Controller Design for a 2-D Parafoil Return System

This thesis will cover the basics of 2-dimensional motion of a parafoil system to determine and
design an altitude controller that will result in the parafoil starting at a location and landing within the
accepted bounds of a target location. It will go over the equations of motion, picking out the key
formulas that map out how a parafoil moves, and determine the key inputs in order to get the desired
outcome of a controlled trajectory. The physics found in the equations of motion will be turned into
state space representations that organize it into differential equations that coding software can make
use of to make trajectory calculations. MATLAB is the software used throughout the paper, and all code
used in the thesis paper will be written out for others to check and modify to their desires. Important
aspects of parafoil gliding motion will be discussed and tested with variables such as the natural glide
angle and velocity and the utilization of checkpoints in trajectory controller design. Lastly, the region of
attraction for the controller designed in this thesis paper will be discussed and plotted in order to show
the relationship between the four input variables, x position, y position, velocity, and theta.
The controller utilized in this thesis paper was able to plot a successful flight trajectory from
10m in the air to a target location 50m away. This plot is found in figure 18. The parafoil undershot the
target location by about 9 centimeters (0.18% error). This is an acceptable amount of error and shows
that the controller was a success in controlling the system to reach its target destination. When
compared to the uncontrolled flight in figure 17, the target will only be reached when a controller is
applied to the system.