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5.5.2014 (17) Development of a Mathematical Model for a Co-Axial Helicopter (Bachelor's Degree Final Year Project, Not Published, Just Sharing) | Muhd Firdaus

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Development of a Mathematical Model for a Co-Axial Helicopter (Bachelor's Degree Final Year Project,Not Published, Just Sharing)

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3

5.6 Final Output: Euler Angle and Altitude

Figure 40: Aerospace Blockset (Body frame to Earth frame transformation block)

; Reading Sequence

Figure 41: Aerospace Blockset (Body frame to Earth frame block)

Referring to figure 40, both forces and moments fed into the aerospace blockset to determine

various output. From figure 41 (1 and 2), it can be seen obviously the failure of the model to

predict the dynamics of helicopter. From figure 41 (3 and 4), the trend does show little promise

of logical dynamics although no steady state achievable. These four main outputs will be

discussed further after the controller design has been implemented in section 5.

0 2 4 6 8 10-1

-0.5

0

0.5

1

Time(s)

R o

l l ( r a d

)

Roll vs. Time

0 2 4 6 8 10-1

-0.5

0

0.5

1

Time(s)

P

i t c h

( r a d

)

Pitch vs. Time

0 2 4 6 8 10-1000

0

1000

2000

3000

4000

Time(s)

Y a w

( r a d

)

Yaw vs. Time

0 2 4 6 8 10-300

-200

-100

0

100

Time(s)

A l t i t u

d e

( m )

Altitude vs. Time

1 2

3 4



40

6.0 Controller Design

6.1 PID controller

Simulink Control Design: Compensator Design is a tool provided by Matlab application to

design controller for any model built. This app (application) should be very useful when it comes

to automated PID tuning where it automatically determines all the parameters values to achieve

the desired stability and minimizes steady state error of the system. PID11

is known to be

Proportional, Integral and Derivatives controller that has the form:

( ( ( (

Figure 42: Altitude PID controller

Figure 42 shows the whole model with PID controller (closed loop system). The method used

was that; each input fed into the system has its own PID controller and loop connected to its

corresponding output. For example, altitude controller (shown in figure 42) loop from its altitude

output and collective input. So, there are 4 PID controllers for representing Roll, Pitch, Yaw and

Altitude motion. The PID was design separately, only one PID controller for each motion tested.

For example, during designing the controller for altitude, no other PID controller was connected

to the model. See appendices (attachment CD/DVD) for each to see how each of these PID was

connected to the model.

11 See appendices (figure 51) for detail information and under mask built-in PID block

Since applying the apps was not possible due to the size of the model, default parameter ( 1, 1, 0) were used to observe whether controller design is the most appropriatesolution and can be improved further to achieve the desired results.

-50

0

50

Altitude of Helicopter vs. Time



41

Figure 43: Altitude output with PID controller

Figure 43: Altitude of helicopter with the respect to the initial position (in this case is ground)

For altitude controller, the output of the PID (input to the system or plant) connected to two

motors since the thrust force were produced by each rotor. The results (figure 19) shows that

after BBK seconds, it achieves the desired altitude (-200 m). Noted that negative (-) values

means the helicopter is increasing in altitude with the respect to the earth. This was clearly

explained in (3.0: Earth Reference Frame). But, it continuously increases as simulation time

increases. This is surely not desirable because the output values should be approximately same as

the desired value after certain amount of time.

0 1 2 3 4 5 6 7 8 9 10-350

-300

-250

-200

-150

-100

Time (s)

A l t i t u d e ( m )

Figure 44: Yaw angle of helicopter

Referring to figure 44, the results shows that after 1 second, the helicopter dynamics has the

same trend as explained before in (5.0 - Figure 13: Moment about z-axis). The yaw angle need to

be compensated when designing a controller to ensure no output (Moment around z= 0 and yaw

angle= 0) if yaw input is 0.

0 1 2 3 4 5 6 7 8 9 10-1000

-500

0

500

1000

1500

2000

Time (s)

Y a w A

n g l e ( r a d )

Yaw Angle vs. Time



42

Figure 45: Roll angle of helicopter

0 1 2 3 4 5 6 7 8 9 10-1

-0.5

0

0.5

1

1.5

2

Time (s)

R o l l a n g l e ( r a d )

Roll Angle vs. Time

0 1 2 3 4 5 6 7 8 9 10-2

-1.5

-1

-0.5

0

0.5

1

Time (s)

R o

l l A n g

l e

Roll Angle vs. Time

Referring to figure 45, the main significant trend suggested that the helicopter performs roll

motion at an angle of 1.5 radians (85) after 3 seconds. Despite its instability characteristics, it is

known that the model maybe accurately built. The model does respond correctly for both positive and negative desired value (positive desired value gives positives output values and vice

versa). The problem arose because of inaccurate parameters of the PID controller.

Figure 46: Pitch angle of helicopter

Noted that from figure 46; it can be seen such responses has identical trend as roll motion. So,

from all these 4 main outputs, maybe tuning the PID controller parameter would solve the

problem.

6.2 Problem Solving:

PID controller parameter was changed and tested its capability in giving accurate results. See

appendices for all responds obtained. This is the list of trial:

0 1 2 3 4 5 6 7 8 9 10-1

0

1

2

Time (s)

P i t c

h A n g

l e ( r a

d )

Pitch Angle vs. Time

0 1 2 3 4 5 6 7 8 9 10-2

-1

0

1 Pitch Angle vs. Time

Time (s)

P i t c

h A n g

l e ( r a

d )



43

appendices for all responds obtained. This is the list of trial:



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