Experimental studies of linear quadratic regulator (LQR) cost matrices weighting to control an accurate take-off position of bicopter unmanned aerial vehicles (UAVs)

Abstract

Controller design for airplane flight control is challenged to achieve an optimum result, particularly for safety purposes. The experiment evaluated the linear quadratic regulator (LQR) method to research the optimal gain of proportional-integral-derivative (PID) to hover accurately the bicopter model by minimizing error. The 3 degree of freedom (DOF) helicopter facility is a suitable bicopter experimental simulator to test its complex multiple input multiple output (MIMO) flight control model to respond to the challenge of multipurpose drone control strategies. The art of LQR setting is how to search for appropriate cost matrices scaling to optimize results. This study aims to accurately optimize take-off position control of the bicopter model by investigating LQR cost matrices variation in actual experiments. From the experimental results of weighted matrix variation on the bicopter simulator, the proposed LQR method has been successfully applied to achieve asymptotic stability of roll angle, although it yielded a significant overshoot. Moreover, the overshoot errors had good linearity to weighting variation. Despite that, the implementation of cost matrices is limited in the real bicopter experiment, and there are appropriate values for achieving an optimal accuracy. Moreover, the unstable step response of the controlled angle occurred because of excessive weighting.