Document Type : Original Article

Authors

Faculty of Aerospace Engineering & Mathematics , K. N. Toosi University of Technology

Abstract

In this research, new adaptation law for updating parameters of the model reference adaptive control and the model reference adaptive control with feedback integrators for a specific class of nonlinear systems with additive parametric uncertainty are presented. The innovation presented in this paper is the consideration of a new form for Lyapunov functions candidate to prove the stability of the closed-loop system. In general, Lyapunov functions candidate, which is used to prove stability and to derive rules for updating control parameters, include two sets of quadratic expressions. The first quadratic expression contains the trajectory tracking error and the second category includes the error of estimating the controller parameters. In this research, it is proved that by selecting quadratic expressions including the variable of trajectory tracking error in the form of power series, a new adaptation law is obtained that includes quadratic expressions in terms of the variable of tracking error in the form of power series. This type of adaptation law can be considered as an adaptation law derived from quadratic Lyapunov functions, except that the gain adaptation matrix parameters vary with time. It has been shown that by using an adaptive controller with a feedback integrator, the tracking error tends to zero faster and the flying object roll angle tracks the reference trajectory after a shorter time. In order to evaluate the control performance of the designed controllers, the system of one degree of freedom of the Wing Rock phenomenon has been used.

Keywords

Main Subjects

Article Title [فارسی]

Model Reference Adaptive Control Using a New Adaptation Law Based on Power-Series Quadratic Lyapunov Functions for the Single Degree of Freedom Wing Rock Phenomenon

Authors [فارسی]

  • Jafar Roshanian
  • Ehsan Rahimzadeh

Faculty of Aerospace Engineering & Mathematics , K. N. Toosi University of Technology

Abstract [فارسی]

In this research, new adaptation law for updating parameters of the model reference adaptive control and the model reference adaptive control with feedback integrators for a specific class of nonlinear systems with additive parametric uncertainty are presented. The innovation presented in this paper is the consideration of a new form for Lyapunov functions candidate to prove the stability of the closed-loop system. In general, Lyapunov functions candidate, which is used to prove stability and to derive rules for updating control parameters, include two sets of quadratic expressions. The first quadratic expression contains the trajectory tracking error and the second category includes the error of estimating the controller parameters. In this research, it is proved that by selecting quadratic expressions including the variable of trajectory tracking error in the form of power series, a new adaptation law is obtained that includes quadratic expressions in terms of the variable of tracking error in the form of power series. This type of adaptation law can be considered as an adaptation law derived from quadratic Lyapunov functions, except that the gain adaptation matrix parameters vary with time. It has been shown that by using an adaptive controller with a feedback integrator, the tracking error tends to zero faster and the flying object roll angle tracks the reference trajectory after a shorter time. In order to evaluate the control performance of the designed controllers, the system of one degree of freedom of the Wing Rock phenomenon has been used.

Keywords [فارسی]

  • Model reference adaptive control
  • Model reference adaptive control with feedback integrator
  • Quadratic Lyapunov functions in the power series
  • New adaptation law
  • Wing Rock phenomenon
[1] P. Osburn, H. Whitaker, A. Kezer,"New Developments in the Design of Adaptive Control Systems", Inst. of Aeronautical Sciences, PP. 39-61, Washington, D.C., 1961.
[2] S.Akhtar, R. Venugopal, D.S. Bernstein,"Logarithmic LyapunovFunctions for Direct Adaptive Stabilization with Normalized Adaptive Laws", International Journal of Control, vol. 77, No.7, PP. 630-638, 2004.
[3] J. Wen, Y. Shi, X. Lu,"Stabilizing a Rotary Inverted Pendulum Based on Logarithmic LyapunovFunction",Journal of Control Science and Engineering, PP. 1-11, 2017.
[4] M. Johansson, A. Rantzer, "Computation of Piecewise Quadratic LyapunovFunctions for Hybrid Systems", InIEEE 1997 European Control Conference (ECC), PP. 2005-2010, 1997.
[5] T. Hu, Z. Lin,"Composite quadratic Lyapunov functions for constrained control systems", IEEE Trans. on Automatic Control, vol. 48, No. 3, PP. 440-450, 2003.
[6] F. Amato, F. Calabrese, C. Cosentino, A. Merola,"Stability Analysis of Nonlinear Quadratic Systems via Polyhedral LyapunovFunctions", InIEEE 2008American Control Conference, PP. 2291-2296.
[7] A.L. Zelentsovsky,"NonquadraticLyapunovFunctions for Robust Stability Analysis of Linear Uncertain Systems" IEEE Trans. on Automatic Control, vol. 39, No. 1, PP. 135-138, 1994.
[8] S. M. Hoseini, "Adaptive quaternion attitude control of aerodynamic flight control vehicles", Journal of Aerospace Science and Technology , vol. 11, No. 2, Summer-Fall 2017.
[9] E. Lavretsky, K. Wise, "Robust and adaptive control with aerospace applications", Springer London, 2013.
[10] K.H. Khalil, J.W. Grizzle, "Nonlinear systems", Prentice Hall Upper Saddle River, NJ, 2002.
[11] B. Ma, X. Deng, B. Wang,"Effects of Wing Locations on Wing Rock Induced by ForebodyVortices", Chinese Journal of Aeronautics, vol. 29, No. 5, PP. 1226- 1236, 2016.
[12] K.W. Lee, P. Ghorawat, S.N. Singh, "Wing Rock Control by Finite-Form Adaptation" Journal of Vibration and Control, vol. 22, No. 11, PP. 2687-2703. 2016.
[13] Y. Dong, Z. Shi, K. Chen, S. Tong, D. Wei,"The Suppression of Flying-Wing Roll Oscillations with Open and Closed-Loop SpanwiseBlowing",Aerospace Science and Technology, vol. 99, 2020;
[14] R. Ohshima, K. Miyaji, "Numerical Simulations of Free-to-Roll Wing Rock Phenomena by the Time Spectral CFD", InAIAA Scitech 2020 Forum 2020 (p. 0540).
[15] P. Konstadinopoulos, D. Mook, A. Nayfeh,"Subsonic Wing Rock of Slender Delta Wings", Journal of Aircraft, vol. 22, No.3, PP. 223-228,1985.
[16] L. Nguyen, L. Yip, J. Chambers,"Self-Induced Wing Rock of Slender Delta Wings", 7th Atmospheric Flight Mechanics Conference, 1981.
[17] K. Orlik-Ruckemann,"Aerodynamic Aspects of Aircraft Dynamics at High Angles of Attack", Journal of Aircraft, vol. 20, No. 9, PP. 737-752, 1983.
[18] G. Padfield,"Nonlinear oscillations at high incidence", AGARD CP-235, 1978.
[19] A.J. Ross, "Lateral Stability at High Angles of Attack, Particularly Wing Rock", AGARD CP-260 10, 1979.
[20] L. Schiff, M. Tobak, G. Malcolm,"Mathematical Modeling of the Aerodynamics of High Angle of Attack Maneuvers", 6th Atmospheric Flight Mechanics Conference, 1980.
[21] A. Sreenatha, M.V. Patki, S.V. Joshi,"Fuzzy Logic Control for Wing Rock Phenomenon ", Mechanics research communications, vol. 27, No. 3, PP. 359-364, 2000.
[22] M. Zribi, S. Alshamali, M. Al-Kendari,"Suppression of the Wing Rock Phenomenon Using Nonlinear Controllers", Nonlinear Dynamics, vol. 71, No. 1, PP. 313-322, 2013.
[23] Z. Liu,"Reinforcement Adaptive Fuzzy Control of Wing Rock Phenomena", IEE Proceedings Control Theory and Applications, vol.152, No. 6, PP. 615-620, 2005.
[24] C.F. Hsu, C.M. Lin, T.Y. Chen, "Neural Network Identification Based Adaptive Control of Wing Rock Motions", IEE Proceedings Control Theory and Applications, vol. 152, No. 1, PP. 65-71, 2005.
[25] C.W. Tao, J.S. Taur, C.W. Chang, Y.H. Chang,"Simplified type-2 fuzzy sliding controller for wing rock system", Fuzzy sets and systems,vol. 207, PP. 111-129, 2012.
[26] H. Yin, X. Zhang, X. Huang, H. Lu, "Two Novel Robust Tracking Control Strategies for Eliminating Aircraft Wing Rock",Institution of Mechanical Engineering Part G: J Aerospace Engineering, 2018.
[27] A. Yousefimanesh, A. Khosravi, P. Sarhadi,"Composite Adaptive PosicastController for the Wing Rock Phenomenon in a Delta Wing Aircraft", Institution of Mechanical Engineering Part G: J Aerospace Engineering, 2019.
[28] A.J. Humaidi, A.H. Hameed ,"Robust MRAC for a wing rock phenomenon in delta wing aircrafts", AUT Journal of Modeling and Simulation, vol .49, No .1, 113- 122, 2017.
[29] B. Andrievsky, et al, "Aircraft wing rock oscillations suppression by simple adaptive control", Aerospace Science and Technology Vol.105, 2020.
[30] J. Roshanian, E. Rahimzadeh, "A Generalization for Model Reference Adaptive Control and Robust Model Reference Adaptive Control Adaptive Laws for a Class of Nonlinear Uncertain Systems with Application to Control of Wing Rock Phenomenon", International Journal of Engineering, Vol.33, no.11, PP: 2372-2383, 2020.
[31] W.L, Keum , S.N. Singh, "Composite Immersion and Invariance-Based Adaptive Wing-Rock Motion Control.", AIAA Scitech 2020 Forum.
[32] W. Dawei, et al, "Robust backstepping control of wing rock using disturbance observer ", Applied Sciences, Vol. 7, no.3, 2017.
[33] A. Nayfeh, J. Elzebda, D. Mook,"Analytical Study of the Subsonic Wing Rock Phenomenon for Slender Delta Wings", Journal of Aircraft, vol. 26, No. 9, PP. 805-809, 1989.