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

摘要

In this work, a new pre-tuning multivariable PID (Proportional Integral Derivative) controllers method for quadrotors is put forward. A procedure based on LQR/LQG (Linear Quadratic Regulator/Gaussian) theory is proposed for attitude and altitude control, which suposes a considerable simplification of the design problem due to only one pretuning parameter being used. With the aim to analyze the performance and robustness of the proposed method, a non-linear mathematical model of the DJI-F450 quadrotor is employed, where rotors dynamics, together with sensors drift/bias properties and noise characteristics of low-cost commercial sensors typically used in this type of applications are considered. In order to estimate the state vector and compensate bias/drift effects in the measures, a combination of filtering and data fusion algorithms (Kalman filter and Madgwick algorithm for attitude estimation) are proposed and implemented. Performance and robustness analysis of the control system is carried out by employing numerical simulations, which take into account the presence of uncertainty in the plant model and external disturbances. The obtained results show the proposed controller design 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.