THIS PPT IS SO USEFUL TO KNOW ABOUT THE SERIES RLC CIRCUIT AND IN THIS WE CAN ALSO HOW THE RESPONSE WILL BE THERE FOR A UNIT STEP RESPONSE AND I ALSO KEPT A MATLAB CODING AND GRAPHS FOR THE SERIES RLC CIRCUIT

1. Academic Year : 2019 - 2020
II Year II - Semester
Control Systems
CASE STUDY 1 ON
UNIT STEP RESPONSE OF A SERIES RLC
CIRCUIT
Faculty:
Mr. B .Siva Rama Rao
Associate Professor,
EEE Dept., REC
Presented by :-
Pediredla Sanjay kumar 18981A0241
1

2. Topic
• Unit step response of a series RLC circuit

3. Contents:
• Introduction
• Types of signals
• Unit step signal
• Series RLC circuit Derivation
• mat lab code & Output graphs
• Conclusion
• References

4. Introduction
• System response is divided and studied in two different states.
• Transient response and steady state response.
• the response of the control systems can be analyzed in both the time
domain and the frequency domain.

5. Types of test signals:
• Step signal : the signal whose value changes from one level (usually
zero) to another level A in zero time.
• Ramp signal: it is a signal which starts at a value of zero and
increases linearly with time .
• Parabolic signal : It gives the idea about how the system will respond
along with acceleration.
• Impulse signal: a unit impulse is defined as a signal which has zero
value everywhere expect at t=0,where its magnitude is infinite .
5

6. Graphical representation of signals:
Step signal Ramp signal
Parabolic signal Impulse signal

7. Unit step signal
• The step signal defines the sudden change in properties of actual
signal. It is being used to see the transient response of system as it
gives you the idea about how the system reply to interruption and
somehow the system stability.
• r(t) = Au(t)
Where , u(t) = 1 for t > 0
= 0 for t < 0
Laplace transform of r(t) = R(s) =A/s
For unit step input A =1

8. Derivation
q
Cdt
dq
R
dt
qd
LV
q
Cdt
qd
L
dt
dq
RV
equationabovein
dt
dq
ingsubstituti
idt
Cdt
di
LiRV
idt
C
V
dt
di
LV
iRV
VVVV
c
l
R
cRl
1
1
1
1
2
2
2
2










Using Kirchhoff's voltage law,
Input is voltage V
Output is taken as charge across capacitor.

9. 1)(
)(
1
1
)(
)(
]
1
)[()(
)(
1
)()()(
.'
)(
1)()(
)(
2
2
2
2
2
2







RCsLCs
C
sV
sq
functiontransfer
C
RsLssV
sq
C
RsLssqsV
sq
C
sRsqsqsLsV
sidesbothontransformslaplacetaking
tq
Cdt
tdq
R
dt
tqd
LtV

10. Mat-lab code

11. output

12. Mat-lab code:

13. output

14. Mat-lab code:

15. output

16. Conclusion
• The typical test signals judge the performance and working of a
control system in the time domain analysis.
• We discussed the four times of signals that are impulse ,step , ramp
and parabolic. These all have different graphs and different effects.
• These typical signals determine the behaviour and nature of a
dynamic system.

17. References
• Control systems engineering by I.G.NAGRATH & M.GOPAL
• http://engineering.electrical-equipment.org/panel-building/typical-
test-signals-in-time-domain-analysis.html
• http://www.electronicsengineering.nbcafe.in/standard-test-signals-
of-control-systems/