Using Linear Quadratic Gaussian Optimal Control for Lateral Motion of Aircraft

Authors: A. Maddi, A. Guessoum, D. Berkani

Abstract:

The purpose of this paper is to provide a practical example to the Linear Quadratic Gaussian (LQG) controller. This method includes a description and some discussion of the discrete Kalman state estimator. One aspect of this optimality is that the estimator incorporates all information that can be provided to it. It processes all available measurements, regardless of their precision, to estimate the current value of the variables of interest, with use of knowledge of the system and measurement device dynamics, the statistical description of the system noises, measurement errors, and uncertainty in the dynamics models. Since the time of its introduction, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. For example, to determine the velocity of an aircraft or sideslip angle, one could use a Doppler radar, the velocity indications of an inertial navigation system, or the relative wind information in the air data system. Rather than ignore any of these outputs, a Kalman filter could be built to combine all of this data and knowledge of the various systems- dynamics to generate an overall best estimate of velocity and sideslip angle.

Keywords: Aircraft motion, Kalman filter, LQG control, Lateral stability, State estimator.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1079436

References:

[1] H. W. Sorenson., "Least-Squares estimation: from Gauss to Kalman", IEEE Spectrum, Vol. 7, pp. 63-68, July 1970.
[2] A. Gelb, "Applied Optimal Estimation", MIT Press, Cambridge, MA. 1974.
[3] P. S. Maybeck, "Applied Optimal EstimationÔÇöKalman Filter Design and Implementation", notes for a continuing education course offered by the Air Force Institute of Technology, Wright-Patterson AFB, Ohio, semiannually since December 1974.
[4] R. Lewis, "Optimal Estimation with an Introduction to Stochastic Control Theory", John Wiley & Sons, Inc. 1986.
[5] A.C. Harvey, "Structural Time Series Models and the Kalman Filter", Cambridge University Press, Cambridge, 1989.
[6] A.L. Gonzalez Blazquez, "Mathematical modelling for analysis of nonlinear aircraft dynamics", Computers and structures, Vol. 37, No 2, pp. 193 -197, July 1990.
[7] R. Azuma and G. Bishop, "Improving Static and Dynamic Registration in an Optical See-Through HMD", SIGGRAPH 94 Conference Proceedings, Annual Conference Series, pp. 197-204, ACM SIGGRAPH, Addison Wesley, July 1994.
[8] J. Simon and K. Jeffery, "A New Extension of the Kalman Filter to nonlinear Systems" In The Proceedings of AeroSense: The 11th International Symposium on Aerospace/Defense Sensing,Simulation and Controls, Multi Sensor Fusion, Tracking and Resource Management II, SPIE, 1997.
[9] A. Maddi, "Modélisation et contr├┤le du vol latéral d-un avion", Magister Thesis, Electronics Department, University of Blida, Algeia, 1997.
[10] M. Grewal and A. Andrews, "Kalman Filtering Theory and Practice Using MATLAB", (Second ed.), New York, NY USA: John Wiley & Sons, Inc., 2001.
[11] P.C. Murphy and V. Klein, "Estimation of Aircraft Unsteady Aerodynamic Parameters From Dynamic Wind Tunnel Testing" , AIAA 2001- 4016, August 2001
[12] G. Bishop, G. Welch, "An Introduction to the Kalman Filter", University of North Carolina at Chapel Hill, Department of Computer Science, SIGGRAPH 2001.
[13] D. Simon, "Optimal state estimation: Kalman, H-infinity, and nonlinear approaches", John Wiley & Sons, 2006.