Background
In the theory of control of UAVs, the thrust force generated by a propeller is typically modeled as a function of the spinning rate depending on a constant thrust coefficient.
However, in the presence of mutual interaction between propellers in multi-rotor vehicles, the model may not be satisfactory. The airflow of adjacent propellers impacts the thrust that a propeller can generate, which is lower than the one without cross-influence. Predicting the loss in thrust is a relevant problem in the control and design of multi-rotor UAVs. To investigate this phenomenon, a reasonable approach is to gather force measurements from sensors mounted on a multi-rotor structure and use them to validate models with a thrust coefficient depending on the configuration and the angular velocity of the adjacent propellers.
Assignment Description
This assignment aims to study the observability of the thrust coefficient from a linear model of the cross-influence between propellers. The student will work on a simplified 2D problem with two propellers only oriented as in the figure. The system is modeled as a mass subject to the sum of the forces generated by the two propellers and the air friction.
Questions
The assignment comprises three questions. Once the student has obtained the associated state space representation of the system, the questions are formulated as follows:
• Is it possible to reconstruct the full state (position and velocity of the mass, and thrust coefficients)?
• If yes, which is the minimal set of measurements?
• If possible, build an observer and show it works in simulation.