems Course Code :EEL213
Question Description Marks
No.
1. (a) Determine the transfer function C(s)/R(S) for the feedback control 5+5
system shown in Fig. 1 using block diagram reduction technique.
H\
Figure 1
(b) Draw signal flow graph of system shown in Fig. 1 and verify the
transfer function C(s)/R(s) obtained in part (a).
2. (a) Determine the transfer function of the system shown in Fig. 2. If this 5+5
system is applied with the unit step input determine and sketch the
output of the system. Calculate delay time (t), rise time (t,), peak time
t,),settling time (ts), and peak overshoot (M,).
R(s) E(s) 25 C(s)
s(s + b)
Figure 2
(b) AP-D Controller 1+ Kps is to be designed with the system G(s) =
1000V2
s(s+ 10)? Determine the value of Kp such that this controller provides the
Phase Margin of 45° at the Gain Crossover frequency w = 10rad/sec.
3. (a) Consider the closed-loop system shown in Fig. 3. Using the Routh 5+5
stability criterion, determine the range of K for stability. Assume that
K>0.
R(s) s-2
C(s)
(s + l(s + 6s + 25)
Figure 3
K(s+3)
(b) The system is defined by forward path gain G(s) = s(s+1) Sketch
the Root Loci of it'sclosed loop system with unity negative feedback as
the gain K is increased. Specify breakaway point, centroid, angle of
asymptotes. Determine the range of K for system to be stable.
4+ (a) The Bode plot of atransfer function G(s) is shown in the Fig. 4. 5+2+3
(GaidB)n 40
32
20
Figure 4
100
8 w (rad/s)
The gain 20log|G(s)) is 32 dB and -8 dB at 1 rad/s and 10 rad/s
respectively. Determine G[S), phase plot for all w, Gain-crossover
frequency, Phase-crossover frequency.
(b) Consider a closed-loop control system with unity negative feedback
and KG(s) in the forward path, where the gain K=2. The complete
Nyquist plot of the transfer function G(s) is shown in the Fig. 5. Note
that the Nyquist contour (region of interest) has been chosen to have
the clockwise sense. Assume G(s) has no poles on the closed right-half
of the complex plane. Determine the number of poles of the closed-loop
transfer function in the closed right-half of the complex plane.
PTO
Im G(s)
Figure 5
+ Re G(8)
0.5
(c) The Nyquist plot of a stable open-loop system G(jw) is plotted in the
frequency range 0sw<0 as shown in Fig. 6 which is found to intersect
a unit circle with center at the origin at the point P = -0.77 - 0.64j. The
points Qand Rlie on G(jw) and assume values Q= 14.40+ 0.00j andR
=-0.21 + 0.00j.Determine the phase margin (PM) and the gain margin
(GM) of the system.
Im(G(jo))
Unit circle
1
R
w-0 Re(Gja))
Q
Figure 6
G(ju)
5 (a) Obtain the transfer function Y,(s)/U,(s) of the mechanical system 5+5
shown in Fig. 7, where u1 and uz are the inputs and y1 and yz are the
outputs.
Figure 7
(b) Consider the transfer function of a compensator G(s) = 10(5+2)
S+20
Plot
the pole Zero in S-plane and determine whether it is Lag or Lead
compensator. Determine at which frequency the maximum or minimum
phase willbe provided by this compensator. Also determine the phase
value at maximum frequency.
