Long Report2

8/6/2019 Long Report2

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TITLE

Computer aided design

OBJECTIVE

y To analyze and to design a control system using the PERISIK program based on the time

domain analysis method.

y To analyze and to design a control system using the PERISIK program based on the

frequency domain analysis method.

INTRODUCTION

Computer Aided Design (CAD) is the use of computers to assist the design process. CAD

software, or environments, provides the user with input-tools for the purpose of streamlining

design processes; drafting, documentation, and manufacturing processes. Specialized CAD

programs exist for various types of design: architectural, engineering, electronics, roadways, and

woven fabrics to name a few. CAD programs usually allow a structure to be built up from

several re-usable 3-dimensional components, and the components (such as gears) may be able to

move in relation to one another. CAD output is often in the form of electronic files for print or

machining operations. It is normally possible to generate engineering drawings to allow the final

design to be constructed.

Root locus analysis is a graphical method for examining how the roots of a system

change with variation of a certain system parameter, commonly the gain of a feedback system. It

can be used to analyze and design the effect of loop gain upon the system¶s transient response

and stability. The graphical of the root locus give us the description of a control system¶s



performance that we are looking for and also serve as a powerful quantitative tool that yield

more information then mathematics method.

A Bode plot is a graph of the transfer function of a linear, time-invariant system

versus frequency, plotted with a log-frequency axis, to show the system's frequency response. It

is usually a combination of a Bode magnitude plot, expressing the magnitude of the frequency

response gain, and a Bode phase plot, expressing the frequency response phase shift.

A Nichols plot is a plot used in signal processing in which the logarithm of the magnitude

is plotted against the phase of a frequency response on orthogonal axes. This plot combines the

two types of Bode plot ² magnitude and phase ² on a single graph, with frequency as a

parameter along the curve.



METHOD

EXPERIMENT A

Figure 1

1. Transfer function in figure 1 was simulated using PERISIK program.

2 PERSIK icon was double clicks to access the program.

3. The data of the transfer function was inserted into the PERISIK system.

4. The transfer function was simulated using the program and value was determined

from the result of simulation.

5. Time response plot was simulated to determine the system unity step response.

6. Value K was determined when damping ration is 0.2 and 0.707.

7. Break point, corresponding gain and third pole were determined.

8. Third pole was determined when damping ratio is 0.707.



EXPERIMENT B

Figure 2

Section A

1. The data of the transfer function was inserted into the PERISIK system.

2. The transfer function was simulated using the program.

3. Gain Margin , Phase Margin Bandwidth , Peak Frequency and Peak Magnitude

was determined from the program.

4. Nichols chart and bode plot were sketched.

5. Table 2 was completed by using Nichols chart method.

Section B

1. Steady state error function was obtained when input is a ramp function. was

calculated when K=1.

2. was obtained using PERISIK.

3. The existence of was checked with PERISIK when it is step input.



Section C

1. was calculated in order to have< 0.2 with ramp input.

2. The value was verified using PERISIK.

3. Ramp Response was sketched

4. Table 3 was completed by using Bode Plot technique and Nichols Chart.

RESULT

Experimental (A)

1. T

he value of obtained is 48 while the value obtained manually is 48.

Figure 1: Root locus (using mathlab)



Figure 2: System Unity step response for k=48( using matlab)

Figure 3:Root locus when damping ration = 0.2 (using matlab)

When damping ration is 0.2, gain (k) is 19.54 while the dominant poles is s= -0.41 +1.9j

(using PERISIK)



Figure 4:Root locus when damping ratio=0.707 (using matlab)

When damping ratio is equal to 0.707, the Gain(k) is 4.12 and dominant poles, s=0.77+0.73j

(using PERISIK)



Time Domain Characteristics =0.2 =0.707

1.Rise Time (Tr ) 0.6162 2.55

2. Maximum Overshoot Time (T p) 1.86 4.52

3. Maximum Overshoot (M p) 1.4733 1.0348

4. Settling Time (Ts) 10.11 5.78

Table 1 Time domain characteristic for =0.2 and 0.707

2. The break point is -0.86 and the corresponding gain is 3.08 and the third pole is -4.31

3. The third pole for the system when damping ratio 0.707 is -4.46



Experimental (B)

Section A

Response Criteria Bode plot Nichols chart Average

1. Gain Margin(db) 29.19 29.64 29.415

2. Phase Margin,(°) 177.37 177.79 177.58

3. Bandwidth , (at-

3dB)

0.37 0.37 0.37

4. Peak

Frequency,(rad/s)

0.01 0.01 0.01

5. Peak Magnitude, 0 0 0

Table 2: Response criteria for Bode plot, Nicholas Chart and their average



Figure 5: Bode Plot (using matlab)

Section B

From calculation

��

From PERISIK Program



Section C

For the less than 0.2 the required K must greater than 52.2.

Let the ess=0.2. Hence the value of K=52.2.

We noted that the decreases when the value of the gain increases.

Response Criteria Bode Plot Nichols Chart Average

1. Gain Margin 3.05 2.97 3.01

2. Phase Margin 179.28 178.85 179.07

3. Bandwidth (-3dB) 3.85 3.37 3.61

4. Peak Frequency 2.51 2.48 2.495

5. Peak Magnitude 13.91 13.78 13.845

Table 3: Response Criteria for Bode plot and Nicholas Chart and their average



DISCUSSION

Experiment A

From the results, we noted that when the damping ratio, of the system increases from

=0.2 to =0.707 the rise time of the system increases from 0.6162s to2.55s while the maximum

overshoot time increases from 1.86s to 4.52s. This has shown that the system¶s rise time and

maximum overshoot time will increases when damping ratio increases. However, the maximum

overshoot decrease from 1.4733s to 1.0348s and settling time will decreases from 10.11s to 5.78s.

Maximum overshoot and settling time can be obtained from the graphical shown in

PERISIK program. The third pole of the system also can be determined through the program.

Besides that from PERISIK program, breakaway point was determined and which is located at -

0.85 and the corresponding gain was 3.08 and damping ratio =0.707. Hence the located of third

pole was located at -4.46

By calculation:

KGH(s) = -1

4.84=

4.84=++8s

S=-4.45

.When damping ratio, =0.707, closed loop pole=-0.707+0.73j

From the calculation, the third pole located 5 times far away with closed loop pole. It has a very

small or negligible effect on the system response.



Experiment B

Gain margin and Phase Margin can be obtained in open loop system while the bandwidth

(-3dB), Peak frequency and peak magnitude were obtained in closed loop system by using

PERISIK.

As shown from the result, data from Bode plot and Nichols chart were almost the same. It

shown that, the response criteria such as Gain margin, Phase Margin, bandwidth (-3dB), Peak

frequency and peak magnitude can be determined through Bode plot and Nichols chart.

The gain and phase margins can be determined by using Bode plots. The gain margin is

found by using the phase plot to find the frequency, where the phase angle is 180°. At this

frequency we look at the magnitude plot to determine the gain margin, which is the gain required

to raise the magnitude curve to 0dB.

The phase margin is found by using the magnitude curve to find the frequency, where

the gain is 0dB. On the phase curve at that frequency, the phase margin is the difference between

the phase value and 180°

Besides, simulated steady state error has some deviation from calculated steady state

error because of the scale. Scaling may result steady state error obtained to be not accurate.

Furthermore, there is no steady state error for step input. The PERISIK show no steady state

error for a unity step input.

The system will oscillate a period of time before it reach steady state. The system is not

stable during the transient state. After it reach steady state, the system is stable.



Conclusion

In conclusion, the objectives have been achieved. For the time domain analysis, the

system is third order system .All the poles are located on the left hand plane of the root locus and

therefore it is consider as a stable system. The rise time and settling time will determine the

performance of the system. Since the third pole located 5 times further from the dominant poles,

it has negligible effect on the response.

For the frequency domain analysis, the Gain Margin and Phase Margin can be obtained

from the Bode plot and Nichols chart in open loop system. Peak magnitude, peak frequency and

bandwidth can be obtained through Bode plot and Nichols chart.

REFERENCE

1. Computer aided design lab sheet

2. Norman S.Nise (2008). Control system Engineering

Documents

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