Control and estimation of a quadcopter dynamical model

Sevkuthan Kurak, Migdat Hodzic


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.


LQ; LQG; Kalman Filtering

Full Text:



Mems-accelerometer. [Online]. Available:

Mems-gyroscope. [Online]. Available:

R. Beard, “Quadrotor dynamics and control rev 0.1,” 2008.

S. BOUABDALLAH, “Design and control of quadrotors with application to autonomous flying,” Ph.D. dissertation, ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE, 2017.

P. Bauer and J. Bokor, “LQ servo control design with kalman filter for a quadrotor uav,” Periodica Polytechnica. Transportation Engineering, vol. 36, no. 1-2, p. 9, 2008.

L. Chrif and Z. M. Kadda, “Aircraft control system using lqg and lqr controller with optimal estimation-kalman filter design,” Procedia Engineering, vol. 80, pp.245–257, 2014.

L. M. Argentim, W. C. Rezende, P. E. Santos, and R. A. Aguiar, “Pid, lqr and lqr-pid on a quadcopter platform,” in Informatics, Electronics & Vision (ICIEV), 2013 International Conference on. IEEE, 2013, pp. 1–6.

T. M Hassan, S. Faiz, D. Hazry, J. M Kamran, A. W. Faizan et al., “Disturbance and noise rejection controller design for smooth takeoff/landing and altitude stabilization of quad-rotor,” 2013.

A. A. Mian and W. Daobo, “Modeling and backstepping-based nonlinear control strategy for a 6 dof quadrotor helicopter,” Chinese Journal of Aeronautics, vol. 21, no. 3, pp. 261–268, 2008.

Y. Xie, Y. Cao, B. Wang, and M. Ding, “Disturbance observer based control of multirotor helicopters based on a universal model with unstructured uncertainties,”Journal of Robotics, vol. 2015, p. 1, 2015.

T. Lee, M. Leok, and N. H. McClamroch, “Nonlinear robust tracking control of a quadrotor uav on se (3),” Asian Journal of Control, vol. 15, no. 2, pp. 391–408, 2013.

Z. Feng, J. Zhu, and R. Allen, “Design of continuous and discrete lqi control systems with stable inner loops,” Shanghai Jiaotong University Journal, vol. 12, no. 6, pp. 787–792, 2007.

S. Widnall, “Lecture l3-vectors, matrices and coordinate transformations,” Dynamics, pp. 1–15, 2009.

R. L. Williams, D. A. Lawrence et al., Linear state-space control systems. John Wiley & Sons, 2007.

F. L. Lewis, L. Xie, and D. Popa, Optimal and robust estimation: with an introduction to stochastic control theory. CRC press, 2007, vol. 29.

C. I. of Tech. Lecture, “Kalman filter.” [Online]. Available:

M. S. Fadali and A. Visioli, Digital control engineering: analysis and design. Academic Press, 2012.

M. L. Notes, “Discrete time observers and lqg control.” [Online]. Available:

L. Guzzella, “Discrete-time control systems,” ETH Zurich, 2009.

W. Reinelt, “Design of optimal control systems with bounded control signals,” in Control Conference (ECC), 2001 European. IEEE, 2001, pp. 348–353.

B. Liu, “Constructive general bounded integral control,” Intelligent Control and Automation, vol. 5, no. 03, p. 146, 2014.

G. C. Konstantopoulos, Q.-C. Zhong, B. Ren, and M. Krstic, “Bounded integral control of input-to-state practically stable nonlinear systems to guarantee closedloop stability,” IEEE Transactions on Automatic Control, vol. 61, no. 12, pp. 4196–4202, 2016.

Sevkuthan Kurak, “Control and Estimation of Quadcopter Dynamical Model”, MSc. Thesis, International University of Sarajevo, September 2017.

B. Durakovic, "Design of Experiments Application, Concepts, Examples: State of the Art," Periodicals of Engineering and Natural Scinces, vol. 5, no. 3, p. 421‒439, 2017.



  • There are currently no refbacks.

Copyright (c) 2018 Migdat Hodzic, Sevkuthan Kurak

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

ISSN: 2303-4521

Digital Object Identifier DOI: 10.21533/pen

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License