Controls

Our system is a single-input, multiple-output (SIMO) system. The system is comprised of several coupled, non-linear governing equations relating one input to several outputs. We implemented a proportional controller to control the drone's attitude (roll, pitch, and yaw). While we successfully created a stable controller to maintain constant attitude, we have been unsuccessful so far at changing the attitude without destabilizing the drone's flight. A conventional Laplace transform and transfer function were insufficient to solve the complicated system of a single-rotor drone, so we had to do some research into alternative methods.

Block Diagram

State Space

• To represent the multiple different relationships between the input and outputs, we converted them into state-space, which uses linear algebra to express transfer functions as matrices.
• To use the state-space approach, we first had to linearize the system around the hover solution through first-order Taylor series approximation.
• We separated the position and attitude components of the controller, making both parts easier to work with in isolation.
• By solving for poles of the system, we were able to find parameter values for a stable hover solution, but our attempts to make the drone change attitude led to massive oscillation.

Time Variant Systems

• Our linearization approach suffered from one key flaw: the system's constant rotation cannot be easily linearized, because any first order approximation will only be valid at small angles.
• We expressed our transfer function in the time domain in terms of two time values: the actual time and the time offset of the input.
• By taking two sequential Laplace transforms, both time parameters can be eliminated, successfully bringing the system into the frequency domain.