A novel PID controller gain tuning method for a quadrotor landing on a ship deck using the invariant ellipsoid technique

Quadrotors are useful in many applications. It is controlled by the thrust of each rotors. The altitude and attitude control is often achieved by PID controller due to its simplicity. Many methods such as the Ziegler Nichols method, Cohen Coon method and loop shaping methods are available to tune the gain with different objectives such as minimizing overshoot or settling time. However, few techniques are able to obtain an optimal controller gain for a system under persistent bounded disturbance. The invariant ellipsoid method based on the invariant set theory is developed to formulate an optimization problem to obtain such an optimal controller gain. The technique is applied to a ship deck landing problem of a quadrotor. The heave motion of the ship deck represents a persistent disturbance acting on the quadrotor which is required to perform a landing operation while maintaining small relative speed with the ship deck. Numerical simulation is performed to demonstrate the ability of the calculated gain to reject disturbance as compared to gain obtained by loop shaping method.