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QP 1

This document outlines the End Semester Assessment (ESA) for the Control Systems course at PES University, Bengaluru, detailing various problems related to control system analysis and design. It includes tasks such as deriving differential equations, drawing signal flow graphs, calculating system stability, and designing compensators. The assessment covers a range of topics including transfer functions, steady-state errors, and controller types.

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46 views4 pages

QP 1

This document outlines the End Semester Assessment (ESA) for the Control Systems course at PES University, Bengaluru, detailing various problems related to control system analysis and design. It includes tasks such as deriving differential equations, drawing signal flow graphs, calculating system stability, and designing compensators. The assessment covers a range of topics including transfer functions, steady-state errors, and controller types.

Uploaded by

anynamewilldo489
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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PES University, Bengaluru

(Established under Karnataka Act 16 of 2013)

END SEMESTER ASSESSMENT (ESA) - Jan - May 2024

UE22EC241B - Control Systems

Total Marks : 100.0

1.a. For the mechanical system shown in Figure:


(i) Write the differential equations describing the system.
(ii) Draw the force-voltage analogous electrical circuit after writing the
corresponding electrical equations.

(8.0 Marks)

1.b. Draw the signal flow graph of the control system shown in figure and
determine the transfer function using Mason’s Gain formula.

(10.0 Marks)
Y (s)
1.c. Find using block diagram reduction technique.
U (s)
(7.0 Marks)

2.a. A closed loop system is represented by the differential equation


d 2c dc
2
+8 = 64 e;
dt dt
where, e=r-c;
c is the output displacement of the shaft and r is the input displacement of the
shaft. Assume zero initial conditions.

Determine :
a) undamped frequency of oscillations
b) damping ratio
c) percentage peak overshoot (8.0 Marks)

2.b. I. For servomechanism with open loop transfer function of a system is G(s) =
20(s+2)
and H (s) = 1 (3 Marks)
s (s+1) (s+3)

a) Determine the TYPE of the system.

b) What type of input signal results in a constant steady state error?

c) Calculate steadystate error.

II. Assuming r (t) = 0.1t . find the range of values of K for the steady state error to be
≤0.005 for the system with
K
G (s) = and H (s) = 1
s (s+1)
(7 Marks) (10.0 Marks)
2.c. Find the sensitivity of the steady state error due to change in parameter K.
K (7.0 Marks)
Given, G(s)= and H (s) = 1 . Assume unit step input.
(s+2) (s+4)

3.a. Build the Routh array and employ R-H criterion to determine the range of
K that stabilizes the closed loop system shown in figure.

(5.0 Marks)

3.b. Sketch the root locus for a nity negative feedback control system having open
loop transfer function.
K (s+1.5)
G (s) =
s (s+1) (s+5)
Show all the relevant calculations and mark them on the graph sheet. (10.0 Marks)

3.c. Determine the transfer function of a system with asymptotic dB plot shown in
fig.

(10.0 Marks)
4.a. The open loop transfer function of a unity feedback control system is
(1+4s)
G (s) =
s 2 (1+s) (1+2s)

a). Using Nyquist criterion, determine whether the closed loop system is stable, or
not.
b) Does the polar plot of the open loop transfer function cross the real axis? If so
find the frequency at which the plot crosses? (10.0 Marks)

K
4.b. A unity feedback control system has G (s) =
s (s+2)
Design a phase lead compensator to satisfy the following specifications:

a) Phase margin = 450

b) Steady state error for a unit ramp input is 5% of the velocity of the ramp.

Use frequency response approach. Sketch the plots for with and without
compensator. (10.0 Marks)

4.c. List the difference between P, PD . PI and PID controllers. Highlight any one
application of each one of them. (5.0 Marks)

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