四旋翼飞行器的LQR优化控制

LQR optimal control for quadrotor aircraft

四旋翼飞行器是一种结构简单、可垂直起降的多旋翼飞行器,并在平面结构上具有4个平均分布且沿中轴线对称的助推器。建立了机体坐标系和空间坐标系,根据飞行器的动力学特性建立其数学模型;利用LQR控制算法对所建立的数学模型进行研究;在满足系统可控可观的条件下,选取半正定和正定的实对称常数矩阵Q和R的值,在控制器中算得最优反馈增益矩阵的值;最后,在给定参数值的情况下,通过所建立的最优控制器对该飞行器的数学模型进行仿真。

Abstract： Quadrotor aircraft is a multi-rotor aircraft with simple structure, which can take off or landing vertically There are four boosters average distributing and keeping axial symmetry on the flat surface of the aircraft. The aircraft body coordinate and space coordinate are set up The mathematic model of the aircraft is built up according to its dynamic characteristics. The LQR control algorithm is selected to carry on a research on the mathematic mode Under the condition of satisfying the controllability and observability of the system, the value of the half positive definite real-symmetric matrix Q and the positive definitereal-symmetric matrix R are selected, and the value of the optimal feedback gain matrix in the controller is calculated. Finally, simulation of the optimal controller for the mathematics model of the quadrotor aircraft is completed under the given parameters.