Parafoil trajectory comparison for optimal control and proportional controller

An autonomously guided parafoil, which is dropped from an altitude, has to reach a specified location on ground considering dispersions like wind, release location and velocity. The parafoil generates lift, it has a glide ratio greater than unity. It has certain degree of control and hence can be steered to the target. In this paper bank angle is taken as the control variable and a three degree of freedom model is considered. A Line of Sight (LOS) guidance was used for guiding the parafoil to the target. In this LOS guidance the bank angle is varied proportional to the LOS angle. The LOS guidance could guide the parafoil to the target, but the bank angle requirement is unacceptably high. In order to minimize the control requirement an optimal control problem was formulated. The cost function is taken to minimize the control and the terminal error. Hamiltonian (H) is formulated and the co states are found numerically. The control obtained is well with in the limits and the parafoil is reaching the targets smoothly. For developing a closed form guidance algorithm, a further simplified system model is required. To reduce the model a quasi-equilibrium glide assumption is made. Using this reduced order model optimal control problem is formulated. The co state values are obtained numerically. The two trajectories obtained are almost identical.