Model-based Control: Difference between revisions

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Ideal:
Solid cuboid


I_roll \approx I_yaw, I_pitch << I_roll, I_yaw
I = 1/12 M ( a^2 + b^2 )


Interestingly, a sphere is not idael from the perspective of PID control/axis coupling.


=== Ideal ===


Solid cuboid
I_roll \approx I_yaw, I_pitch << I_roll, I_yaw
 
I = 1/12 M ( a^2 + b^2 )
 


Interestingly, a sphere is not idael from the perspective of PID control/axis coupling.


Camera Panasonic:
=== Camera Panasonic ===


{| class="wikitable" style="text-align: center;"
{| class="wikitable" style="text-align: center;"
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|}
|}


pitch:  I \propto  2.5^2 + 5.5^2 = 36.5   -> 1
{| class="wikitable" style="text-align: center;"
 
!axis
roll:  I \propto  5.5^2 + 9^2 = 111.25   -> 3.05
!approximate moment of inertia
 
!relative ratio
yaw:    I \propto  2.5^2 + 9^2 = 87.25     -> 2.39
|-
 
| pitch || I \propto  2.5^2 + 5.5^2 = 36.5 || 1
 
|-
| roll || I \propto  5.5^2 + 9^2 = 111.25 || 3.05
|-
| yaw || I \propto  2.5^2 + 9^2 = 87.25 || 2.39
|}


Camera GoPro Hero5:
=== Camera GoPro Hero5 ===


{| class="wikitable" style="text-align: center;"
{| class="wikitable" style="text-align: center;"
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|}
|}


{| class="wikitable" style="text-align: center;"
!axis
!approximate moment of inertia
!relative ratio
|-
| pitch || I \propto  2.5^2 + 4.5^2 = 26.5 ||  1
|-
| roll || I \propto  4.5^2 + 6.3^2 = 59.94 || 2.26
|-
| yaw || I \propto  2.5^2 + 6.3^2 = 45.94 ||  1.73
|}


pitch:  I \propto  2.5^2 + 4.5^2 = 26.5    ->  1
=== Camera Mobius ===
 
roll:  I \propto  4.5^2 + 6.3^2 = 59.94  ->  2.26
 
yaw:    I \propto  2.5^2 + 6.3^2 = 45.94  ->  1.73
 
 
 
Camera Mobius:


{| class="wikitable" style="text-align: center;"
{| class="wikitable" style="text-align: center;"
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|}
|}


pitch:  I \propto  6^2 + 2^2 = 40   ->  1
{| class="wikitable" style="text-align: center;"
 
!axis
roll:  I \propto  2^2 + 3^2 = 13   -> 0.325
!approximate moment of inertia
 
!relative ratio
yaw:    I \propto  6^2 + 3^2 = 45   ->  1.125
|-
| pitch || I \propto  6^2 + 2^2 = 40 || 1
|-
| roll || I \propto  2^2 + 3^2 = 13 || 0.325
|-
| yaw || I \propto  6^2 + 3^2 = 45 || 1.125
|}

Revision as of 13:07, 6 September 2019

Moments of Inertia

https://en.wikipedia.org/wiki/Moment_of_inertia

https://en.wikipedia.org/wiki/List_of_moments_of_inertia


Solid cuboid

I = 1/12 M ( a^2 + b^2 )


Ideal

I_roll \approx I_yaw, I_pitch << I_roll, I_yaw

Interestingly, a sphere is not idael from the perspective of PID control/axis coupling.

Camera Panasonic

width height length
2.5 cm 5.5 cm 9 cm
axis approximate moment of inertia relative ratio
pitch I \propto 2.5^2 + 5.5^2 = 36.5 1
roll I \propto 5.5^2 + 9^2 = 111.25 3.05
yaw I \propto 2.5^2 + 9^2 = 87.25 2.39

Camera GoPro Hero5

width height length
2.5 cm 4.5 cm 6.3 cm
axis approximate moment of inertia relative ratio
pitch I \propto 2.5^2 + 4.5^2 = 26.5 1
roll I \propto 4.5^2 + 6.3^2 = 59.94 2.26
yaw I \propto 2.5^2 + 6.3^2 = 45.94 1.73

Camera Mobius

width height length
6 cm 2 cm 3 cm
axis approximate moment of inertia relative ratio
pitch I \propto 6^2 + 2^2 = 40 1
roll I \propto 2^2 + 3^2 = 13 0.325
yaw I \propto 6^2 + 3^2 = 45 1.125
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