EXPERIMENT
Response of First Order System – (Sinusoidal
response)
1. EXCLUSIVE SUMMARY
The objective of this experiment is to
study the response of first order subjected to sinusoidal response. To achieve
this objective, the apparatus shown in the figure 2 was used. The maximum
temperature reached in the thermobath and thermowell are 50 ◦C and 42 ◦C
respectively. The minimum temperature reached in the thermobath and thermowell
are 32 ◦C and 36 ◦C respectively. The period of oscillation is 60 sec. Initial
amplitude and output amplitude of first order sinusoidal response is 9 ◦C and 3
◦C respectively. The amplitude of the system is 0.333. The frequency of
oscillation (ω) is 0.105 radian/sec. Time constant from amplitude ratio is
27.03 sec. the phase lag is 60 ◦C. time constant from phase lag is 3.05 sec.
2. INTRODUCTION
SINUSOIDAL INPUT- This function is represented mathematically by the
equations
Where
A is the amplitude and is the radian
frequency [1]. The radian frequency is related to the frequency f in cycles per
unit time by ω = 2πf. Figure 1 shows the graphical representation of this
function. The transform is
3. OBJECTIVE
To study the response of a first order system subjected to a
sinusoidal response.
4. Experimental Setup
 |
| First order sinusoidal set-up |
The apparatus consist
two thermometer. First thermometer is for thermowell and second is for
thermobath. Water is flowing continuously. Water level indicator is attached to
the vessel contacting heating coil.
5. Procedure
1. Start the clean water supply
by opening the inlet valve of heating bath and maintain constant water flow
through the heating bath. Keeping constant level in “Water head” indication
tube can ensure this.
2. Insert the thermometer and
thermo well in heating bath.
3. Ensue that cyclic timer is
set to @30 seconds on time and @30 seconds off time. Switch on Mains to heat
the water in heating bath.
4. After some time observe
sinusoidal response of the heating bath temperature on thermometer. The amplitude (temperature range) can be
changed by adjusting water flow rate and period can be changed by adjusting on
time, off time of the cyclic timer. (Period = On time + off time)
5. At steady state note
amplitude ratio and phase lag (Refer observations)
6. Results and Discussions
 |
Above figure shown the first order
sinusoidal response. Temperature of the bath and thermowell represent on the
y-axis and time on the x-axis. The maximum temperature reached in the
thermobath and thermowell are 50 ◦C
and 42 ◦C respectively. The
minimum temperature reached in the thermobath and thermowell are 32 ◦C and 36 ◦C respectively. The period of oscillation is 60
sec. Initial amplitude and output amplitude of first order sinusoidal response
is 9 ◦C and 3 ◦C respectively. The amplitude of
the system is 0.333. The frequency of oscillation (ω) is 0.105 radian/sec. Time
constant from amplitude ratio is 27.03 sec. the phase lag is 60 ◦C. time constant from phase lag
is 3.05 sec.
7. CONCLUSIONS
The maximum
temperature reached in the thermobath and thermowell are 50 ◦C
and 42 ◦C respectively. The minimum temperature reached in
the thermobath and thermowell are 32 ◦C and 36 ◦C
respectively. The period of oscillation is 60 sec. Initial amplitude and output
amplitude of first order sinusoidal response is 9 ◦C
and 3 ◦C respectively. The amplitude of the system is
0.333. The frequency of oscillation (ω) is 0.105 radian/sec. Time constant from
amplitude ratio is 27.03 sec. the phase lag is 60 ◦C.
time constant from phase lag is 3.05 sec.
8. REFERENCE
1. Coughanowr
D., LeBlanc S., ‘Process Systems Analysis and Control’, Mc-Graw Hill Science Engineering
Math, 2nd Edition, 2008, P-87-92.
1. Coughanowr
D., LeBlanc S., ‘Process Systems Analysis and Control’, Mc-Graw Hill Science
Engineering Math, 2nd Edition, 2008, P-92-97
