Control and Estimation of a Quadcopter Dynamical Model

Abstract

The main motivation for this paper is to apply LQ and LQG methodologies for quadcopter control system. The developed control system is for both the rectangular position (xy) and altitude (z) as well as the orientation (attitude - angles around the axes) based on 6-Degree of Freedom (6DOF) mathematical model. 6DOF refers to the model with 3 linear and 3 angular motions. The altitude and attitude controllers are designed and the results presented in both the continuous and the discrete time cases. For the controller design, a nonlinear mathematical model was obtained first for 6DOF. The next step was to linearize the nonlinear model in hovering mode, and the final step was the reduction of the resulted linear model to be used as starting model for the controller design. The reduced linear model was tested for controllablity and observability. The control goal was to track a spatial trajectory with the quadcopter center of gravity under environment disturbances and sensor measurement errors. For this purpose, designed LQ controller was augmented by Kalman Filter state observer. The resultant controllers provide precise and robust performance for an input reference signal and for a regulation problem. After the transient response (of order of few seconds) the tracking error is acceptable which provides safe handling even under disturbances and measurement noises. The transient response can be furrther recuded by controllers fine tunning.