Design, Assemble and Testing of Multi-copter for Marine Services by integrating four quadcopters and achieving stability.

1. Design and Simulation of a
Multicopter
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W
Jaidev Sanketi EAU0512252
Srinivasa Raghavan EAU0812382
Sundus Awan EAU0812425
Rishika Kasliwal EAU0812361

2. RECAP
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W

3. OBJECTIVES
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W
Conduct experiments
Proof of concept through
mathematical modelling
 Simulate results
Program the flight controller

4. METHODOLOGY
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W
Hover stability
Linear motion
Test Bench
Simulation
Test Bench
Software
Hardware
Automation

5. MATHEMATICAL MODEL
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W
Drone
Model
Hover
Stability
Attitude
Control
Altitude
Control
Linear
Motion
Take-Off
Forward
Movement
Drone Trajectory Loop
Drone Altitude Loop
Drone Attitude Loop
Quad Attitude Loop

6. DYNAMIC MODELING (Quadcopter)
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W
𝑥
𝑦
𝑧
= -g
0
0
1
+
Σ𝑇𝑖,𝑗
𝑚
𝑆𝜓𝑆𝜙 + 𝐶𝜓𝑆𝜃𝐶𝜙
𝑆𝜓𝑆𝜃𝐶𝜙 − 𝐶𝜓𝑆𝜙
𝐶𝜃𝐶𝜙
Equations of Motion
Equations of Angular Acceleration
𝐼 𝑥 𝜙
𝐼 𝑦 𝜃
𝐼𝑧 𝜓
=
𝑇𝑖,3 − 𝑇𝑖,1 𝑙 𝑞
𝑇𝑖,4 − 𝑇𝑖,2 𝑙 𝑞
𝑀𝑖,1 + 𝑀𝑖,3 − 𝑀𝑖,2 − 𝑀𝑖,4
𝑻𝒊= 𝑲 𝒇 𝝎𝒊
𝟐 𝑴𝒊 = 𝑲 𝒎 𝝎𝒊
𝟐
𝑻𝒉𝒓𝒖𝒔𝒕 𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏 𝑴𝒐𝒎𝒆𝒏𝒕 𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏

7. TEST BENCH EXPERIMENT
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W

8. DYNAMIC MODELING (Quadcopter)
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W
𝑇𝑖= 𝐾𝑓 𝜔𝑖
2
𝐹𝑖 = 4𝑇𝑖
4 𝐹𝑖 𝑐𝑜𝑠𝜃 𝑞 = 𝑚𝑔
𝜔ℎ = 𝜔𝑖 =
𝑚𝑔
16𝑘𝑐𝑜𝑠𝜃 𝑞
𝐹ℎ= 4𝐾𝑓 𝜔ℎ
2

9. DYNAMIC MODELING (Drone)
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W
Equations of Motion
Equations of Angular Acceleration
𝑥
𝑦
𝑧
= −𝑔
0
0
1
+
Σ𝐹𝑖,𝑗
𝑚
𝐶 𝜓 𝑞
𝐶 𝜃 𝑞
𝑆 𝜓 𝑞
𝐶 𝜓 𝑞
𝑆 𝜃 𝑞
−𝑆 𝜓 𝑞
𝐶 𝜃 𝑞
𝐶 𝜓 𝑞
−𝑆 𝜓 𝑞
𝑆 𝜃 𝑞
−𝑆 𝜃 𝑞
0 𝐶 𝜃 𝑞
𝐼 𝑥 𝜙 = 𝑙 𝐹3 𝑐𝜃3 − 𝐹1 𝑐𝜃1 − 𝐶′
1 𝜃 𝑑 + 𝑀1 𝑠𝜃1 − 𝑀3 𝑠𝜃3 + (𝑀2
′
+ 𝑀4
′
)
𝐼 𝑦 𝜃 = 𝑙 𝐹4 𝑐𝜃4 − 𝐹2 𝑐𝜃2 − 𝐶′
2 𝜙 𝑑 + 𝑀4 𝑠𝜃4 − 𝑀2 𝑠𝜃2 + (𝑀1
′
+ 𝑀3
′
)
𝐼𝑧 𝜑 = 𝑙 𝐹1 𝑠𝜃1 + 𝐹2 𝑠𝜃2 + 𝐹3 𝑠𝜃3 + 𝐹4 𝑠𝜃4 + 𝐶′
3 𝜃 𝑑 + 𝑀1 𝑐𝜃1 − 𝑀2 𝑐𝜃2 + 𝑀3 𝑐𝜃3 − 𝑀4 𝑐𝜃4
Hovering with Tilted Arms (Roll) Hovering with Tilted Arms (Pitch)
𝝓 𝒅 = 𝜽2 2 𝜽 𝒅 = 𝜽1 2
𝜽3 = -𝜽1
𝜽4 = -𝜽2

10. ATTITUDE CONTROL
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W
𝜃1
𝑑𝑒𝑠
𝜃2
𝑑𝑒𝑠
𝜃3
𝑑𝑒𝑠
𝜃4
𝑑𝑒𝑠
=
1 0 1 0
0 1 0 1
1 0 1 0
0 1 0 1
2𝜃ℎ
𝑑𝑒𝑠
2𝜙ℎ
𝑑𝑒𝑠
Δ𝜃ℎ
Δ𝜙ℎ
𝐹1
𝑑𝑒𝑠
𝐹2
𝑑𝑒𝑠
𝐹3
𝑑𝑒𝑠
𝐹4
𝑑𝑒𝑠
=
1 0 − 1 1
1 1 0 − 1
1 0 1 1
1 − 1 0 1
𝐹ℎ
Δ𝐹 𝜙,𝑑
Δ𝐹𝜃,𝑑
Δ𝐹 𝜓,𝑑
Δ𝐹𝜃,𝑑 = 𝑘 𝑝,𝜃(𝜃 𝑑𝑒𝑠
ℎ − 𝜃 𝑑) − 𝑘 𝑑,𝜃(𝑞 𝑑𝑒𝑠
𝑑
− 𝑞 𝑑)
Δ𝐹 𝜙,𝑑 = 𝑘 𝑝,𝜙 𝜙 𝑑𝑒𝑠
ℎ − 𝜙 𝑑 − 𝑘 𝑑,𝜙(𝑞 𝑑𝑒𝑠
𝑑
− 𝑞 𝑑)
Δ𝐹 𝜓,𝑑 = 𝑘 𝑝,𝜓(𝜓 𝑑𝑒𝑠
ℎ
− 𝜓 𝑑) − 𝑘 𝑑,𝜙(𝑟 𝑑𝑒𝑠
𝑑
−𝑟𝑑)
Δ𝜃ℎ = 𝑘 𝑝,𝜃ℎ(𝜃 𝑑𝑒𝑠
𝑑 − 𝜃 𝑑) − 𝑘 𝑑,𝜃ℎ 𝑞
Δ𝜙ℎ = 𝑘 𝑝,𝜙ℎ(𝜙 𝑑𝑒𝑠
𝑑 − 𝜙 𝑑) − 𝑘 𝑑,𝜙ℎ 𝑝
Force Matrix Angle Matrix
Control Laws (PD) Control Laws (PD)
𝜔ℎ = 𝜔𝑖 =
𝑚𝑔
16𝑘𝑐𝑜𝑠𝜃 𝑞
𝜔ℎ = 𝜔𝑖 =
𝑚𝑔
16𝑘𝑐𝑜𝑠(𝜃2/2)
Angular Velocity Matrix
𝜔1
𝜔3
𝜔5
𝜔7
𝜔9
𝜔11
𝜔13
𝜔15
=
𝜔2
𝜔4
𝜔6
𝜔8
𝜔10
𝜔12
𝜔14
𝜔16
=
1 1
1 −1
0 1
0 −1
1 0
1 0
1 −1
1 1
1 0
1 0
−1 1
1 −1
0 1
0 −1
1 1
−1 −1
∗
𝜔ℎ + Δ𝜔 𝑓
Δ𝜔 𝜃
Δ𝜔 𝜙
Δ𝜔 𝜓
Control Laws (PD)
Δ𝜔 𝜃 = 𝑘 𝑝,𝜃(𝜃 𝑑𝑒𝑠
ℎ − 𝜃 𝑑) − 𝑘 𝑑,𝜃(𝑞 𝑑𝑒𝑠
𝑑
− 𝑞 𝑑)
Δ𝜔 𝜙 = 𝑘 𝑝,𝜙(𝜙 𝑑𝑒𝑠
ℎ
− 𝜙 𝑑) − 𝑘 𝑑,𝜙(𝑞 𝑑𝑒𝑠
𝑑
− 𝑞 𝑑)
Δ𝜔 𝜓 = 𝑘 𝑝,𝜓(𝜓 𝑑𝑒𝑠
ℎ
− 𝜓 𝑑) − 𝑘 𝑑,𝜙(𝑟 𝑑𝑒𝑠
𝑑
−𝑟𝑑)

11. ALTITUDE CONTROL
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W
𝑟 𝑑𝑒𝑠
=
8𝐾 𝑚⍵ 𝑛
𝐼𝑧
∆⍵ 𝜓
𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑡𝑒
𝑟 𝑑𝑒𝑠
∆𝜔 𝑓 =
𝑚
8𝑘 𝑓 𝐹 𝑛
( 𝑟 𝑑𝑒𝑠
)
∆𝑭 𝒇 = 𝟎. 𝟓𝒌(∆𝝎 𝒇) 𝟐
𝐹1
𝑑𝑒𝑠
𝐹2
𝑑𝑒𝑠
𝐹3
𝑑𝑒𝑠
𝐹4
𝑑𝑒𝑠
=
1 0 − 1 1
1 1 0 − 1
1 0 1 1
1 − 1 0 1
𝐹ℎ + Δ𝐹𝑓
Δ𝐹 𝜙,𝑑
Δ𝐹𝜃,𝑑
Δ𝐹 𝜓,𝑑
Force Matrix

12. LINEAR MOTION MODELING
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W
𝐹𝑥 = 0
𝐹1 𝑠𝑖𝑛𝜃1 − 𝐹3 𝑠𝑖𝑛𝜃3 = 0
𝐹𝑦 = 0
𝐹1 𝑐𝑜𝑠𝜃1 − 𝐹3 𝑐𝑜𝑠𝜃3 − 𝑊 = 0
𝑀𝑐 = 0;
𝐹1 𝑐𝑜𝑠𝜃1 𝑙 − 𝐹3 𝑐𝑜𝑠𝜃3 𝑙 = 0
𝒕𝒂𝒏𝜽 𝟏 − 𝒕𝒂𝒏𝜽 𝟑 = 𝟎
𝜃1 = 𝜃3
𝐹𝑥 = 0
𝐹1 𝑠𝑖𝑛𝜃1 − 𝐹3 𝑠𝑖𝑛𝜃3 = 0
𝐹𝑦 = 0
𝐹1 𝑐𝑜𝑠𝜃1 − 𝐹3 𝑐𝑜𝑠𝜃3 − 𝑊 = 0
𝑀𝑐 = 0;
𝐹1 𝑐𝑜𝑠𝜃1 𝑙 − 𝐹3 𝑐𝑜𝑠𝜃3 𝑙 = 0
𝒕𝒂𝒏𝜽 𝟏 − 𝒕𝒂𝒏𝜽 𝟑 = 𝟎
Hover (No Wind) Take-Off (No Wind)
Angular Take-Off Analogy

13. LINEAR MOTION MODELING
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W
𝐹1 𝑠𝑖𝑛𝜃1 − 𝐹1 𝑠𝑖𝑛𝜃3 − 𝐹𝑛 = 0
𝑾
𝟒
(𝒕𝒂𝒏𝜽 𝟏 − 𝒕𝒂𝒏𝜽 𝟑) = 𝑭 𝒏
𝐹1 𝑐𝑜𝑠𝜃1 =
𝑊
4
Slow Forward Motion Faster Forward Motion Fastest Forward Motion
𝜃1 = 𝜃3

14. SIMULATION
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W
Simulation
Simulink Simmechanics

15. SIMULINK SIMULATION
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W

16. SIMULINK RESULTS- AT HOVER
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W

17. ATTITUDE CONTROL
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W

18. SIMULINK LONGITUDINAL RESPONSE AT DISTURBANCE
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W
LONGITUDINAL STABILITY AT 5 DEGREESLONGITUDINAL STABILITY AT 15 DEGREES

19. TEST BENCH EXPERIMENT
M O D E L S I M U L A T I O NO V E R V I E W A U T O M A T I O N
ɵ = 30 degrees
Throttle input Force
40% 10N
80% 20N
100% 25N

20. SIMULINK LATERAL RESPONSE AT DISTURBANCE
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W
LATERAL STABILITY AT 5 DEGREESLATERAL STABILITY AT 15 DEGREES

21. ALTITUDE CONTROL
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W

22. A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W
SIMULINK LONGITUDINAL RESPONSE AT DISTURBANCE

23. A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W
SIMULINK LATERAL RESPONSE AT DISTURBANCE
5 DEGREES 15 DEGREES

24. SIMMECHANICS SIMULATION
A U T O M A T I O NM O D E L S I M U L A T I O NO V E R V I E W
NORMAL TAKE-OFFANGULAR TAKE-OFF

25. AUTOMATION
M O D E L S I M U L A T I O NO V E R V I E W A U T O M A T I O N

26. AUTOMATION
M O D E L S I M U L A T I O NO V E R V I E W A U T O M A T I O N

27. CONCLUSION
A U T O M A T I O NO V E R V I E W M O D E L S I M U L A T I O N

28. Thank you for your
patience!