MIMO PID Controller Tuning Method for Quadrotor Based on LQR/LQG Theory

In this work a new pre-tuning multivariable PID controllers method for quadrotors is put forward. A procedure based on LQR/LQG theory is proposed for attitude and altitude control. With the aim of analyzing performance and robustness of the proposed method, a non-linear mathematical model of the DJI-F450 quadrotor is employed, where rotors dynamics, togheter with sensors drift/bias properties and noise characteristics of low-cost comercial sensors typically used in this type of applications (such as MARG with MEMS technology and LIDAR) are considered. In order to estimate the state vector and compensate bias/drift effects on rate gyros of the MARG, a combination of filtering and data fusion algorithms (Kalman filter and Madgwick algorithm for attitude estimation) are proposed and implemented. Performance and robutsness analysis of the control system is carried out by means of numerical simulations, which take into account the presence of uncertainty in the plant model and external disturbances. The obtained results show that the proposed pre-tuning method for multivariable PID controller is robust with respect to: a) parametric uncertainty in the plant model, b) disturbances acting at the plant input, c) sensors measurement and estimation errors.