PID Parameter Optimization of an UAV Longitudinal Flight Control System
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.
[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).
[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).
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:61543", author = "Kamran Turkoglu and Ugur Ozdemir and Melike Nikbay and Elbrous M. Jafarov", title = "PID Parameter Optimization of an UAV Longitudinal Flight Control System", 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.", volume = "2", number = "9", pages = "1077-6", }
