design of mechatronic systems

BRUNEL UNIVERSITY

Design of Mechatronic Systems

EE5510 – Dr. Mohamed Darwish

Student Number: 0631151 Submission Date: 05/03/2012

0631151 – Page 1

Introduction

Mechatronics is a science of optimizing the design of electromechanical products and devices. The mechatronic system has four fundamental disciplines or on the other hand is a combination of four engineering field as follow: electronical, mechanical, computer science and information technology [1] in order to design and manufacture useful products.

The purpose of this assignment is to carry out some theoretical and simulation work using OrCAD-PSpice in order to understand the principles and applications of phase-controlled rectifiers, and recognise their effects on power network such as power factor and current harmonics, and finally to be able to compare the results between theoretical and practical work.

To build a controlled rectifier or a phase-controlled rectifier, the diodes in the rectifier circuit are replaced by silicon-controlled rectifiers (SCR). These circuits produce a variable DC output voltage whose magnitude is varied by phase control, that is, by controlling the duration of the conduction period by varying the point at which a gate signal is applied to the SCR [2]. The phase control is a procedure to control the rectifier output when we adjust the delay time of the gate pulse repeatedly since the gate pulse must be provided in order to conduct an SCR when the anode-to-cathode voltage becomes positive in the circuit.

Controlled rectifiers provide DC power for various applications, such as DC motor speed control, battery charging and high-voltage DC transmission. For frequencies less than 400Hz phase control is suited. The main weakness of phase control is radio frequency interference (RFI) which is due to the chopped half-sine wave produces strong harmonies that interfere with radio, television and other communication equipment [2].

Figure-1 shows a single-phase controlled rectifier feeding a resistive load which the theoretical and simulations needs to be done on it.

Figure-1

0631151 – Page 2

Theoretical Work

i. The Output Voltage (Vdc)

The average DC output voltage can be controlled from zero to its maximum positive value by varying the triggering angle, this value of DC voltage can be calculated as below:

𝑉𝑜𝑜𝑜(𝑎𝑎𝑎) =1𝜋�𝑉𝑚𝑎𝑚 sin 𝜃 𝑑𝜃 ⟹ 𝑉𝑜𝑜𝑜(𝑎𝑎𝑎) =

𝑉𝑚𝑎𝑚𝜋

[− cos 𝜃]𝛼𝜋𝜋

𝛼

Note that the peak load voltage (Vm) is equal to √2𝑣𝑖𝑛, which vin is given at 60V. The results of the theoretical output voltage (Vdc) at different triggering angles (a) are shown in Table-1.

Alpha 18° 36° 54° 72° 90° 108° 126° 144° 162° 180°

Vdc 52.70 48.86 42.89 35.36 27.01 18.66 11.13 5.16 1.32 0

0

10

20

30

40

50

60

0 18 36 54 72 90 108 126 144 162 180

Out

put V

olta

ge (V

dc)

Triggering Angle (°)

𝑉𝑜𝑜𝑜(𝑎𝑎𝑎) =𝑉𝑚𝑎𝑚𝜋

(1 + cos𝛼)

Table-1 – The theoretical output voltage (vdc) in terms of triggering angle

Figure-2 – The theoretical output voltage (vdc)

0631151 – Page 3

ii. The Power factor (P.F.)

In order to calculate the power factor (P.F.), iin is required as well as load and apparent power values. Since the iin value is calculating from the equation below:

𝑖𝑖𝑛(𝑟𝑚𝑟) =𝑉𝑖𝑛(𝑟𝑚𝑟)

𝑅�1 −

𝛼𝜋

+sin 2𝛼

2𝜋

Therefore the power factor can be expressed as:

𝑃.𝐹. =𝐿𝑜𝑎𝑑 𝑃𝑜𝑤𝑒𝑟

𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑃𝑜𝑤𝑒𝑟=𝑃𝑜𝑜𝑜(𝑎𝑎𝑎)

𝑆=𝑉𝑜𝑜𝑜(𝑎𝑎𝑎) × 𝐼𝑜𝑜𝑜(𝑎𝑎𝑎)

𝑣𝑖𝑛(𝑟𝑚𝑟) × 𝑖𝑖𝑛(𝑟𝑚𝑟)

From the equation which was subtracted, the results were calculated and are shown in Table-2.

Alpha 18° 36° 54° 72° 90° 108° 126° 144° 162° 180°

P.F. 0.774 0.680 0.554 0.417 0.287 0.175 0.089 0.034 0.006 0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 18 36 54 72 90 108 126 144 162 180

Pow

er F

acto

r (P.

F.)


𝑃.𝐹. =√2𝜋 (1 + cos𝛼)

�1 − 𝛼𝜋 + sin 2𝛼

2𝜋

Table-2 – The theoretical power factor (P.F.) in terms of triggering angle

Figure-3 – The theoretical power factor (P.F.)

0631151 – Page 4

iii. The Total Harmonic Distortion (THD)

The investigation into the harmonic distortion begins with a Fourier analysis of the fundamental component of the input current. Using Figure-1, which shows the input current waveform, the Fourier series component can be expressed as:

𝑎𝑛 =1𝜋� 𝑓(𝜔𝑡) cos(𝑛𝜔𝑡)𝑑(𝜔𝑡)(1)2𝜋

0

𝑏𝑛 =1𝜋� 𝑓(𝜔𝑡) sin(𝑛𝜔𝑡)𝑑(𝜔𝑡)2𝜋

0

Since in determining the THD this analysis is only concerned with the fundamental component (n=1), the above equations must only be used for n equal to one. The derivation of a1 and b1 is summarized below.

Since both a1 and b1 are magnitude and at the same frequency they must be changes rms values and their geometric mean must calculated.

𝐼1(𝑟𝑚𝑟) = �𝑎12 + 𝑏12

2×

1𝑅

The total rms value is calculated from:

𝐼𝑜(𝑟𝑚𝑟) = 𝑖𝑖𝑛(𝑟𝑚𝑟) =𝑉𝑖𝑛(𝑟𝑚𝑟)

𝑅�1 −

𝛼𝜋

+sin 2𝛼

2𝜋

Therefore the THD can be shown as

The results of the theoretical THD at different triggering angles (a) are shown in Table-3.

𝑎1 =𝑉𝑚𝑎𝑚2𝜋

(cos 2𝛼 − 1)

𝑏1 =𝑉𝑚𝑎𝑚2𝜋

[sin 2𝛼 + 2(𝜋 − 𝛼)]

𝑇𝑇𝑇 =�𝐼𝑜(𝑟𝑚𝑟)

2 − 𝐼1(𝑟𝑚𝑟)2

𝐼1(𝑟𝑚𝑟)

0631151 – Page 5

Alpha 18° 36° 54° 72° 90° 108° 126° 144° 162° 180°

I(t) 5.316 5.202 4.921 4.442 3.771 2.952 2.056 1.176 0.428 0

I(1) 5.301 5.108 4.675 4.005 3.161 2.243 1.365 0.641 0.166 0

THD 0.075 0.193 0.329 0.479 0.651 0.856 1.127 1.537 2.384 ∞

Alpha V(out) P.F. I(t) I(1) THD

18° 52.70 0.774 5.316 5.301 0.075

36° 48.86 0.680 5.202 5.108 0.193

54° 42.89 0.554 4.921 4.675 0.329

72° 35.36 0.417 4.442 4.005 0.479

90° 27.01 0.287 3.771 3.161 0.651

108° 18.66 0.175 2.952 2.243 0.856

126° 11.13 0.089 2.056 1.365 1.127

144° 5.16 0.034 1.176 0.641 1.537

162° 1.32 0.006 0.428 0.166 2.384

180° 0 0 0 0 ∞

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 18 36 54 72 90 108 126 144 162 180

Tota

l Har

mon

ic D

isto

rtio

n (T

HD)


Table-3 – The theoretical total harmonic distortion (THD) in terms of triggering angle

Figure-4 – The theoretical total harmonic distortion (THD)

Table-4 – The theoretical results in terms of triggering angles

0631151 – Page 6

Simulation Work

The circuit in Figure-1 has been simulated using OrCAD-PSpice software (Figure-5) and the results for output voltage (Vdc), the power factor (P.F.) and total harmonic distortion are shown in Table-5 and they are plotted in order to compare them with the theoretical results.

Figure-5 shows how the circuit was designed and also the triggering angles are defined using Parameter reference by naming it Alfa in order to be able to calculate them separately. Table-5 shows the results which are gained from OrCAD-PSpice software.

Alpha V(out) P.F. I(t) I(1) THD Efficiency

18° 52.711 0.977 5.2571 5.2164 0.125 0.978

36° 51.341 0.974 5.2402 5.1865 0.144 0.978

54° 47.124 0.950 5.1186 4.9980 0.221 0.979

72° 40.479 0.891 4.8113 4.5725 0.327 0.979

90° 32.071 0.788 4.2772 3.9130 0.441 0.979

108° 22.735 0.640 3.5104 3.0812 0.546 0.978

126° 15.462 0.500 2.6448 2.1770 0.690 0.975

144° 9.1579 0.346 1.8324 1.3152 0.970 0.970

162° 4.1788 0.195 1.0363 0.608 1.380 0.960

180° 1.0210 0.068 0.363 0.149 2.222 0.927

Figure-5

Table-5 – The simulation results in terms of triggering angles using OrCAD-PSpice software

0631151 – Page 7

0

10

20

30

40

50

60

0 18 36 54 72 90 108 126 144 162 180

Out

put V

olta

ge (V

dc)


Figure-7 – The simulation output voltage (vdc)

Figure-6 – The simulation output voltages (vdc) in terms of triggering angles

Figure-8 – The simulation power factors (P.F.) in terms of triggering angles

0631151 – Page 8

0

0.2

0.4

0.6

0.8

1

1.2

0 18 36 54 72 90 108 126 144 162 180

Pow

er F

acto

r (P.

F.)


First Harmonic Values (I1)

Figure-9 – The simulation power factor (P.F.)

Figure-10 – The simulation It(rms) in terms of triggering angles

Figure-11 – The simulation plot to get the values for I1 (first harmonic)

0631151 – Page 9

Figure-6 and 7 show the results for the output voltage which was taken from the simulation software and are to be compared with the theoretical results in the discussion. Also the results for the power factor are shown in Figure-8 and 9 which was calculated in OrCAD-PSpice software by dividing the values of real power by apparent power.

In order to get the values for It and I1 from the software, the average function for the input current has been used to get the values for It and also by getting the maximum value in Fourier function of the input current which is shown in Figure-11, the values for I1 were taken. Figure-12 shows the simulation result for the total harmonic distortion which is taken from Figure-10 and 11.

Figure-13 and 14 show the efficiency of the circuit in terms of triggering angle from the simulation which the results are also shown in Table-5.

0.0

0.5

1.0

1.5

2.0

2.5

0 18 36 54 72 90 108 126 144 162 180

Tota

l Har

mon

ic D

isto

rtio

n (T

HD)


Figure-12 - The simulation total harmonic distortion (THD)

Figure-13 – The rectifier circuit efficiency in terms of triggering angle

0631151 – Page 10

Practical Work

1) Circuit in Figure-1

The circuit in Figure-1 was connected in the SEP Lab in order to verify the theoretical work and be able to compare the theoretical and observed results. The results which are taken from the practical work are shown in Table-6 below.

The Figures-15, 16 and 17 are computed from the results which were taken in the lab showing the output voltage, power factor and total harmonic distortion respectively.

Alpha V(out) P.F. I(t) I(1) THD

18° 48.5 0.993 4.912 4.902 0.064

36° 45.5 0.970 4.827 4.742 0.190

54° 40.2 0.912 4.578 4.369 0.313

72° 33.2 0.812 4.134 3.751 0.463

90° 25.4 0.680 3.524 2.969 0.639

108° 17.3 0.524 2.737 2.088 0.848

126° 10 0.353 1.852 1.231 1.124

144° 4.57 0.193 1.014 0.565 1.490

162° 0.49 0.044 0.225 0.0648 3.325

180° 0 0 0 0 ∞

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

0 18 36 54 72 90 108 126 144 162 180

The

Effic

ienc

y


Table-6 – The practical results in terms of triggering angle

Figure-14 – The rectifier circuit efficiency in terms of triggering angle

0631151 – Page 11

0

10

20

30

40

50

60

0 18 36 54 72 90 108 126 144 162 180

Out

put V

olta

ge (V

dc)


0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 18 36 54 72 90 108 126 144 162 180

Pow

er F

acto

r (P.

F.)


Figure-16 – The practical power factor (P.F.)

Figure-15 – The practical output voltage (vdc)

Left – The trigger angle at 90o Right – The trigger angle at 0o

0631151 – Page 12

2) Circuit in Figure-18

The circuit shown in Figure-18 was connected in the lab in order to get the results for motor speed, motor voltage and the power factor in terms of triggering angle (at no load). The difference in this circuit is that there is no resistive load and circuit is performing at no load, instead a DC motor is connected to the circuit with a 100V supply a resistive load of 398 ohms which are shown in the figure below (Figure-18).

After running the circuit, the results were observed and taken into computer to same them, the taken results are shown in Table-7 and they are plotted in Figure-19, 20 and 21 for the motor speed, voltage and power factor respectively.

0

1

1

2

2

3

3

4

0 18 36 54 72 90 108 126 144 162 180

Tota

l Har

mon

ic D

isto

rtio

n (T

HD)


Figure-17 - The practical total harmonic distortion (THD)

Figure-18

0631151 – Page 13

Alpha Motor Speed V(out) P.F.

18° 882 48.9 0.857

36° 816 45.7 0.808

54° 690 40.5 0.739

72° 548 33.2 0.637

90° 376 25.2 0.537

108° 210 17.5 0.425

126° 58 10.3 0.306

144° 0 4.34 0.175

162° 0 0.026 0.064

180° 0 0 0

i. Motor Speed

By using a speed meter which was placed in the circuit, the motor speed was observed at every triggering angle, therefore the results which shown in Table-7 are plotted in Figure-19.

The maximum speed which was observed was at 934 rpm at 0° angle and also came to its minimum at angle of 144° which can be seen in the Figure-19.

0

100

200

300

400

500

600

700

800

900

1000

0 18 36 54 72 90 108 126 144 162 180

Mot

or S

peed

(rpm

)


Table-7 – The practical results in terms of triggering angle

Figure-19 – The motor speed in terms of triggering angle

0631151 – Page 14

ii. Motor Voltage

The motor voltage was also taken from the voltage meter device which was placed in the circuit, therefore the observed results were shown in Table-7 and Figure-20 shows them in a plot.

iii. The Power Factor

The power factor results which were observed in the experiment are plotted versus their triggering angle in Figure-21. The actual results are also available in Table-7 which already been mentioned.

0

10

20

30

40

50

60

0 18 36 54 72 90 108 126 144 162 180

Mot

or V

olta

ge (V

)


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 18 36 54 72 90 108 126 144 162 180

Pow

er F

acto

r (P.

F.)


Figure-20 – The motor voltage in terms of triggering angle

Figure-21 – The motor power factor (P.F.) in terms of triggering angle

0631151 – Page 15

iv. Torque/Speed Characteristics

In order to effectively design with D.C. motors, it is necessary to understand their characteristic curves. For every motor, there is a specific Torque/Speed curve and Power curve. In order to calculate the results for the torque and speed characteristics of the motor, then the triggering angle was set at 90° and the torque of the motor was calculated by multiplying the diameter of the motor (0.076m) with the difference in the load applied to the motor.

The results for each individual torque and its speed are shown in Table-8.

Torque (NM)

0.988

1.064

1.14

1.216

1.292

1.368

1.444

1.52

1.748

1.824

1.976

2.052

Speed (rpm) 340 328 310 294 276 258 240 198 116 94 30 0

The maximum value for the torque represents the point on the graph at which the torque is a maximum, but the shaft is not rotating and that is called the stall torque.

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300 350

Torq

ue (N

M)

Speed (rpm)

Torque/Speed Curve

Table-8 – The results for torque and speed of the motor

Figure-22 – The Torque/Speed characteristics of the motor at 90°

0631151 – Page 16

Discussion

As it can be seen in Figure-23 also according to the results which already are taken, very similar results were achieved in all methods of theoretical, simulation and practical. The value of the output voltage (Vdc) or Vout(rms) is just above 50V at angle of 18 degree and reduces to zero at 180, In fact, the time of thrysistor are controlled by the triggering angles when triggering angle is high , it means that Vout are 0 in period then it cause less value for output voltage of r.m.s.

The results for the power factor in the plot shows that the results for simulation and practical are similar and the ratio starts at 1 and goes to its minimum of 0 at 180 degrees. The theoretical results are slightly different, and it could be due to some miss-calculations.

0

10

20

30

40

50

60

0 18 36 54 72 90 108 126 144 162 180

Out

put V

olta

ge (V

dc)


Theoretical Simulation Practical

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 18 36 54 72 90 108 126 144 162 180

Pow

er F

acto

r (P.

F.)



Figure-23 – The comparison of the output voltage results

Figure-24 – The comparison of the power factor results

0631151 – Page 17

According to Figure-25 and the results from the tables, it can be seen that the results of theoretical and practical are almost the same and the simulation results are also similar with a bit of changes as the trigger angle increases. The starting value for total harmonic distortion is about zero in all methods and up to 90 degrees are still about the same value.

The efficiency in the theoretical work is at 1 or 100%, due to ideal conditions which output power and input power are equal and there is no loss. On the other hand the efficiency in the simulation was calculated and the results were shown in Figure-14 which varies from 97.9% to 96% and comes to its lowest value of 92.7% at angle of 180 degrees.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 18 36 54 72 90 108 126 144 162 180

Tota

l Har

mon

ic D

isto

rtio

n (T

HD)



0

0.25

0.5

0.75

1

1.25

1.5

0 18 36 54 72 90 108 126 144 162 180

The

Effic

ienc

y


Theoretical Simulation

Figure-25 – The comparison of the total harmonic distortion results

Figure-26 – The efficiency comparison

0631151 – Page 18

Conclusion

Voltage controller controls output voltage by changing triggering angle. In fact the triggering angle is the time period that avoid to pass current at the particular time so by increasing the period of time which avoids to pass the current, output voltage and rms will decreases and goes to its minimum value of zero at 180° which is a complete sinusoidal.

The output voltage and the output power are proportion to each other; a decrease in the output voltage will result in output power decrease in terms of triggering angle. All the values for which voltage and current and power are at their maximum when the triggering angle is at zero (0°) but on the other hand they are equal to zero at 180° due to no signal allowance to pass power factor.

Results show that the obtained and observed results which were collected from theoretical, simulation and practical works are very similar to each other and perhaps sometimes about the same, and the only differences in them are due to human errors and miss-calculations which occurs in the theoretical work or either miss-read the results from practical work. In total, it can be concluded that the results from theoretical or simulation are more accurate compare to the practical work.

References

[1] Devdas Shetty, Richard Kolk, “Mechatronics System Design”, Volume 1, PWS publish England, (1997), Pages 1-15.

[2] Single-Phase Controlled Rectifiers, Chapter 6, Pages 150-187.

[3] Dr. Mohamed Darwish, “Rectifier Circuits (AC/DC) Lecture Notes”, Brunel University, School of Engineering and Design, 2011-12, Pages 32-60.

[4] McCarty, M., Taufik, T., Pratama, A., and Anwari, M., "Harmonic Analysis of Input Current of Single-Phase Controlled Bridge Rectifier", Symposium on Industrial Electronics and Applications, IEEE, pp. 520-5242009, Kuala Lumpur, Malaysia, October 4-6, 2009.

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