lab 3 cs exp 1

8/7/2019 lab 3 cs exp 1

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DEPARTMENT OF MECHATRONICS ENGINEERING

MECHATRONICS ENGINEERING LAB III

MCT 3229

EXPERIMENT 1

(DYNAMICS RESPONSE OF FIRST ORDER AND SECOND

ORDER SYSTEM)

SECTION 2

GROUP MEMBERS :

1) FITRI BIN KHOSIM ( 0818449 )

2) MOHD SYAHID B MOHD ILIAS ( 0816661 )

3) ABDUL FATAH MOHAMAD ( 0535673 )

DATE OF EXPERIMENT : 24 FEBRUARY 2011

DATE OF SUBMISSION : 03 MARCH 2011

8/7/2019 lab 3 cs exp 1


8/7/2019 lab 3 cs exp 1


8/7/2019 lab 3 cs exp 1


Figure 5: Step response of second order system with various ζ

LIST OF EQUIPMENT

• DC power supply.

• Computer unit with MATLAB software.• Breadboard.

• Tektronix digital oscilloscope.

• Resistor.

• Capacitor.

• Inductor.

• On-Off switch.

• Multimeter.

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PROCEDURE

• Modeling and Experimental Validation of a First Order System

i) An RC-series circuit and on-off switch is built on the breadboard.

ii) 5V DC voltage of power supply is applied.

iii) Oscilloscope is prepared to analyze the output voltage of the circuit.

iv) Output cable of power supply (5V DC) is connected to the circuit and the on-off

switch is switched on to give step response to the circuit.

v) The output response of the circuit is observed by looking at the plot of oscilloscope.

vi) The value of R and C is changed to vary the value of τ. Another value of R and C is

used to get τ which is higher than before and the experiment is repeated.

• Modeling and Experimental Validation of a Second Order System

i) An RLC-series circuit is constructed on the breadboard.

ii) 5V DC voltage of power supply is applied.

iii) Oscilloscope is prepared to analyze the output voltage of the circuit.

iv) Output cable of power supply (5V DC) is connected to the circuit and the on-off

switch is switched on to give step response to the circuit.

v) The output response of the circuit is observed by looking at the plot of oscilloscope.

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vi) The value of R, L or C is changed to vary the value of ζ and ωn. Another value of R, L

or C is used to get at least two different step response in order to investigate the effect

of changing parameter.

RESULT & CALCULATION

• Modeling and Experimental Validation of a First Order System

o R = 100Ω, and C = 100 µF, then τ = 0.01.

Output waveform using oscilloscope

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Output waveform using MATLAB

o

R = 1kΩ and C = 100 µF thenτ

= 0.1



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• Modeling and Experimental Validation of a Second Order System

o L = 10mH



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o

L = 100mH


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Discussion:

In this first part of this experiment, we construct RC circuit which behaves as a first

order system when the 5V DC voltage is the input and the voltage across the capacitor is

the output. From the circuit below, we obtain the transfer function of the circuit and

identify specific parameters of the system that affect system response. We identify two

system parameters that individually affect the DC gain and the time constant.

Vo / (1/sC) + (Vo – Vi) / R = 0

Vo ((1/sC) + (1/R)) = Vi / R

Vo/Vi = 1/ (R (sC + 1/R))

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G(s) = 1/ (sRC + 1) ----------------------- (1)

The standard form of transfer function of a first-order function is:

----------------------- (2)

Then, by comparing the equation (1) and (2), τ = RC.

In second part, we construct RLC circuit which behaves as a second-order system

with the voltage across the capacitor as output. From the circuit below, we obtain the

transfer function of the system and identify specific parameters of the system that affect

system response.

sCVo +Vo/R + (Vo – Vi)/sL = 0

Vo (sC + 1/R + 1/sL) = Vi/sL

Vo/Vi = (1/sL) / (sC + 1/R +1/sL)

G(s) = 1 / (LCs2 + sL/R +1)

= (1/LC) / (s2 + s/RC + 1/LC) ----------------------- (3)

The standard for the second order system is:

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----------------------- (4)

Then, when we comparing the equation (3) and (4) to find the value of ζ and ωn:

a) ωn = √ (1/LC)

b) 2ζωn = 1/RC

ζ =√ (L/ 4R 2C)

From these equations, we can calculate the value of:i. Time-constant, τ – the time for the step response takes to reach the 63% of its final

value

τ = 1/ ζωn

ii. Settling time, Ts – the time for the waveform to reach and stay within 2% of its

final value

Ts = 4τ

iii. Peak value, T P - the time requires to reach the first or maximum, peak.

iv. Percentage overshoot, PO - a ratio between the different between system time

response and final value.

When are using R = 10 kΩ, C = 100 µF, L = 100mH, we get this graph

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S e c o n d O r d e r S y s te m S t e p R e s p o n

- 1

0

1

2

3

4

5

6

1 7 2 0 1 4 3 92 1 5 82 8 7 73 5 9 64 3 1 55 0 3 45 7 5 36 4 7 27 1 9 17 9 1 08 6 2 99 3 4 8

T im e

Voltage, V

Then we change the value of R = 10 kΩ, C = 1000µF, L = 100mH, the graph obtained is

S e c o n d O rd e r S y s te m S t e p R e s p o n

0

1

2

3

4

5

6

1 7 1 4 1 4 2 72 1 4 02 8 5 33 5 6 64 2 7 94 9 9 25 7 0 56 4 1 87 1 3 17 8 4 48 5 5 79 2 7 09 9

T im e

Voltage, V

Conclusion:

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As a conclusion, we successfully obtain the model of first-order and second-order

system and identify the effect of system parameter on its response to a step input. From

the first-order system, we can calculate the time constant, τ and steady-state DC gain, K.

Then, from the second-order system, we can determine the value of time constant, τ ,

setting time, Ts, peak value, Tp, and percentage overshoot, PO. Alhamdulillah, overall,

we manage to finish this experiment and fulfill all the objectives of this experiment.

Alhamdulillah,we hope that the knowledge in this experiment will benefit us in the

future.

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lab 3 cs exp 1