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Modelling and simulation a multi quadcopter concept
- 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!