PID Parameter Optimization of an UAV Longitudinal Flight Control System

Authors: Kamran Turkoglu, Ugur Ozdemir, Melike Nikbay, Elbrous M. Jafarov

Abstract:

In this paper, an automatic control system design based on Integral Squared Error (ISE) parameter optimization technique has been implemented on longitudinal flight dynamics of an UAV. It has been aimed to minimize the error function between the reference signal and the output of the plant. In the following parts, objective function has been defined with respect to error dynamics. An unconstrained optimization problem has been solved analytically by using necessary and sufficient conditions of optimality, optimum PID parameters have been obtained and implemented in control system dynamics.

Keywords: Optimum Design, KKT Conditions, UAV, Longitudinal Flight Dynamics, ISE Parameter Optimization.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1079352

References:

[1] P. Fabiani, V. Fuertes, A. Piquereau, R. Mampey and F. Teichteil- Konigsbuch, "Autonomous flight and navigation of VTOL UAVs: from autonomy demonstrations to out-of-sight flights" in Aerospace Science and Technology, Vol. 11, Issues 2-3, p:183-193, March-April 2007
[2] E. Layer, "Theoretical principles for establishing a hierarchy of dynamic accuracy with the integral-square-error as an example" IEEE Transactions in Instrumentation and Measurement , Volume 46, Issue 5, Oct. 1997 pp:1178 - 1182
[3] I.W. Selesnick, M. Lang, C.S. Burrus, "Constrained least square design of FIR filters without specified transition bands" in IEEE Transactions on Signal Processing, Volume 44, Issue 8, Aug. 1996 pp:1879 - 1892.
[4] J. Lin and J. G. Proakis, "An enhanced optimal windowed RLS algorithm for fading multipath channel estimation" in MILCOM '93. `Communications on the Move'. Conference Record (Cat. No.93CH3260-7), 1993, p 1003-7 vol.3.
[5] P.K. Kalra, " An approach for handling the nonlinearities of HVDC system for stability analysis" in IEEE Transactions on Power Electronics, v 5, n 3, July 1990, p 371-7.
[6] C. S. Burrus, A. W. Soewito and R. A. Gopinath, " Least squared error FIR filter design with transition bands" in IEEE Transactions on Signal Processing, v 40, n 6, June 1992, p 1327-40.
[7] J. Jiang, "Optimal gain scheduling controller for a diesel engine" in IEEE Control Systems Magazine, v 14, n 4, Aug. 1994, p 42-8.
[8] C. Jie, Q. Li and O. Toker, "Limitations on maximal tracking accuracy" in IEEE Transactions on Automatic Control, v 45, n 2, Feb. 2000, p 326- 31.
[9] E. Layer, "Mapping error of linear dynamic systems caused by reducedorder model" in IEEE Transactions on Instrumentation and Measurement, v 50, n 3, June 2001, p 792-800.
[10] J. H. Blakelock, Automatic Control of Aircrafts and Missiles, Wiley, 1991.
[11] K. Turkoglu, Investigation the Modes of Hezarfen UAV and Automatic Control Systems- Design, BSc Thesis, Istanbul Technical University, Istanbul, Turkey. 2007.
[12] K. Ogata, Modern Control Engineering, Addison Wesley, 1992.
[13] Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1101, 2000.
[14] Kaplan, W. Advanced Calculus, 4th ed. Reading, MA: Addison-Wesley, p. 501, 1992.
[15] D. E. Kirk, Optimal Control Theory : An Introduction, 2nd editions, Dover Publications, 2007.
[16] J. S. Arora, Introduction to Optimum Design, Academic Press; 2nd edition (May 19, 2004).