Analysis of the LQR algorithm in the field of testing the dynamics of quadcopter movement

Abstract

-The subject of this article is to present the issues related to the LQR control algorithm used in the linear model describing the dynamics of the flying object in terms of tracking its flight trajectory. The use of the LQR regulator is also a method of calculating the optimal K-feedback reinforcement, with this type of reinforcement used to control the system in the form of a control signal can be determined by tuning the Q and R weight matrix elements in the LQR method. Based on the above, the main research goal of the article is to develop an algorithm for the control system implemented on the quadrotor using the LQR method to obtain the best K-feedback gain in flight state with unstable motion. To this end, a mathematical model describing the essence of linear-quadratic control using the LQR controller is presented in this paper. It should be noted that due to the fact that only four states can be controlled at the same time in a quadrotor, hence the flight trajectories are determined on the basis of four states, while the three-dimensional position, position of the tested object in the coordinate system and rotation along the axis are described as deviation movement. In addition, the work also designed on the basis of the created linear model of a linear quadrotor LQR control approach for this model due to the fact that the performance of the linear model and non-linear model around a specified nominal point is almost identical. The control system based on the LQR algorithm was developed in the Matlab/Simulink environment, and the results obtained in the form of graphs for the quantities characterizing the dynamics of the tested object were used to assess the effectiveness of the LQR method used. In the final part of the work, practical conclusions have been formulated based on the research (analysis, models, simulations) and analysis of the results obtained.