Picked from the software, topic, and level of “Class Quadrotor Sliding Mode Control #6: 3D Path Tracking Test with Disturbance and Stability Analysis”.
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Introduction
Here is the final result, the quadrotor tracks a 3D figure-eight path while being subjected to random wind. PID deviates by 1.4 meters, whereas SMC with an observer only deviates by 1.5 cm. Let's get started. Hello, welcome to the final episode of the quadrotor control series using sliding mode control. The test in the previous episode used neat wind. In the real world, wind blows randomly. Today, we will test the three controllers on a more challenging 3D path with random wind, then check its stability using a Lyapunov function.
Step 1: Eight-shaped trajectory & random wind
Create a file named test_underscore_path_underscore_3D.py. The path is a 3D figure-eight, moving in the shape of an 8 in the horizontal plane while ascending and descending, with a period of 12 seconds. The wind consists of an average wind of 1.5 N in the X direction and -1 N in the Y direction, plus random gusts generated by the Ornstein-Uhlenbeck process, so the wind changes but remains bounded, similar to real turbulence.
Step 2: Comparison & Lyapunov function
We will simulate 24 seconds for PID, SMC, and SMC with observer and small gain. Run. The wind force averages at 2.38 N and peaks at 4.49 N, quite strong for a 1.2 kg drone. PID has an RMSI of 0.249 meters, SMC 0.097 meters, and SMC with observer only 0.015 meters, more than 16 times more accurate than PID. The Lyapunov function V equals half of S squared on the altitude channel, decreasing from 0.0005 to 0.00001, the sign of the system is stable.
"Step 3: 3D trajectory & error"
Let's look at the graphs. On the 3D plot, the SMC with observer path almost covers the dashed reference line, while PID drifts along with the wind. The chaotic graph shows PID and SMC fluctuating in response to disturbances, while SMC with an observer steadily approaches zero. Theoretically, SMC ensures S approaches zero as long as the gain is larger than the residual disturbance, and the observer makes the residual disturbance small enough so that even a small gain is sufficient.
Done!
Done, and the series is complete. We have built a complete control research for a quadrotor, 6 degrees of freedom model, multi-level PID, sliding mode control theory, SMC for quadrotor, disturbance observer, up to 3D path tracking test with random wind and Lyapunov analysis. For further research, try super twisting SMC, extended state-based observer, motor and battery models, or implementation on a real flight controller. Thank you for following this series. Currently working on a thesis, dissertation, or research in the field of control systems, drones, and UAVs. Cerdas Inovasi Digital helps implement control systems, from 6 degrees of freedom quadrotor modeling, Hierarchical PID control, sliding mode control, up to disturbance observer for wind, as well as opening a Python programming course for electrical and mechatronic engineering. Want to master the entire series, from quadrotor models up to 3D path tracking tests with wind? All 6 episodes, complete with step-by-step PDF guides and source code, are available for premium tutorial subscribers. Subscribe starting at Rp69.000 per month, save 28% with the 12-month package, or pay once Rp999.000 for lifetime access. Want just one class? Buy the single class with lifetime access. Subscribe now at the premium page cerdasinovasidigital.com Contact our WhatsApp, or visit cerdasinovasidigital.com Thank you for watching, see you in the next episode.
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