Controle linear quadrático gaussiano de um quadricóptero baseado em um filtro de Kalman estendido com variável instrumental

Abstract

Given the transformations and promotion of technologies and modernization in different areas of society, such as the use of Unmanned Aerial Vehicles performing numerous automated activities, it is necessary to create algorithms with efficiency and safety to avoid losses and damages in their functions. Aerial systems are, for the most part, multiple input and multiple output systems, time-varying, susceptible to disturbances and measurement noise, becoming a challenging scenario in the area of system identification. Given this, such dynamics must be considered in the identification process. Therefore, the objective of this work is to develop an algorithm capable of jointly estimating the states and parameters of systems, mitigating the interference of measurement noise and external disturbances in the real-time identification process. Based on these principles, the creation of the joint estimation algorithm Extended Kalman Filter with Instrumental Variables was established. The proposed algorithm stands out for its theoretical commitment to minimizing interference from dynamics that can affect the reliability of parameters calculated by identification methods already consolidated in the literature, such as Extended Kalman Filter (EKF) and Recursive Least Squares (RLS). The proposed method was tested to calculate the stochastic linear model of the autopilot system of the unmanned aerial quadcopter, Parrot’s AR Drone 2.0 model, taking into account scenarios in which the sensor signal presents a signal-to-noise ratio of 100, 50, 10. Its performance was compared with RLS and EKF parameter estimation. To evaluate the state estimates, the root-mean-square deviation norm index was used and, to evaluate the parameters, the Euclidean distance between the real parameters and the estimated parameters was used. Finally, the data collected by the methods were used to tune the Gaussian Quadratic Linear Control controller, thus allowing comparison of the impact of the identification method on the closed-loop behavior of the aerial system. To enable discussion and comparison of control algorithms, the Squared Error Integral and Squared Control Integral indices were applied to evaluate the control performance, the gain margin and the phase margin to measure system robustness.