Control and estimation of a quadcopter dynamical model

The main motivation for this paper is to apply LQ and LQG methodologies for quadcopter control system. The developed control system is for both the rectangular position (xy) and altitude (z) as well as the orientation (attitude - angles around the axes) based on 6-Degree of Freedom (6DOF) mathematical model. 6DOF refers to the model with 3 linear and 3 angular motions. The altitude and attitude controllers are designed and the results presented in both the continuous and the discrete time cases. For the controller design, a nonlinear mathematical model was obtained first for 6DOF. The next step was to linearize the nonlinear model in hovering mode, and the final step was the reduction of the resulted linear model to be used as starting model for the controller design. The reduced linear model was tested for controllablity and observability. The control goal was to track a spatial trajectory with the quadcopter center of gravity under environment disturbances and sensor measurement errors. For this purpose, designed LQ controller was augmented by Kalman Filter state observer. The resultant controllers provide precise and robust performance for an input reference signal and for a regulation problem. After the transient response (of order of few seconds) the tracking error is acceptable which provides safe handling even under disturbances and measurement noises. The transient response can be further reduced by controllers fine tuning.

[1]  Constructive General Bounded Integral Control , 2014 .

[2]  Katsuhiko Ogata,et al.  Discrete-time control systems (2nd ed.) , 1995 .

[3]  Labane Chrif,et al.  Aircraft Control System Using LQG and LQR Controller with Optimal Estimation-Kalman Filter Design , 2014 .

[4]  Samir Bouabdallah,et al.  Design and control of quadrotors with application to autonomous flying , 2007 .

[5]  Miroslav Krstic,et al.  Bounded Integral Control of Input-to-State Practically Stable Nonlinear Systems to Guarantee Closed-Loop Stability , 2016, IEEE Transactions on Automatic Control.

[6]  Robert L. Williams,et al.  Linear State-Space Control Systems , 2007 .

[7]  Alexandros Soumelidis,et al.  LQ servo control design with Kalman filter for a quadrotor UAV , 2008 .

[8]  Ashfaq Ahmad Mian,et al.  Modeling and Backstepping-based Nonlinear Control Strategy for a 6 DOF Quadrotor Helicopter , 2008 .

[9]  Biao Wang,et al.  Disturbance Observer Based Control of Multirotor Helicopters Based on a Universal Model with Unstructured Uncertainties , 2015, J. Robotics.

[10]  Taeyoung Lee,et al.  Nonlinear Robust Tracking Control of a Quadrotor UAV on SE(3) , 2013 .

[11]  F. Lewis,et al.  Optimal and Robust Estimation: With an Introduction to Stochastic Control Theory, Second Edition , 2007 .

[12]  Antonio Visioli,et al.  Digital Control Engineering: Analysis and Design , 2009 .

[13]  B. Duraković.  Design of Experiments Application, Concepts, Examples: State of the Art , 2017 .

[14]  Paulo E. Santos,et al.  PID, LQR and LQR-PID on a quadcopter platform , 2013, 2013 International Conference on Informatics, Electronics and Vision (ICIEV).

[15]  Randal Beard,et al.  Quadrotor Dynamics and Control Rev 0.1 , 2008 .

[16]  Wolfgang Reinelt,et al.  Design of optimal control systems with bounded control signals , 2001, 2001 European Control Conference (ECC).