Lab Report 1_EELE3314
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Running head: EELE3318L LAB FOR DC MACHINES
1
EELE3318L Lab for DC Machines LAB #5 Synchronous Motor
2
EELE3318L LAB FOR DC MACHINES
Results and Pre-Lab Calculations
- First Order System
Calculated c(t)
4(1-e^(-t))
Calculated Tr (s)
Calculated Ts (s)
2.2
3.9
Rise time: Tr = 2.2/a = 2.2/1 = 2.2s Setting line: Ts = 3.9/a = 3.9/1 = 3.9
- Second Order System
Calculated c(t)
(1-1.05409*(e^-t)*sin(3t+1.249))u(t)
Calculated ζ
Calculated wn (rad/s)
Calculated DC gain
kdc
Calculated P.O. (%)
0.316227766
3.16227766
1
35.09198072
ζ term: 2 ζ wn = 2 so ζ=1/wn=1/3.16227766=0.316227766
wn term: wn^2 = 10 so wn=10^(1/2)
kdc: kdc*wn^2 = 10 so kdc = 10/wn^2 Calculated P.O. (%): %OS = e^(−ζπ/√1−ζ^2) ×100 = e^(−(0.316227766*
π)/√1−(0.316227766)
^2) ×100 = 35.09198072
Calculated Tr (s)
Calculated Tp (s)
Calculated Ts (s)
0.40573666
1.047197551
4
Rise time: Tr = (2.16ζ+0.60)/ωn = (2.16*0.316227766
+0.60)/(3.16227766
) = 0.40573666
Peak time: Tp = π/(ωn(√1−
𝜁
^2)) = π/(3.16227766
*(√1−
(0.316227766
)
^2)) =1.047197551
Settling time:
Ts = 4/ζωn
= 4/(3.16227766
*0.316227766) = 4 - Procedure 1.2 Measured c(t)
Measured c(t)
4(1-e^(-t))
- Procedure 1.3 Measured parameters
3
EELE3318L LAB FOR DC MACHINES
Measured Tr (s)
Measured Ts (s)
2.19
3.91
- Procedure 2.4 Measured parameters
Measured Tr (s)
Measured Tp (s)
Measured Ts (s)
Measured P.O. (%)
0.4259
1.0592
3.5359
35%
- Procedure 2.5 Plot Pole-Zero Map
Measured Poles
Measured Zeroes
-1+3i
-1-3i
- Procedure 2.6 Find damping factor, natural frequency, and DC gain
Measured ζ
Measured wn (rad/s)
Measured DC gain kdc
0.316
3.16
1
- Procedure 2.7 Measure the influence of damping factor
Required ζ
Measured ζ
Measured Tr (s)
Measured Tp (s)
Measured Ts (s)
Mea
P.O
0ζ
0
NaN
NaN
NaN
Infi
1ζ
0.316
0.4257
1.0607
3.5365
2ζ
0.632
0.6117
1.2913
1.8947
3ζ
0.948
0.9811
2.7517
1.6541
4ζ
1.264
1.4831
4.4232
2.695
5ζ
1.58
1.973
6.1253
3.5855
6ζ
1.896
2.4468
8.1132
4.4289
7ζ
2.212
2.9113
9.6826
5.2512
8ζ
2.528
3.3695
11.2209
6.0618
9ζ
2.844
3.8244
12.7402
6.8655
10ζ
3.16
4.276
14.247
7.6643
- Procedure 2.8 Measure the influence of natural frequency
Required wn (rad/s)
Measured wn (rad/s)
Measured Tr (s)
Measured Tp (s)
Measured Ts (s)
Mea
P.O
0.5wn
1.58
0.8518
2.1184
7.0719
1.0wn
3.16
0.4259
1.0592
3.5359
1.5wn
4.74
0.2839
0.7061
2.3573
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4
EELE3318L LAB FOR DC MACHINES
2.0wn
6.32
0.213
0.5296
1.768
2.5wn
7.91
0.1704
0.4237
1.4144
Procedure
1. Step Response of First Order System - Code for Entire Section 1
5
EELE3318L LAB FOR DC MACHINES
6
EELE3318L LAB FOR DC MACHINES
1.1 Step response of G(s) - Lines 1 through 12 give us the step-response 1.2 Finding c(t) - Lines 1 through 5 and 15 through 21, give us the c(t) equation in terms of given values of
transfer function. Then in plotting the graph for c(t) step response, we find that it is identical to
the step response using the step() function of the transfer function.
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EELE3318L LAB FOR DC MACHINES
1.3 Finding Tr and Ts - Lines 1 through 13 give us the necessary information to use the stepinfo() function, which gives
us a rise time of 2.197s (approximately 2.2s) and settling time of 3.9121s (approximately 3.9s),
as shown in the screenshot below.
8
EELE3318L LAB FOR DC MACHINES
1. Step Response of First Order System - Code for Entire Section 1 Code 3.3 Calculate R2 and X2 from Locked 3.9 Analyzing Figure 1 and T vs speed Characteristics for an Induction Motor vs DC motor
From the torque vs speed characteristics for an induction motor, we can observe that these
characteristics are essentially linear between no load and full load. This is because the rotor
resistance is significantly higher than the rotor reactance in this range, so the induced torque,
magnetic field in the rotor, and rotor current increase linearly with increasing speed (or slip).
This can all be obtained from the equation for the torque-speed characteristics of an induction
motor, given by Tind = [3*VTH^2*(R2/s)]/{wsync*[(RTH+R2/s)^2 + (XTH + X2)^2]}. From
this equation we can clearly see that when the s value is very small (which it is in the linear
region), it means the R2/s terms become very large and the RTH and XTH+X2 terms become
9
EELE3318L LAB FOR DC MACHINES
negligible in comparison, so the equation becomes Tind = (3*VTH*s)/(R2*wsync). This
equation means that the induced torque changes linearly with s (which is changed by the speed in
the rotor relative to the synchronous speed), which is why this the induced torque and speed have
a linear relationship in this region in Figure 1. When comparing the torque vs speed characteristics for an induction motor with that of the
DC motor we can observe that the linear characteristics for the induction motor between no load
and full load are different than the torque-speed characteristics of a DC motor. In a DC motor,
the torque-speed characteristics should be ideally linear for a constant flux; however, in practice
they are not due to the presence of an armature reaction that impacts flux. When a load is
connected to a DC motor, a current flows through the armature and causes its own internal flux,
which distorts the flux as the load increase. This distortion results in an increase in armature
current as the load is increased, which results in a non-linear response of the speed of the
machine to an increase in torque. In an induction motor there is no armature current present
because it is a singly excited machine and there is only one magnetic field present. So, in this
region of a small s value (between full load and no load), the linear characteristics of torque and
speed are not distorted. 3. 10 Why is it not safe to run the induction motor on overload or overvoltage?
You should not run an induction motor on overload because when it is on overload it draws a current that is higher than its rated value. When it is running above its rated current the stator and rotor windings can be destroyed/burn up. Even though this overheating is occurring the machine may continue to run, but it will damage components while it runs.
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EELE3318L LAB FOR DC MACHINES
Conclusion
The purpose of this lab was to study the performance of the asynchronous or induction
motor. In an induction motor, a three-phase voltage is applied to the stator windings which
results in the creation of a rotating magnetic field in the stator that rotates at the synchronous
speed. The rotor is comprised of several bars all shorted together so that current can flow through
them. The rotating magnetic field of the stator rotates relative to the rotor, which results in an
induced current in the rotor, which goes through all the bars that are shorted. These induced
currents result in magnetic fields in the rotor that tries to oppose the field of the stator. In
accordance with Lenz’s law, the direction of rotation that would oppose the current induced by
the field of the stator would be in the direction of rotation of the stator. So, in opposing this
current, the rotor begins to rotate in the same direction as the stator. The rotor speeds up and
rotates at a value close to the synchronous speed, but never equal to it. If the rotor were to hit the
synchronous speed (a slip value of 1) the relative speed of the rotor bars and stator magnetic field
would go to zero, resulting in an induced voltage and induced torque of zero; so, the rotor would
slow down until it stopped rotating. The value of slip represents the speed of the rotor bars
relative to the magnetic field and should never reach zero or one, as previously discussed. This
value of slip is important, as it allows for the frequency and speed of the rotor to be found easily.
These are the basic principles of induction motors required to understand the findings in the lab. In one portion of the experiment, the DC test, no load test, and locked rotor test were
performed to obtain the equivalent circuit of the induction motor. The equivalent circuit obtained
was in line with theoretical expectations, as these types of motors typically have a very high
magnetizing reactance when compared to the stator and rotor reactance. Similarly, their core
resistance is also much higher than the stator and rotor resistances as found in the experiment. In
11
EELE3318L LAB FOR DC MACHINES
the second portion of the experiment, the impact on efficiency, power factor, and different types
of power (reactive, real, and apparent) when the load of the motor was increased from no load to
full load were observed. From these values the torque-speed characteristics at these various loads
were also determined. In terms of the impact on efficiency, power factor, and different types of
power with load, it was found that the input real power of the load increased a fair amount with
an increase in load. This increase in input real power resulted in an increase in the power factor
as the load was increased. Furthermore, this increase in both input and output power resulted in
an increase in efficiency with an increase in load. These findings are in line with the expected
theory. In terms of the slip of the rotor and frequency of the rotor, it was found that both
increased with an increase in load because an increase in load resulted in a decrease in the speed
of the rotor (from Pout=wm*T we see that increasing torque increases output power and
decreases speed). An interesting point here is that even though the slip increased from no load to
full load, these values for slip were still quite small, hitting a maximum value of 0.09389
(9.389%) at full load. This small value for slip is precisely the reason that the torque-speed
characteristics of the induction motor are linear in nature between no load and full load, because
the small slip results in an equation for Tind that only becomes dependent on constants and a
changing value for slip, meaning that the slip (which is dependent on the rotor speed relative to
the stator) and induced torque change proportionally to one another. This is shown by Tind =
(3*VTH*s)/(R2*wsync).
Overall, the performance of this lab was successful. The lab helped students to understand
the function of induction motors and observe their operation at different loads, as well as
understand how to model an equivalent circuit using obtained experimental results. In this lab it
was found that the operation of an induction is very similar to that of a transformer, because the
12
EELE3318L LAB FOR DC MACHINES
stator (primary winding) induces a voltage and current in the rotor (secondary winding), much
like a transformer. While they are similar, one major difference between the induction motor and
the transformer is that in the induction motor the speed/frequency of the stator and rotor are not
equal to one another, unlike the transformer.
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AUTO CONTROLDNO COPIED ANSWERS, SHOW FULL SOLUTION
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Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY